Chapter 5 Uncertainty and Consumer Behavior. Introduction Choice with certainty is reasonably...
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Transcript of Chapter 5 Uncertainty and Consumer Behavior. Introduction Choice with certainty is reasonably...
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Chapter 5
Uncertainty and Consumer Behavior
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Introduction
• Choice with certainty is reasonably straightforward
• How do we make choices when certain variables such as income and prices are uncertain (making choices with risk)?
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Describing Risk• To measure risk we must know:
1. All of the possible outcomes
2. The probability or likelihood that each outcome will occur
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Describing Risk
• Interpreting Probability1. Objective Interpretation
• Based on the observed frequency of past events
2. Subjective Interpretation• Based on perception that an outcome will occur
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Interpreting Probability
• Subjective Probability– Different information or different abilities to
process the same information can influence the subjective probability
– Based on judgment or experience
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Describing Risk
• With an interpretation of probability, must determine 2 measures to help describe and compare risky choices1. Expected value
2. Variability
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Describing Risk
• Expected Value– The weighted average of the payoffs or
values resulting from all possible outcomes• Expected value measures the central tendency;
the payoff or value expected on average
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Expected Value – An Example
• Investment in offshore drilling exploration:
• Two outcomes are possible– Success – the stock price increases from $30
to $40/share– Failure – the stock price falls from $30 to
$20/share
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Expected Value – An Example
• Objective Probability– 100 explorations, 25 successes and 75
failures– Probability (Pr) of success = 1/4 and the
probability of failure = 3/4
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Expected Value – An Example
failure) of )(valuePr(failure
success) of )(valuePr(success EV
)($20/share43)($40/share41 EV
$25/share EV
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Expected Value
• In general, for n possible outcomes:– Possible outcomes having payoffs X1, X2, …,
Xn
– Probabilities of each outcome is given by Pr1, Pr2, …, Prn
nn2211 XPr...XPrXPr E(X)
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Describing Risk
• Variability– The extent to which possible outcomes of an
uncertain event may differ– How much variation exists in the possible
choice
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Variability – An Example
• Suppose you are choosing between two part-time sales jobs that have the same expected income ($1,500)
• The first job is based entirely on commission
• The second is a salaried position
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• There are two equally likely outcomes in the first job: $2,000 for a good sales job and $1,000 for a modestly successful one
• The second pays $1,510 most of the time (.99 probability), but you will earn $510 if the company goes out of business (.01 probability)
Variability – An Example
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Variability – An Example
Outcome 1 Outcome 2
Prob. Income Prob. Income
Job 1: Commission .5 2000 .5 1000
Job 2: Fixed Salary .99 1510 .01 510
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1500$ .5($1000).5($2000))E(X1
Variability – An Example
• Income from Possible Sales Job
Job 1 Expected Income
$1500.01($510).99($1510) )E(X2
Job 2 Expected Income
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Variability
• While the expected values are the same, the variability is not
• Greater variability from expected values signals greater risk
• Variability comes from deviations in payoffs– Difference between expected payoff and
actual payoff
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Variability – An Example
Deviations from Expected Income ($)
Outcome 1
Deviation Outcome 2
Deviation
Job 1$2000 $500 $1000 -$500
Job 21510 10 510 -900
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Variability
• Average deviations are always zero so we must adjust for negative numbers
• We can measure variability with standard deviation – The square root of the average of the squares
of the deviations of the payoffs associated with each outcome from their expected value
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Variability
• Standard deviation is a measure of risk– Measures how variable your payoff will be– More variability means more risk– Individuals generally prefer less variability –
less risk
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Variability
• The standard deviation is written:
2222
11 )(Pr)(Pr XEXXEX
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Standard Deviation – Example 1
Deviations from Expected Income ($)
Outcome 1
Deviation
Outcome 2
Deviation
Job 1 $2000 $500 $1000 -$500
Job 2 1510 10 510 -900
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Standard Deviation – Example 1 • Standard deviations of the two jobs are:
500000,250
)000,250($5.0)000,250($5.0
1
1
50.99900,9
)100,980($01.0)100($99.0
2
2
2222
11 )(Pr)(Pr XEXXEX
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Standard Deviation – Example 1
• Job 1 has a larger standard deviation and therefore it is the riskier alternative
• The standard deviation also can be used when there are many outcomes instead of only two
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Standard Deviation – Example 2
• Job 1 is a job in which the income ranges from $1000 to $2000 in increments of $100 that are all equally likely
• Job 2 is a job in which the income ranges from $1300 to $1700 in increments of $100 that, also, are all equally likely
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Outcome Probabilities - Two Jobs
Income
0.1
$1000 $1500 $2000
0.2
Job 1
Job 2
Job 1 has greater spread: greater
standard deviationand greater risk
than Job 2.
Probability
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Decision Making – Example 1
• What if the outcome probabilities of two jobs have unequal probability of outcomes?– Job 1: greater spread and standard deviation– Peaked distribution: extreme payoffs are less
likely that those in the middle of the distribution
– You will choose job 2 again
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Unequal Probability Outcomes
Job 1
Job 2
The distribution of payoffsassociated with Job 1 has a greater spread and standard
deviation than those with Job 2.
Income
0.1
$1000 $1500 $2000
0.2
Probability
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Decision Making – Example 2
• Suppose we add $100 to each payoff in Job 1 which makes the expected payoff = $1600– Job 1: expected income $1,600 and a
standard deviation of $500– Job 2: expected income of $1,500 and a
standard deviation of $99.50
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Decision Making – Example 2
• Which job should be chosen?– Depends on the individual– Some may be willing to take risk with higher
expected income– Some will prefer less risk even with lower
expected income
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Risk and Crime Deterrence
• Attitudes toward risk affect willingness to break the law
• Suppose a city wants to deter people from double parking
• Monetary fines may be better than jail time
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Risk and Crime Deterrence
• Costs of apprehending criminals are not zero, therefore– Fines must be higher than the costs to society– Probability of apprehension is actually less
than one
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Risk and Crime Deterrence - Example
• Assumptions:1. Double-parking saves a person $5 in terms
of time spent searching for a parking space
2. The driver is risk neutral
3. Cost of apprehension is zero
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Risk and Crime Deterrence - Example
• A fine greater than $5.00 would deter the driver from double parking– Benefit of double parking ($5) is less than the
cost ($6.00) equals a net benefit that is negative
– If the value of double parking is greater than $5.00, then the person would still break the law
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Risk and Crime Deterrence - Example
• The same deterrence effect is obtained by either – A $50 fine with a 0.1 probability of being
caught resulting in an expected penalty of $5
or– A $500 fine with a 0.01 probability of being
caught resulting in an expected penalty of $5
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Risk and Crime Deterrence - Example
• Enforcement costs are reduced with high fine and low probability
• Most effective if drivers don’t like to take risks
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Preferences Toward Risk
• Can expand evaluation of risky alternative by considering utility that is obtained by risk– A consumer gets utility from income– Payoff measured in terms of utility
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Preferences Toward Risk - Example
• A person is earning $15,000 and receiving 13.5 units of utility from the job
• She is considering a new, but risky job– 0.50 chance of $30,000– 0.50 chance of $10,000
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Preferences Toward Risk - Example
• Utility at $30,000 is 18
• Utility at $10,000 is 10
• Must compare utility from the risky job with current utility of 13.5
• To evaluate the new job, we must calculate the expected utility of the risky job
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Preferences Toward Risk
• The expected utility of the risky option is the sum of the utilities associated with all her possible incomes weighted by the probability that each income will occur
E(u) = (Prob. of Utility 1) *(Utility 1)
+ (Prob. of Utility 2)*(Utility 2)
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Preferences Toward Risk – Example
• The expected is:E(u) = (1/2)u($10,000) + (1/2)u($30,000)
= 0.5(10) + 0.5(18)
= 14– E(u) of new job is 14, which is greater than
the current utility of 13.5 and therefore preferred
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Preferences Toward Risk• People differ in their preference toward
risk
• People can be risk averse, risk neutral, or risk loving
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Preferences Toward Risk
• Risk Averse– A person who prefers a certain given income
to a risky income with the same expected value
– The person has a diminishing marginal utility of income
– Most common attitude towards risk• Ex: Market for insurance
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Risk Averse - Example
• A person can have a $20,000 job with 100% probability and receive a utility level of 16
• The person could have a job with a 0.5 chance of earning $30,000 and a 0.5 chance of earning $10,000
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Risk Averse – Example
• Expected Income of Risky JobE(I) = (0.5)($30,000) + (0.5)($10,000)
E(I) = $20,000
• Expected Utility of Risky Job
E(u) = (0.5)(10) + (0.5)(18)
E(u) = 14
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Risk Averse – Example
• Expected income from both jobs is the same – risk averse may choose current job
• Expected utility is greater for certain job– Would keep certain job
• Risk averse person’s losses (decreased utility) are more important than risky gains
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Risk Averse
• Can see risk averse choices graphically
• Risky job has expected income = $20,000 with expected utility = 14 – Point F
• Certain job has expected income = $20,000 with utility = 16– Point D
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Income ($1,000)
Utility
The consumer is risk averse because she would prefer a certain income of
$20,000 to an uncertain expected income =
$20,000
E
10
10 20
14
16
18
0 16 30
A
C
D
Risk Averse Utility Function
F
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Preferences Toward Risk
• A person is said to be risk neutral if they show no preference between a certain income, and an uncertain income with the same expected value
• Constant marginal utility of income
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Risk Neutral
• Expected value for risky option is the same as utility for certain outcomeE(I) = (0.5)($10,000) + (0.5)($30,000)
= $20,000
E(u) = (0.5)(6) + (0.5)(18) = 12
• This is the same as the certain income of $20,000 with utility of 12
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Income ($1,000)10 20
Utility
0 30
6A
E
C
12
18
The consumer is riskneutral and is indifferentbetween certain eventsand uncertain events
with the same expected income.
Risk Neutral
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Preferences Toward Risk
• A person is said to be risk loving if they show a preference toward an uncertain income over a certain income with the same expected value– Examples: Gambling, some criminal activities
• Increasing marginal utility of income
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Risk Loving
• Expected value for risky option – point FE(I) = (0.5)($10,000) + (0.5)($30,000)
= $20,000
E(u) = (0.5)(3) + (0.5)(18) = 10.5
• Certain income is $20,000 with utility of 8 – point C
• Risky alternative is preferred
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Income ($1,000)
Utility
0 10 20 30
The consumer is riskloving because she
would prefer the gamble to a certain income.
Risk Loving
3A
E
C8
18
F10.5
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Preferences Toward Risk
• The risk premium is the maximum amount of money that a risk-averse person would pay to avoid taking a risk
• The risk premium depends on the risky alternatives the person faces
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Risk Premium – Example
• From the previous example– A person has a .5 probability of earning
$30,000 and a .5 probability of earning $10,000
– The expected income is $20,000 with expected utility of 14
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Risk Premium – Example
• Point F shows the risky scenario – the utility of 14 can also be obtained with certain income of $16,000
• This person would be willing to pay up to $4000 (20 – 16) to avoid the risk of uncertain income
• Can show this graphically by drawing a straight line between the two points – line CF
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Income ($1,000)
Utility
0 10 16
Here, the risk premium is $4,000 because a certain income of $16,000 gives the person
the same expected utility as the
uncertain income with expected value
of $20,000.
10
18
30 40
20
14
A
CE
G
20
Risk Premium
F
Risk Premium – Example
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Risk Aversion and Indifference Curves
• Can describe a person’s risk aversion using indifference curves that relate expected income to variability of income (standard deviation)
• Since risk is undesirable, greater risk requires greater expected income to make the person equally well off
• Indifference curves are therefore upward sloping
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Risk Aversion and Indifference Curves
Standard Deviation of Income
ExpectedIncome
Highly Risk Averse: Anincrease in standarddeviation requires a large increase in income to maintainsatisfaction.
U1
U2
U3
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Risk Aversion and Indifference Curves
Standard Deviation of Income
ExpectedIncome
Slightly Risk Averse:A large increase in standarddeviation requires only a small increase in incometo maintain satisfaction.
U1
U2
U3
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Reducing Risk
• Consumers are generally risk averse and therefore want to reduce risk
• Three ways consumers attempt to reduce risk are:1. Diversification
2. Insurance
3. Obtaining more information
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Reducing Risk
• Diversification– Reducing risk by allocating resources to a
variety of activities whose outcomes are not closely related
• Example: – Suppose a firm has a choice of selling air
conditioners, heaters, or both– The probability of it being hot or cold is 0.5– How does a firm decide what to sell?
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Income from Sales of Appliances
Hot WeatherCold
Weather
Air conditioner sales
$30,000 $12,000
Heater sales 12,000 30,000
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Diversification – Example
• If the firm sells only heaters or air conditioners their income will be either $12,000 or $30,000
• Their expected income would be:– 1/2($12,000) + 1/2($30,000) = $21,000
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Diversification – Example
• If the firm divides their time evenly between appliances, their air conditioning and heating sales would be half their original values
• If it were hot, their expected income would be $15,000 from air conditioners and $6,000 from heaters, or $21,000
• If it were cold, their expected income would be $6,000 from air conditioners and $15,000 from heaters, or $21,000
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Diversification – Example
• With diversification, expected income is $21,000 with no risk
• Better off diversifying to minimize risk
• Firms can reduce risk by diversifying among a variety of activities that are not closely related
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Reducing Risk – The Stock Market
• If invest all money in one stock, then take on a lot of risk– If that stock loses value, you lose all your
investment value
• Can spread risk out by investing in many different stocks or investments– Ex: Mutual funds
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Reducing Risk – Insurance
• Risk averse are willing to pay to avoid risk
• If the cost of insurance equals the expected loss, risk averse people will buy enough insurance to recover fully from a potential financial loss
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The Law of Large Numbers
• Insurance companies know that although single events are random and largely unpredictable, the average outcome of many similar events can be predicted
• When insurance companies sell many policies, they face relatively little risk
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Reducing Risk – Actuarially Fair
• Insurance companies can be sure total premiums paid will equal total money paid out
• Companies set the premiums so money received will be enough to pay expected losses
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The Value of Information
• Risk often exists because we don’t know all the information surrounding a decision
• Because of this, information is valuable and people are willing to pay for it
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The Value of Information
• The value of complete information– The difference between the expected value of
a choice with complete information and the expected value when information is incomplete
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The Value of Information – Example
• Per capita milk consumption has fallen over the years
• The milk producers engaged in market research to develop new sales strategies to encourage the consumption of milk
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The Value of Information – Example
• Findings– Milk demand is seasonal with the greatest
demand in the spring– Price elasticity of demand is negative and
small– Income elasticity is positive and large
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The Value of Information – Example
• Milk advertising increases sales most in the spring
• Allocating advertising based on this information in New York increased profits by 9% or $14 million
• The cost of the information was relatively low, while the value was substantial (increased profits)
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Behavioral Economics
• Sometimes individuals’ behavior contradicts basic assumptions of consumer choice– More information about human behavior might
lead to better understanding– This is the objective of behavioral
economics• Improving understanding of consumer choice by
incorporating more realistic and detailed assumptions regarding human behavior
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Behavioral Economics
• There are a number of examples of consumer choice contradictions– You take at trip and stop at a restaurant that
you will most likely never stop at again. You still think it fair to leave a 15% tip rewarding the good service.
– You choose to buy a lottery ticket even though the expected value is less than the price of the ticket
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Behavioral Economics
• Reference Points– Economists assume that consumers place a
unique value on the goods/services purchased
– Psychologists have found that perceived value can depend on circumstances
• You are able to buy a ticket to the sold out Cher concert for the published price of $125. You find out you can sell the ticket for $500 but you choose not to, even though you would never have paid more than $250 for the ticket.
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Behavioral Economics
• Reference Points (cont.)– The point from which an individual makes a
consumption decision– From the example, owning the Cher ticket is
the reference point• Individuals dislike losing things they own• They value items more when they own them than
when they do not• Losses are valued more than gains• Utility loss from selling the ticket is greater than
original utility gain from purchasing it
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Behavioral Economics
• Experimental Economics– Students were divided into two groups– Group one was given a mug with a market
value of $5.00– Group two received nothing– Students with mugs were asked how much
they would take to sell the mug back• Lowest price for mugs, on average, was $7.00
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Behavioral Economics
• Experimental Economics (cont.)– Group without mugs was asked minimum
amount of cash they would except in lieu of the mug
• On average willing to accept $3.50 instead of getting the mug
– Group one had reference point of owning the mug
– Group two had reference point of no mug
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Behavioral Economics
• Fairness– Individuals often make choices because they
think they are fair and appropriate• Charitable giving, tipping in restaurants
– Some consumers will go out of their way to punish a store they think is “unfair” in their pricing
– Manager might offer higher than market wages to make for happier working environment or more productive worker
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Chapter 6
Production
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Introduction
• Our study of consumer behavior was broken down into 3 steps: – Describing consumer preferences– Consumers face budget constraints– Consumers choose to maximize utility
• Production decisions of a firm are similar to consumer decisions– Can also be broken down into three steps
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Production Decisions of a Firm
1. Production Technology– Describe how inputs can be transformed into
outputs• Inputs: land, labor, capital and raw materials• Outputs: cars, desks, books, etc.
– Firms can produce different amounts of outputs using different combinations of inputs
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Production Decisions of a Firm
2. Cost Constraints– Firms must consider prices of labor, capital
and other inputs– Firms want to minimize total production costs
partly determined by input prices– As consumers must consider budget
constraints, firms must be concerned about costs of production
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Production Decisions of a Firm
3. Input Choices– Given input prices and production
technology, the firm must choose how much of each input to use in producing output
– Given prices of different inputs, the firm may choose different combinations of inputs to minimize costs• If labor is cheap, firm may choose to produce with
more labor and less capital
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Production Decisions of a Firm
• If a firm is a cost minimizer, we can also study– How total costs of production vary with output– How the firm chooses the quantity to
maximize its profits
• We can represent the firm’s production technology in the form of a production function
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The Technology of Production
• Production Function:– Indicates the highest output (q) that a firm can
produce for every specified combination of inputs
– For simplicity, we will consider only labor (L) and capital (K)
– Shows what is technically feasible when the firm operates efficiently
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The Technology of Production
• The production function for two inputs:
q = F(K,L)– Output (q) is a function of capital (K) and labor
(L)– The production function is true for a given
technology• If technology increases, more output can be
produced for a given level of inputs
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The Technology of Production
• Short Run versus Long Run– It takes time for a firm to adjust production
from one set of inputs to another– Firms must consider not only what inputs can
be varied but over what period of time that can occur
– We must distinguish between long run and short run
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The Technology of Production
• Short Run– Period of time in which quantities of one or
more production factors cannot be changed– These inputs are called fixed inputs
• Long Run– Amount of time needed to make all production
inputs variable
• Short run and long run are not time specific
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Production: One Variable Input
• We will begin looking at the short run when only one input can be varied
• We assume capital is fixed and labor is variable– Output can only be increased by increasing
labor– Must know how output changes as the
amount of labor is changed (Table 6.1)
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Production: One Variable Input
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Production: One Variable Input
• Observations:1. When labor is zero, output is zero as well
2. With additional workers, output (q) increases up to 8 units of labor
3. Beyond this point, output declines• Increasing labor can make better use of existing
capital initially• After a point, more labor is not useful and can be
counterproductive
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Production: One Variable Input
• Firms make decisions based on the benefits and costs of production
• Sometimes useful to look at benefits and costs on an incremental basis– How much more can be produced when at
incremental units of an input?
• Sometimes useful to make comparison on an average basis
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Production: One Variable Input
• Average product of Labor - Output per unit of a particular product
• Measures the productivity of a firm’s labor in terms of how much, on average, each worker can produce
L
q
Input Labor
Output APL
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Production: One Variable Input
• Marginal Product of Labor – additional output produced when labor increases by one unit
• Change in output divided by the change in labor
L
q
Input Labor
Output MPL
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Production: One Variable Input
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Production: One Variable Input
• We can graph the information in Table 6.1 to show– How output varies with changes in labor
• Output is maximized at 112 units
– Average and Marginal Products• Marginal Product is positive as long as total output
is increasing• Marginal Product crosses Average Product at its
maximum
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At point D, output is maximized.
Labor per Month
Outputper
Month
0 2 3 4 5 6 7 8 9 101
Total Product
60
112
A
B
C
D
Production: One Variable Input
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Average Product
Production: One Variable Input
10
20
Outputper
Worker
30
80 2 3 4 5 6 7 9 101 Labor per Month
E
Marginal Product
•Left of E: MP > AP & AP is increasing•Right of E: MP < AP & AP is decreasing•At E: MP = AP & AP is at its maximum•At 8 units, MP is zero and output is at max
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Marginal and Average Product
• When marginal product is greater than the average product, the average product is increasing
• When marginal product is less than the average product, the average product is decreasing
• When marginal product is zero, total product (output) is at its maximum
• Marginal product crosses average product at its maximum
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Product Curves
• We can show a geometric relationship between the total product and the average and marginal product curves– Slope of line from origin to any point on the
total product curve is the average product– At point B, AP = 60/3 = 20 which is the same
as the slope of the line from the origin to point B on the total product curve
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Product Curves
10
30
q/L
80 2 3 4 5 6 7 9 101Labor
q
112
Labor
0 2 3 4 5 6 7 8 9 101
C
60 B20
AP is slope of line from origin to point on TP curve
TP
MP
AP
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Product Curves
• Geometric relationship between total product and marginal product– The marginal product is the slope of the line
tangent to any corresponding point on the total product curve
– For 2 units of labor, MP = 30/2 = 15 which is slope of total product curve at point A
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Product Curves
Labor0 2 3 4 5 6 7 8 9 101
q
60
112
30
15
10
30
q
4 80 2 3 5 6 7 9 101Labor
A
MP is slope of line tangent to corresponding point on TP curve
TP
MP
AP
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Production: One Variable Input
• From the previous example, we can see that as we increase labor the additional output produced declines
• Law of Diminishing Marginal Returns: As the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease
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Law of Diminishing Marginal Returns
• When the use of labor input is small and capital is fixed, output increases considerably since workers can begin to specialize and MP of labor increases
• When the use of labor input is large, some workers become less efficient and MP of labor decreases
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Law of Diminishing Marginal Returns
• Typically applies only for the short run when one variable input is fixed
• Can be used for long-run decisions to evaluate the trade-offs of different plant configurations
• Assumes the quality of the variable input is constant
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Law of Diminishing Marginal Returns
• Easily confused with negative returns – decreases in output
• Explains a declining marginal product, not necessarily a negative one– Additional output can be declining while total
output is increasing
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Law of Diminishing Marginal Returns
• Assumes a constant technology– Changes in technology will cause shifts in the
total product curve– More output can be produced with same
inputs– Labor productivity can increase if there are
improvements in technology, even though any given production process exhibits diminishing returns to labor
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The Effect of Technological Improvement
Output
50
100
Labor pertime period0 2 3 4 5 6 7 8 9 101
A
O1
C
O3
O2
B
Moving from A to B to C, labor productivity is
increasing over time
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Production: Two Variable Inputs
• Firm can produce output by combining different amounts of labor and capital
• In the long run, capital and labor are both variable
• We can look at the output we can achieve with different combinations of capital and labor – Table 6.4
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Production: Two Variable Inputs
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Production: Two Variable Inputs
• The information can be represented graphically using isoquants– Curves showing all possible combinations of
inputs that yield the same output
• Curves are smooth to allow for use of fractional inputs– Curve 1 shows all possible combinations of
labor and capital that will produce 55 units of output
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Isoquant Map
Labor per year1 2 3 4 5
Ex: 55 units of output can be produced with
3K & 1L (pt. A) OR
1K & 3L (pt. D)
q1 = 55
q2 = 75
q3 = 90
1
2
3
4
5Capitalper year
D
E
A B C
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Production: Two Variable Inputs
• Diminishing Returns to Labor with Isoquants
• Holding capital at 3 and increasing labor from 0 to 1 to 2 to 3 – Output increases at a decreasing rate (0, 55,
20, 15) illustrating diminishing marginal returns from labor in the short run and long run
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Production: Two Variable Inputs
• Diminishing Returns to Capital with Isoquants
• Holding labor constant at 3 increasing capital from 0 to 1 to 2 to 3– Output increases at a decreasing rate (0, 55,
20, 15) due to diminishing returns from capital in short run and long run
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Diminishing Returns
Labor per year1 2 3 4 5
Increasing labor holding capital
constant (A, B, C) OR
Increasing capital holding labor constant
(E, D, C
q1 = 55
q2 = 75
q3 = 90
1
2
3
4
5Capitalper year
D
E
A B C
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Production: Two Variable Inputs
• Substituting Among Inputs– Companies must decide what combination of
inputs to use to produce a certain quantity of output
– There is a trade-off between inputs, allowing them to use more of one input and less of another for the same level of output
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Production: Two Variable Inputs
• Substituting Among Inputs – Slope of the isoquant shows how one input
can be substituted for the other and keep the level of output the same
– The negative of the slope is the marginal rate of technical substitution (MRTS)
• Amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant
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Production: Two Variable Inputs
• The marginal rate of technical substitution equals:
)( qLKMRTS
InputLaborinChange
InputCapitalinChangeMRTS
of level fixed a for
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Production: Two Variable Inputs
• As labor increases to replace capital– Labor becomes relatively less productive– Capital becomes relatively more productive– Need less capital to keep output constant– Isoquant becomes flatter
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Marginal Rate ofTechnical Substitution
Labor per month
1
2
3
4
1 2 3 4 5
5Capital per year
Negative Slope measures MRTS;
MRTS decreases as move down the indifference curve
1
1
1
1
2
1
2/3
1/3
Q1 =55
Q2 =75
Q3 =90
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MRTS and Isoquants
• We assume there is diminishing MRTS– Increasing labor in one unit increments from 1 to 5
results in a decreasing MRTS from 1 to 1/2– Productivity of any one input is limited
• Diminishing MRTS occurs because of diminishing returns and implies isoquants are convex
• There is a relationship between MRTS and marginal products of inputs
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MRTS and Marginal Products• If we increase labor and decrease capital
to keep output constant, we can see how much the increase in output is due to the increased labor– Amount of labor increased times the marginal
productivity of labor
))(( LMPL
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MRTS and Marginal Products
• Similarly, the decrease in output from the decrease in capital can be calculated– Decrease in output from reduction of capital
times the marginal produce of capital
))(( KMPK
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MRTS and Marginal Products
• If we are holding output constant, the net effect of increasing labor and decreasing capital must be zero
• Using changes in output from capital and labor we can see
0 K))((MP L))((MP KL
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MRTS and Marginal Products
• Rearranging equation, we can see the relationship between MRTS and MPs
MRTSK
L
MP
L
K
)(
)
))(
L
KL
KL
(MP
K))((MP- (MP
0 K))((MP L))((MP
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Isoquants: Special Cases
• Two extreme cases show the possible range of input substitution in production
1. Perfect substitutes– MRTS is constant at all points on isoquant– Same output can be produced with a lot of
capital or a lot of labor or a balanced mix
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Perfect Substitutes
Laborper month
Capitalper
month
Q1 Q2 Q3
A
B
C
Same output can be reached with mostly capital or mostly labor (A or C) or with equal amount of both (B)
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Isoquants: Special Cases
2. Perfect Complements– Fixed proportions production function– There is no substitution available between
inputs– The output can be made with only a specific
proportion of capital and labor– Cannot increase output unless increase both
capital and labor in that specific proportion
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Fixed-ProportionsProduction Function
Labor per month
Capitalper
month
L1
K1Q1
A
Q2
Q3
B
C
Same output can only be produced with one set of inputs.
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Returns to Scale
• In addition to discussing the tradeoff between inputs to keep production the same
• How does a firm decide, in the long run, the best way to increase output?– Can change the scale of production by
increasing all inputs in proportion– If double inputs, output will most likely
increase but by how much?
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Returns to Scale
• Rate at which output increases as inputs are increased proportionately– Increasing returns to scale– Constant returns to scale– Decreasing returns to scale
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Returns to Scale
• Increasing returns to scale: output more than doubles when all inputs are doubled– Larger output associated with lower cost
(cars)– One firm is more efficient than many (utilities)– The isoquants get closer together
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Increasing Returns to Scale
10
20
30
The isoquants move closer together
Labor (hours)5 10
Capital(machine
hours)
2
4
A
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Returns to Scale• Constant returns to scale: output
doubles when all inputs are doubled– Size does not affect productivity
– May have a large number of producers
– Isoquants are equidistant apart
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Returns to Scale
Constant Returns:
Isoquants are
equally spaced
20
30
Labor (hours)155 10
A
10
Capital(machine
hours)
2
4
6
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Returns to Scale• Decreasing returns to scale: output less
than doubles when all inputs are doubled– Decreasing efficiency with large size
– Reduction of entrepreneurial abilities
– Isoquants become farther apart
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Returns to Scale
Labor (hours)
Capital(machine
hours)
Decreasing Returns:Isoquants get further apart
1020
10
4
A
30
5
2
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Chapter 7
The Cost of Production
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Measuring Cost:Which Costs Matter?
• For a firm to minimize costs, we must clarify what is meant by costs and how to measure them– It is clear that if a firm has to rent equipment
or buildings, the rent they pay is a cost– What if a firm owns its own equipment or
building?• How are costs calculated here?
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Measuring Cost:Which Costs Matter?
• Accountants tend to take a retrospective view of firms’ costs, whereas economists tend to take a forward-looking view
• Accounting Cost– Actual expenses plus depreciation charges for
capital equipment
• Economic Cost– Cost to a firm of utilizing economic resources
in production, including opportunity cost
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Measuring Cost:Which Costs Matter?
• Economic costs distinguish between costs the firm can control and those it cannot– Concept of opportunity cost plays an
important role
• Opportunity cost– Cost associated with opportunities that are
foregone when a firm’s resources are not put to their highest-value use
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Opportunity Cost
• An Example– A firm owns its own building and pays no rent
for office space– Does this mean the cost of office space is
zero?– The building could have been rented instead– Foregone rent is the opportunity cost of using
the building for production and should be included in the economic costs of doing business
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Opportunity Cost
• A person starting their own business must take into account the opportunity cost of their time– Could have worked elsewhere making a
competitive salary
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Measuring Cost:Which Costs Matter?
• Although opportunity costs are hidden and should be taken into account, sunk costs should not
• Sunk Cost– Expenditure that has been made and cannot
be recovered– Should not influence a firm’s future economic
decisions
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Sunk Cost
• Firm buys a piece of equipment that cannot be converted to another use
• Expenditure on the equipment is a sunk cost– Has no alternative use so cost cannot be
recovered – opportunity cost is zero– Decision to buy the equipment might have
been good or bad, but now does not matter
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Prospective Sunk Cost
• An Example– Firm is considering moving its headquarters– A firm paid $500,000 for an option to buy a
building– The cost of the building is $5 million for a total
of $5.5 million– The firm finds another building for $5.25
million– Which building should the firm buy?
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Prospective Sunk Cost
The first building should be purchased
• The $500,000 is a sunk cost and should not be considered in the decision to buy
• What should be considered is– Spending an additional $5,250,000 or– Spending an additional $5,000,000
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Measuring Cost:Which Costs Matter?
• Some costs vary with output, while some remain the same no matter the amount of output
• Total cost can be divided into:
1. Fixed Cost– Does not vary with the level of output
2. Variable Cost – Cost that varies as output varies
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Fixed and Variable Costs
• Total output is a function of variable inputs and fixed inputs
• Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or…
VC FC TC
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Fixed and Variable Costs
• Which costs are variable and which are fixed depends on the time horizon
• Short time horizon – most costs are fixed• Long time horizon – many costs become
variable• In determining how changes in production
will affect costs, must consider if fixed or variable costs are affected.
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Fixed Cost Versus Sunk Cost
• Fixed cost and sunk cost are often confused
• Fixed Cost– Cost paid by a firm that is in business
regardless of the level of output
• Sunk Cost – Cost that has been incurred and cannot be
recovered
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Measuring Cost:Which Costs Matter?
• Personal Computers– Most costs are variable – Largest component: labor
• Software– Most costs are sunk– Initial cost of developing the software
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Measuring Costs
• Marginal Cost (MC):– The cost of expanding output by one unit– Fixed costs have no impact on marginal cost,
so it can be written as:
Δq
ΔTC
Δq
ΔVC MC
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Measuring Costs
• Average Total Cost (ATC)– Cost per unit of output– Also equals average fixed cost (AFC) plus
average variable cost (AVC)
q
TVC
q
TFC
q
TC ATC
AVCAFC q
TC ATC
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A Firm’s Short Run Costs
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A Firm’s Short Run Costs
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Determinants of Short Run Costs
• The rate at which these costs increase depends on the nature of the production process– The extent to which production involves
diminishing returns to variable factors
• Diminishing returns to labor– When marginal product of labor is decreasing
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Determinants of Short Run Costs
• If marginal product of labor decreases significantly as more labor is hired– Costs of production increase rapidly– Greater and greater expenditures must be made to
produce more output
• If marginal product of labor decreases only slightly as increase labor– Costs will not rise very fast when output is increased
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Determinants of Short Run Costs – An Example
• Assume the wage rate (w) is fixed relative to the number of workers hired
• Variable costs is the per unit cost of extra labor times the amount of extra labor: wL
q
Lw
q
VC MC
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Determinants of Short Run Costs – An Example
• Remembering that
L MPL
Q
LMP
1
Q
L Qunit 1 afor L
And rearranging
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Determinants of Short Run Costs – An Example
• We can conclude:
LMP MCw
…and a low marginal product (MPL) leads to a high marginal cost (MC) and vice versa
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Determinants of Short Run Costs
• Consequently– MC decreases initially with increasing returns
• 0 through 4 units of output
– MC increases with decreasing returns• 5 through 11 units of output
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Cost Curves for a Firm
Output
Cost($ peryear)
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
VC
Variable costincreases with production and
the rate varies withincreasing and
decreasing returns.
TC
Total costis the vertical
sum of FC and VC.
FC50
Fixed cost does notvary with output
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Cost Curves
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Output (units/yr)
Co
st (
$/u
nit
) MC
ATC
AVC
AFC
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Cost Curves
• When MC is below AVC, AVC is falling• When MC is above AVC, AVC is rising• When MC is below ATC, ATC is falling• When MC is above ATC, ATC is rising• Therefore, MC crosses AVC and ATC at the
minimums– The Average – Marginal relationship
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Cost Curves for a Firm
• The line drawn from the origin to the variable cost curve:– Its slope equals AVC– The slope of a point
on VC or TC equals MC
– Therefore, MC = AVC at 7 units of output (point A)
1 2 3 4 5 6 7 8 9 10 11 12 13
Output
P
100
200
300
400
FC
VC
TC
A
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Cost in the Long Run
• In the long run a firm can change all of its inputs
• In making cost minimizing choices, must look at the cost of using capital and labor in production decisions
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Cost Minimizing Input Choice
• How do we put all this together to select inputs to produce a given output at minimum cost?
• Assumptions– Two Inputs: Labor (L) and capital (K)– Price of labor: wage rate (w)– The price of capital
• r = depreciation rate + interest rate
• Or rental rate if not purchasing
• These are equal in a competitive capital market
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Cost in the Long Run
• The Isocost Line– A line showing all combinations of L & K that
can be purchased for the same cost– Total cost of production is sum of firm’s labor
cost, wL, and its capital cost, rK:
C = wL + rK– For each different level of cost, the equation
shows another isocost line
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Cost in the Long Run
• Rewriting C as an equation for a straight line:– K = C/r - (w/r)L– Slope of the isocost:
• -(w/r) is the ratio of the wage rate to rental cost of capital.
• This shows the rate at which capital can be substituted for labor with no change in cost
rwLK
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Choosing Inputs
• We will address how to minimize cost for a given level of output by combining isocosts with isoquants
• We choose the output we wish to produce and then determine how to do that at minimum cost– Isoquant is the quantity we wish to produce– Isocost is the combination of K and L that
gives a set cost
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Producing a Given Output at Minimum Cost
Labor per year
Capitalper
year
Isocost C2 shows quantity Q1 can be produced with
combination K2,L2 or K3,L3.However, both of these
are higher cost combinationsthan K1,L1.
Q1
Q1 is an isoquant for output Q1.
There are three isocost lines, of which 2 are possible choices in
which to produce Q1.
C0 C1 C2
AK1
L1
K3
L3
K2
L2
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Input Substitution When an Input Price Change
• If the price of labor changes, then the slope of the isocost line changes, -(w/r)
• It now takes a new quantity of labor and capital to produce the output
• If price of labor increases relative to price of capital, and capital is substituted for labor
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Input Substitution When an Input Price Change
C2
The new combination of K and L is used to produce Q1.
Combination B is used in place of combination A.K2
L2
B
C1
K1
L1
A
Q1
If the price of laborrises, the isocost curve
becomes steeper due to the change in the slope -(w/L).
Labor per year
Capitalper
year
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Cost in the Long Run
• How does the isocost line relate to the firm’s production process?
K
LMP
MP- MRTS L
K
rw
LK
lineisocost of Slope
costminimizesfirmwhenrw
MPMP
K
L
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Cost in the Long Run• The minimum cost combination can then
be written as:
– Minimum cost for a given output will occur when each dollar of input added to the production process will add an equivalent amount of output.
rwKL MPMP
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Cost in the Long Run
• If w = $10, r = $2, and MPL = MPK, which input would the producer use more of?– Labor because it is cheaper
– Increasing labor lowers MPL
– Decreasing capital raises MPK
– Substitute labor for capital until
r
MP
w
MP KL
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Cost in the Long Run
• Cost minimization with Varying Output Levels– For each level of output, there is an isocost
curve showing minimum cost for that output level
– A firm’s expansion path shows the minimum cost combinations of labor and capital at each level of output
– Slope equals K/L
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A Firm’s Expansion Path
Expansion Path
The expansion path illustratesthe least-cost combinations oflabor and capital that can be used to produce each level of
output in the long-run.
Capitalper
year
25
50
75
100
150
50Labor per year
100 150 300200
A
$2000
200 Units
B
$3000
300 Units
C
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Expansion Path and Long Run Costs
• Firm’s expansion path has same information as long-run total cost curve
• To move from expansion path to LR cost curve– Find tangency with isoquant and isocost– Determine min cost of producing the output
level selected– Graph output-cost combination
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A Firm’s Long Run Total Cost Curve
Long Run Total Cost
Output, Units/yr100 300200
Cost/ Year
1000
2000
3000
D
E
F
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Long Run Versus Short Run Cost Curves
• In the short run, some costs are fixed
• In the long run, firm can change anything including plant size– Can produce at a lower average cost in long
run than in short run– Capital and labor are both flexible
• We can show this by holding capital fixed in the short run and flexible in long run
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Capital is fixed at K1.To produce q1, min cost at K1,L1.If increase output to Q2, min cost
is K1 and L3 in short run.
The Inflexibility of Short Run Production
Long-RunExpansion Path
Labor per year
Capitalper
year
L2
Q2
K2
D
C
F
E
Q1
A
BL1
K1
L3
PShort-RunExpansion Path
In LR, can change capital and min costs falls to K2 and L2.
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Long Run VersusShort Run Cost Curves
• Long-Run Average Cost (LAC)– Most important determinant of the shape of
the LR AC and MC curves is relationship between scale of the firm’s operation and inputs required to minimize cost
1. Constant Returns to Scale– If input is doubled, output will double– AC cost is constant at all levels of output
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Long Run Versus Short Run Cost Curves
2. Increasing Returns to Scale– If input is doubled, output will more than
double– AC decreases at all levels of output
3. Decreasing Returns to Scale– If input is doubled, output will less than
double– AC increases at all levels of output
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Long Run Versus Short Run Cost Curves
• In the long run:– Firms experience increasing and decreasing
returns to scale and therefore long-run average cost is “U” shaped.
– Source of U-shape is due to returns to scale instead of decreasing returns to scale like the short-run curve
– Long-run marginal cost curve measures the change in long-run total costs as output is increased by 1 unit
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Long Run Versus Short Run Cost Curves
• Long-run marginal cost leads long-run average cost:– If LMC < LAC, LAC will fall– If LMC > LAC, LAC will rise– Therefore, LMC = LAC at the minimum of LAC
• In special case where LAC is constant, LAC and LMC are equal
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Long Run Average and Marginal Cost
Output
Cost($ per unitof output
LAC
LMC
A
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Long Run Costs
• As output increases, firm’s AC of producing is likely to decline to a point
1. On a larger scale, workers can better specialize
2. Scale can provide flexibility – managers can organize production more effectively
3. Firm may be able to get inputs at lower cost if can get quantity discounts. Lower prices might lead to different input mix.
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Long Run Costs
• At some point, AC will begin to increase1. Factory space and machinery may make it
more difficult for workers to do their jobs efficiently
2. Managing a larger firm may become more complex and inefficient as the number of tasks increase
3. Bulk discounts can no longer be utilized. Limited availability of inputs may cause price to rise.
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Long Run Costs
• When input proportions change, the firm’s expansion path is no longer a straight line– Concept of return to scale no longer applies
• Economies of scale reflects input proportions that change as the firm changes its level of production
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Economies and Diseconomies of Scale
• Economies of Scale– Increase in output is greater than the increase
in inputs
• Diseconomies of Scale– Increase in output is less than the increase in
inputs
• U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels
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Long Run Costs
• Increasing Returns to Scale– Output more than doubles when the quantities
of all inputs are doubled
• Economies of Scale– Doubling of output requires less than a
doubling of cost
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Long Run Costs
• Economies of scale are measured in terms of cost-output elasticity, EC
• EC is the percentage change in the cost of production resulting from a 1-percent increase in output
ACMC
QQCCEC
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Long Run Costs
• EC is equal to 1, MC = AC– Costs increase proportionately with output– Neither economies nor diseconomies of scale
• EC < 1 when MC < AC– Economies of scale– Both MC and AC are declining
• EC > 1 when MC > AC– Diseconomies of scale– Both MC and AC are rising
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Long Run Versus Short Run Cost Curves
• We will use short and long run costs to determine the optimal plant size
• We can show the short run average costs for 3 different plant sizes
• This decision is important because once built, the firm may not be able to change plant size for a while
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Long Run Cost with Economiesand Diseconomies of Scale
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Long Run Cost withConstant Returns to Scale
• The optimal plant size will depend on the anticipated output– If expect to produce q0, then should build
smallest plant: AC = $8
– If produce more, like q1, AC rises
– If expect to produce q2, middle plant is least cost
– If expect to produce q3, largest plant is best
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Long Run Cost with Economiesand Diseconomies of Scale
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Long Run Cost withConstant Returns to Scale
• What is the firm’s long run cost curve?– Firms can change scale to change output in
the long run– The long run cost curve is the dark blue
portion of the SAC curve which represents the minimum cost for any level of output
– Firm will always choose plant that minimizes the average cost of production
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Long Run Cost with Economiesand Diseconomies of Scale
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Long Run Cost withConstant Returns to Scale
• The long-run average cost curve envelops the short-run average cost curves
• The LAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels
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Chapter 8
Profit Maximization and Competitive Supply
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Perfectly Competitive Markets
• The model of perfect competition can be used to study a variety of markets
• Basic assumptions of Perfectly Competitive Markets1. Price taking
2. Product homogeneity
3. Free entry and exit
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Perfectly Competitive Markets
1. Price Taking– The individual firm sells a very small share of
the total market output and, therefore, cannot influence market price
– Each firm takes market price as given – price taker
– The individual consumer buys too small a share of industry output to have any impact on market price
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Perfectly Competitive Markets
2. Product Homogeneity– The products of all firms are perfect
substitutes– Product quality is relatively similar as well as
other product characteristics– Agricultural products, oil, copper, iron,
lumber– Heterogeneous products, such as brand
names, can charge higher prices because they are perceived as better
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Perfectly Competitive Markets
3. Free Entry and Exit– When there are no special costs that make it
difficult for a firm to enter (or exit) an industry– Buyers can easily switch from one supplier
to another– Suppliers can easily enter or exit a market
• Pharmaceutical companies are not perfectly competitive because of the large costs of R&D required
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When are Markets Competitive?
• Few real products are perfectly competitive
• Many markets are, however, highly competitive– They face relatively low entry and exit costs– Highly elastic demand curves
• No rule of thumb to determine whether a market is close to perfectly competitive– Depends on how they behave in situations
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Profit Maximization
• Do firms maximize profits?– Managers in firms may be concerned with
other objectives• Revenue maximization• Revenue growth• Dividend maximization• Short-run profit maximization (due to bonus or
promotion incentive)– Could be at expense of long run profits
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Profit Maximization
• Implications of non-profit objective– Over the long run, investors would not support
the company– Without profits, survival is unlikely in
competitive industries
• Managers have constrained freedom to pursue goals other than long-run profit maximization
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Marginal Revenue, Marginal Cost, and Profit Maximization
• We can study profit maximizing output for any firm, whether perfectly competitive or not– Profit () = Total Revenue - Total Cost– If q is output of the firm, then total revenue is
price of the good times quantity– Total Revenue (R) = Pq
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Marginal Revenue, Marginal Cost, and Profit Maximization
• Costs of production depends on output– Total Cost (C) = C(q)
• Profit for the firm, , is difference between revenue and costs
)()()( qCqRq
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Marginal Revenue, Marginal Cost, and Profit Maximization
• Firm selects output to maximize the difference between revenue and cost
• We can graph the total revenue and total cost curves to show maximizing profits for the firm
• Distance between revenues and costs show profits
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Marginal Revenue, Marginal Cost, and Profit Maximization
• Revenue is a curve, showing that a firm can only sell more if it lowers its price
• Slope of the revenue curve is the marginal revenue– Change in revenue resulting from a one-unit increase
in output
• Slope of the total cost curve is marginal cost– Additional cost of producing an additional unit of
output
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Marginal Revenue, Marginal Cost, and Profit Maximization
• If the producer tries to raise price, sales are zero• Profit is negative to begin with, since revenue is
not large enough to cover fixed and variable costs
• As output rises, revenue rises faster than costs increasing profit
• Profit increases until it is maxed at q*• Profit is maximized where MR = MC or where
slopes of the R(q) and C(q) curves are equal
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Profit Maximization – Short Run
0
Cost,Revenue,
Profit($s per
year)
Output
C(q)
R(q)A
B
(q)q0 q*
Profits are maximized where MR (slope at A) and MC (slope at B) are equal
Profits are maximized where R(q) – C(q) is maximized
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Marginal Revenue, Marginal Cost, and Profit Maximization
• Profit is maximized at the point at which an additional increment to output leaves profit unchanged
MCMR
MCMR
q
C
q
R
q
CR
0
0
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The Competitive Firm
• Demand curve faced by an individual firm is a horizontal line– Firm’s sales have no effect on market price
• Demand curve faced by whole market is downward sloping– Shows amount of goods all consumers will
purchase at different prices
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The Competitive Firm
d$4
Output (bushels)
Price$ per bushel
100 200
FirmIndustry
D
$4
S
Price$ per bushel
Output (millions of bushels)
100
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The Competitive Firm
• The competitive firm’s demand– Individual producer sells all units for $4
regardless of that producer’s level of output– MR = P with the horizontal demand curve– For a perfectly competitive firm, profit
maximizing output occurs when
ARPMRqMC )(
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Choosing Output: Short Run
• We will combine revenue and costs with demand to determine profit maximizing output decisions
• In the short run, capital is fixed and firm must choose levels of variable inputs to maximize profits
• We can look at the graph of MR, MC, ATC and AVC to determine profits
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q2
A Competitive Firm
10
20
30
40
Price
50
MC
AVC
ATC
0 1 2 3 4 5 6 7 8 9 10 11Outputq*
AR=MR=PA
q1 : MR > MCq2: MC > MRq*: MC = MR
q1
Lost Profit for q2>q*Lost Profit
for q2>q*
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Choosing Output: Short Run
• The point where MR = MC, the profit maximizing output is chosen– MR = MC at quantity, q*, of 8– At a quantity less than 8, MR > MC, so more
profit can be gained by increasing output– At a quantity greater than 8, MC > MR,
increasing output will decrease profits
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A Competitive Firm – Positive Profits
10
20
30
40
Price
50
0 1 2 3 4 5 6 7 8 9 10 11Outputq2
MC
AVC
ATC
q*
AR=MR=PA
q1
D
C B Profits are determined
by output per unit times quantity
Profit per unit = P-AC(q) = A to B
Total Profit = ABCD
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The Competitive Firm
• A firm does not have to make profits
• It is possible a firm will incur losses if the P < AC for the profit maximizing quantity– Loss
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A Competitive Firm – Losses
Price
Output
MC
AVC
ATC
P = MRD
At q*: MR = MC and P < ATCLosses = (P- AC) x q* or ABCD
q*
A
BC
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Short Run Production
• Why would a firm produce at a loss?– Might think price will increase in near future– Shutting down and starting up could be costly
• Firm has two choices in short run– Continue producing– Shut down temporarily– Will compare profitability of both choices
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Short Run Production
• When should the firm shut down?– If AVC < P < ATC, the firm should continue
producing in the short run• Can cover all of its variable costs and some of its
fixed costs
– If AVC > P < ATC, the firm should shut down• Cannot cover its variable costs or any of its fixed
costs
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A Competitive Firm – Losses
Price
Output
P < ATC but AVC so firm will continue to produce in short run
MC
AVC
ATC
P = MRD
q*
A
BC
Losses
EF
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Competitive Firm – Short Run Supply
• Supply curve tells how much output will be produced at different prices
• Competitive firms determine quantity to produce where P = MC– Firm shuts down when P < AVC
• Competitive firms’ supply curve is portion of the marginal cost curve above the AVC curve
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A Competitive Firm’sShort-Run Supply CurvePrice($ per
unit)
Output
MC
AVC
ATC
P = AVC
P2
q2
The firm chooses theoutput level where P = MR = MC,
as long as P > AVC.
P1
q1
S
Supply is MC above AVC
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A Competitive Firm’sShort-Run Supply Curve
• Supply is upward sloping due to diminishing returns
• Higher price compensates the firm for the higher cost of additional output and increases total profit because it applies to all units
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A Competitive Firm’sShort-Run Supply Curve
• Over time, prices of product and inputs can change
• How does the firm’s output change in response to a change in the price of an input?– We can show an increase in marginal costs
and the change in the firm’s output decisions
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MC2
q2
Input cost increases and MC shifts to MC2
and q falls to q2.
MC1
q1
The Response of a Firm toa Change in Input PricePrice($ per
unit)
Output
$5
Savings to the firmfrom reducing output
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The Short-Run Market Supply Curve
• As price rises, firms expand their production• Increased production leads to increased demand
for inputs and could cause increases in input prices
• Increases in input prices cause MC curve to rise• This lowers each firm’s output choice• Causes industry supply to be less responsive to
change in price than would be otherwise
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Elasticity of Market Supply
• Elasticity of Market Supply– Measures the sensitivity of industry output to
market price– The percentage change in quantity supplied,
Q, in response to 1-percent change in price
)//()/( PPQQEs
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Elasticity of Market Supply
• When MC increases rapidly in response to increases in output, elasticity is low
• When MC increases slowly, supply is relatively elastic
• Perfectly inelastic short-run supply arises when the industry’s plant and equipment are so fully utilized that new plants must be built to achieve greater output
• Perfectly elastic short-run supply arises when marginal costs are constant
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Producer Surplus in the Short Run
• Price is greater than MC on all but the last unit of output
• Therefore, surplus is earned on all but the last unit
• The producer surplus is the sum over all units produced of the difference between the market price of the good and the marginal cost of production
• Area above supply curve to the market price
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ProducerProducerSurplusSurplus
Producer surplus is area above MC
to the price
Producer Surplus for a FirmPrice($ per
unit ofoutput)
Output
AVCAVCMCMC
AABB
PP
qq**
At q* MC = MR.Between 0 and q,
MR > MC for all units.
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The Short-Run Market Supply Curve
• Sum of MC from 0 to q*, it is the sum of the total variable cost of producing q*
• Producer Surplus can be defined as the difference between the firm’s revenue and its total variable cost
• We can show this graphically by the rectangle ABCD– Revenue (0ABq*) minus variable cost (0DCq*)
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Producer surplus is also ABCD = Revenue minus variable costs
Producer Surplus for a FirmPrice($ per
unit ofoutput)
Output
ProducerProducerSurplusSurplus
AVCAVCMCMC
AABB
PP
qq**
CCDD
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Producer Surplus Versus Profit
• Profit is revenue minus total cost (not just variable cost)
• When fixed cost is positive, producer surplus is greater than profit
VC- R PS Surplus Producer
FC - VC- R Profit
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Producer Surplus Versus Profit
• Costs of production determine magnitude of producer surplus– Higher cost firms have less producer surplus– Lower cost firms have more producer surplus– Adding up surplus for all producers in the
market given total market producer surplus– Area below market price and above supply
curve
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DD
PP**
QQ**
ProducerProducerSurplusSurplus
Market producer surplus isthe difference between P*
and S from 0 to Q*.
Producer Surplus for a Market
Price($ per
unit ofoutput)
Output
SS
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Choosing Output in the Long Run
• In short run, one or more inputs are fixed– Depending on the time, it may limit the
flexibility of the firm
• In the long run, a firm can alter all its inputs, including the size of the plant
• We assume free entry and free exit– No legal restrictions or extra costs
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Choosing Output in the Long Run
• In the short run, a firm faces a horizontal demand curve– Take market price as given
• The short-run average cost curve (SAC) and short-run marginal cost curve (SMC) are low enough for firm to make positive profits (ABCD)
• The long-run average cost curve (LRAC)– Economies of scale to q2
– Diseconomies of scale after q2
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q1
BC
AD
In the short run, thefirm is faced with fixedinputs. P = $40 > ATC.Profit is equal to ABCD.
Output Choice in the Long RunPrice
Output
P = MR$40
SACSMC
q3q2
$30
LAC
LMC
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Output Choice in the Long Run
Price
Outputq1
BC
ADP = MR$40
SACSMC
q3q2
$30
LAC
LMC
In the long run, the plant size will be increased and output increased to q3.
Long-run profit, EFGD > short runprofit ABCD.
FG
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Long-Run Competitive Equilibrium
• For long run equilibrium, firms must have no desire to enter or leave the industry
• We can relate economic profit to the incentive to enter and exit the market
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Long-Run Competitive Equilibrium
• Zero-Profit– A firm is earning a normal return on its
investment– Doing as well as it could by investing its
money elsewhere– Normal return is firm’s opportunity cost of
using money to buy capital instead of investing elsewhere
– Competitive market long run equilibrium
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Long-Run Competitive Equilibrium
• Entry and Exit– The long-run response to short-run profits is
to increase output and profits– Profits will attract other producers– More producers increase industry supply,
which lowers the market price– This continues until there are no more profits
to be gained in the market – zero economic profits
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Long-Run Competitive Equilibrium – Profits
S1
Output Output
$ per unit ofoutput
$ per unit ofoutput
LAC
LMC
D
S2
$40 P1
Q1
Firm Industry
Q2
P2
q2
$30
•Profit attracts firms•Supply increases until profit = 0
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Long-Run Competitive Equilibrium – Losses
S2
Output Output
$ per unit ofoutput
$ per unit ofoutput
LAC
LMC
D
S1
P2
Q2
Firm Industry
Q1
P1
q2
$20
$30
•Losses cause firms to leave•Supply decreases until profit = 0
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Long-Run Competitive Equilibrium
1. All firms in industry are maximizing profits– MR = MC
2. No firm has incentive to enter or exit industry– Earning zero economic profits
3. Market is in equilibrium– QD = QS
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Chapter 9
The Analysis of Competitive Markets
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Consumer and Producer Surplus
• When government controls price, some people are better off– May be able to buy a good at a lower price
• But what is the effect on society as a whole?– Is total welfare higher or lower and by how much?
• A way to measure gains and losses from government policies is needed
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Consumer and Producer Surplus
1. Consumer surplus is the total benefit or value that consumers receive beyond what they pay for the good– Assume market price for a good is $5– Some consumers would be willing to pay
more than $5 for the good– If you were willing to pay $9 for the good and
pay $5, you gain $4 in consumer surplus
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Consumer and Producer Surplus
• The demand curve shows the willingness to pay for all consumers in the market
• Consumer surplus can be measured by the area between the demand curve and the market price
• Consumer surplus measures the total net benefit to consumers
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Consumer and Producer Surplus
2. Producer surplus is the total benefit or revenue that producers receive beyond what it costs to produce a good– Some producers produce for less than
market price and would still produce at a lower price
– A producer might be willing to accept $3 for the good but get $5 market price
– Producer gains a surplus of $2
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Consumer and Producer Surplus
• The supply curve shows the amount that a producer is willing to take for a certain amount of a good
• Producer surplus can be measured by the area between the supply curve and the market price
• Producer surplus measures the total net benefit to producers
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Consumer and Producer Surplus
Between 0 and Q0 producers receive
a net gain from selling each product--
producer surplus.
ConsumerSurplus
Quantity
Price
S
D
Q0
5
9
Between 0 and Q0
consumer A receives a net gain from buying
the product-- consumer surplus.
ProducerSurplus
3
QD QS
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Consumer and Producer Surplus
• To determine the welfare effect of a governmental policy, we can measure the gain or loss in consumer and producer surplus
• Welfare Effects– Gains and losses to producers and
consumers
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Consumer and Producer Surplus
• When government institutes a price ceiling, the price of a good can’t go above that price
• With a binding price ceiling, producers and consumers are affected
• How much they are affected can be determined by measuring changes in consumer and producer surplus
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Consumer and Producer Surplus
• When price is held too low, the quantity demanded increases and quantity supplied decreases
• Some consumers are worse off because they can no longer buy the good– Decrease in consumer surplus
• Some consumers are better off because they can buy it at a lower price– Increase in consumer surplus
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Consumer and Producer Surplus
• Producers sell less at a lower price
• Some producers are no longer in the market
• Both of these producer groups lose and producer surplus decreases
• The economy as a whole is worse off since surplus that used to belong to producers or consumers is simply gone
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The loss to producers is the sum of
rectangle A and triangle C
B
A C
Consumers that can buy the good gain A
Price Control and Surplus Changes
Quantity
Price
S
D
P0
Q0
Pmax
Q1 Q2
Consumers that cannot buy, lose B
Triangles B and C are losses to society – dead weight loss
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Price Controls and Welfare Effects
• The total loss is equal to area B + C
• The deadweight loss is the inefficiency of the price controls – the total loss in surplus (consumer plus producer)
• If demand is sufficiently inelastic, losses to consumers may be fairly large– This can have effects in political decisions
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B
APmax
C
Q1
With inelastic demand, triangle B can be larger
than rectangle A and consumers suffer net
losses from price controls.
S
D
Price Controls With Inelastic Demand
Quantity
Price
P0
Q2
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Price Controls and Natural Gas Shortages
• From example in Chapter 2, 1975 Price controls created a shortage of natural gas
• What was the effect of those controls?– Decreases in surplus and overall loss for
society– We can measure these welfare effects from
the demand and supply of natural gas
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Price Controls and Natural Gas Shortages
• QS = 14 + 2PG + 0.25PO
– Quantity supplied in trillion cubic feet (Tcf)
• QD = -5PG + 3.75PO
– Quantity demanded (Tcf)
• PG = price of natural gas in $/mcf
• PO = price of oil in $/b
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Price Controls and Natural Gas Shortages
• Using PO = $8/b and gives equilibrium values for natural gas– PG = $2/mcf and QG = 20 Tcf
• Price ceiling was set at $1/mcf
• Showing this graphically, we can see and measure the effects on producer and consumer surplus
GS
GD QQ
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B
A
C
The gain to consumers is rectangle A minus triangle
B, and the loss to producers is rectangle A
plus triangle C.
SD
2.00
2.40
Price($/mcf)
Quantity (Tcf)0 5 10 15 20 25 3018
(Pmax)1.00
Price Controls and Natural Gas Shortages
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Price Controls and Natural Gas Shortages
• Measuring the Impact of Price Controls– A = (18 billion mcf) x ($1/mcf) =
$18 billion– B = (1/2) x (2 b. mcf) x ($0.40/mcf) =
$0.4 billion– C = (1/2) x (2 b. mcf) x ($1/mcf) =
$1 billion
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Price Controls and Natural Gas Shortages
• Measuring the Impact of Price Controls in 1975– Change in consumer surplus
• = A - B = 18 - 0.4 = $17.6 billion Gain
– Change in producer surplus• = A + C = 18 + 1 = $19.0 billion Loss
– Dead Weight Loss• = B + C = 0.4 + 1 = $1.4 billion Loss
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The Efficiency ofa Competitive Market
• In the evaluation of markets, we often talk about whether it reaches economic efficiency– Maximization of aggregate consumer and
producer surplus
• Policies such as price controls that cause dead weight losses in society are said to impose an efficiency cost on the economy
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The Efficiency ofa Competitive Market
• If efficiency is the goal, then you can argue that leaving markets alone is the answer
• However, sometimes market failures occur– Prices fail to provide proper signals to
consumers and producers– Leads to inefficient unregulated competitive
market
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Types of Market Failures
1. Externalities– Costs or benefits that do not show up as part
of the market price (e.g. pollution)– Costs or benefits are external to the market
2. Lack of Information– Imperfect information prevents consumers
from making utility-maximizing decisions
• Government intervention may be desirable in these cases
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The Efficiency of a Competitive Market
• Other than market failures, unregulated competitive markets lead to economic efficiency
• What if the market is constrained to a price higher than the economically efficient equilibrium price?
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BA
C
Price Control and Surplus Changes
Quantity
Price
S
D
P0
Q0
Pmin
Q1 Q2
When price is regulated to be no lower than Pmin, the
deadweight loss given by triangles B and C
results.
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The Efficiency of a Competitive Market
• Deadweight loss triangles B and C give a good estimate of the efficiency cost of policies that force price above or below market clearing price
• Measuring effects of government price controls on the economy can be estimated by measuring these two triangles