Q1. Explain the Law of Diminishing Marginal utility? State it’s assumption.

A1. The graph displayed at the right is Edgar Millbottom's marginal utility curve for riding the Monster Loop Death Plunge roller coaster during a day at the Shady Valley Amusement Park. By transforming this curve ever so slightly, Edgar's demand curve for roller coaster rides can be derived.

But first, consider the marginal utility curve itself.

The vertical axis measures marginal utility in utils and the horizontal axis measures quantity in rides on the roller coaster.

The marginal utility curve has a negative slope, illustrating the law of diminishing marginal utility.

Marginal utility curve intersects the horizontal axis at 6 rides. Marginal utility is positive up to that point, then becomes negative after.

The task at hand is to transform this marginal utility curve into a demand curve. To do this, though, a little more information is needed.

Adjusting the Rule

According to the rule of consumer equilibrium, people like Edgar buy goods such that the marginal utility-price ratio for each good is equal, satisfying this equation:marginal utility of good 1

price of good 1=

marginal utility of good 2

price of good 2

However, in the derivation of Edgar's demand curve for roller coaster rides, the key comparison is not between roller coaster

rides and ONE other good, but with ALL other alternatives. The big assumption, therefore, is that Edgar achieves consumer equilibrium and satisfies this rule of consumer equilibrium for ALL other goods.

If so, then Edgar has a "standard" or "benchmark" marginal utility-price ratio. For the sake of exposition, suppose that Edgar's benchmark marginal utility-price ratio is 2 utils per dollar. In other words, Edgar purchases all sorts of different goods such that the last dollar spent on each good generates 2 utils of satisfaction.

It this case, it is possible to specify the rule of consumer equilibrium as:

marginal utility of roller coaster rides

price of roller coaster rides

=

marginal utility of all other goods

price of all other goods

= 2 utils per dollar

If this equation is rearranged just a little, the result is:

marginal utility of roller coaster rides

2 utils per dollar=price of roller coaster rides

The beauty of this equation is that the price that Edgar is willing and able to pay for roller coaster rides (his demand price) is now connected to the marginal utility derived from those rides.

Making the Conversion

In terms of the original marginal utility graph, dividing the marginal utility on the vertical axis by 2 utils per dollar transforms the marginal

The Conversion

utility curve into a demand curve. Click the [Demand Curve] button to make this happen.

Not much changes upon clicking the [Demand Curve] button. One change is the measurement units on the vertical axis from utils to dollars. The other change is the elimination of that part of the curve in the negative range of marginal utility and price (negative prices are not relevant). Feel fee to click the [Reset] and [Demand Curve] buttons a couple of times to confirm that not much changes.

Multiple button clicks should serve to emphasize that the marginal utility curve and the demand curve are closely related, that demand is based on marginal utility, and that the law of diminishing marginal utility is the foundation for the law of demand.

Assumption

An assumption is that as you consume more and more of a good the marginal utils will decrease with every additional unit. Utils measure consumers happiness level. If you had one ice cream you would be very happy, if you had two ice creams you would be happy, if you had three ice creams you would feel like you were getting suck. This demonstrates that with every additional unit of a good, the happiness you get from that additional good is not as much as the happiness that came from the good before.

Q2. Differentiate between movement along a demand curve and shift of the demand curve?

Movement along a demand curve is caused due to change in its own price of the commodity. It is also known as quantity demanded. If the price of good X increases to Rs.8, the quantity demanded of good X moves along the demand curve to the left, resulting in new quantity demanded of 1 unit of good X. The change in the quantity demanded due to

the Rs.3 increase in the price of good X is 2 lesser unit of good X. Similarly, a decrease in the price of good X from Rs. 8 to Rs. 5 would induce a movement along the demand curve to the right, and the change in the quantity demanded would be 1 more unit of good X.

Shift in demand curve is caused due to non-price factor of its own good, i.e. factors other than price of the quantity demanded. These are change in technology, change in price of substitute goods, change in incomer of the consumer, etc.

Q3. Explain price elasticity of demand. Explain the total revenue and the geometric method of finding it?

A3. An important aspect of a product's demand curve is how much the quantity demanded changes when the price changes. The economic measure of this response is the price elasticity of demand.

Price elasticity of demand is calculated by dividing the proportionate change in quantity demanded by the proportionate change in price. Proportionate (or percentage) changes are used so that the elasticity is a unit-less value and does not depend on the types of measures used (e.g. kilograms, pounds, etc).

As an example, if a 2% increase in price resulted in a 1% decrease in quantity demanded, the price elasticity of demand would be equal to approximately 0.5. It is not exactly 0.5 because of the specific definition for elasticity uses the average of the initial and final values when calculating percentage change. When the elasticity is calculated over a certain arc or section of the demand curve, it is referred to as the arc elasticity and is defined as the magnitude (absolute value) of the following:

Q2 - Q1

( Q1 + Q2 ) / 2

P2 - P1

( P1 + P2 ) / 2

where

        Q1  =  Initial quantity        Q2  =  Final quantity        P1  =  Initial price        P2  =  Final price

The average values for quantity and price are used so that the elasticity will be the same whether calculated going from lower price to higher price or from higher price to lower price. For example, going from $8 to $10 is a 25% increase in price, but going from $10 to $8 is only a 20% decrease in price. This asymmetry is eliminated by using the average price as the basis for the percentage change in both cases.

For slightly easier calculations, the formula for arc elasticity can be rewritten as:

( Q2 - Q1 ) ( P2 + P1 )

( Q2 + Q1 ) ( P2 - P1 )

To better understand the price elasticity of demand, it is worthwhile to consider different ranges of values.

In this case, the change in quantity demanded is proportionately larger than the change in price. This means that an increase in price would result in a decrease in revenue, and a decrease in

price would result in an increase in revenue. In the extreme case of near infinite elasticity, the demand curve would be nearly horizontal, meaning than the quantity demanded is extremely sensitive to changes in price. The case of infinite elasticity is described as being perfectly elastic and is illustrated below:

Perfectly Elastic Demand Curve

From this demand curve it is easy to visualize how an extremely small change in price would result in an infinitely large shift in quantity demanded.

Q4. What is Production function? How is it different from iso-quant? Explain the three stages of production.

Production function is a technical relationship between inputs and outputs. It is a Q= f (L,K). There are two types of production functions:

a) Short Run: Short Run is a time period where some of the factors are fixed and some are variable. Q= f (L,K). It is also known as Returns to factor.

b) Long Run: Long Run is a time period where all the factors are variable. Q= f (L,K). It is also known as Return to Scale.

Iso-Quant- iso-quant means "equal quantity". It means given the inputs, same quantity of goods are produced.

But in production function, it is not always necessary that the outputs will be equal.

The three stages of productions are:

i) Increasing at increasing rate: In the initial stages, when the resources are under-utilised, marginal product increases at increasing rate, as a result the total product increases at increasing rate.

ii) Increasing at diminishing rate: In the later stages, when the resources are utilized, marginal product starts decreasing but remains positive, therefore, as a result total product increases but at diminishing rate.

iii) Diminshing: When the resources are over-utilised, marginal product tends to become negative and total product starts declining.