Lecture 3 Public Economics

NPTEL-Economics-Public Economics

1 Indian Institute Of Technology, Kanpur

Module 2

THEORETICAL TOOLS & APPLICATION

Lectures (3 - 7)

Topics

2.1 Tools of Public Economics

2.2 Constrained Utility Maximization

2.3 Marginal Rates of Substitution

2.4 Constrained Utility Maximization:

Budget Constraints

2.5 Substitution Effects and Income Effects

2.6 Putting the Tools to Work the Effect of Temporary

Assistance Programs on the Budget Constraint

2.7 Budget Constraint

2.8 The Effect of Temporary Assistance Programs on the

Budget Constraint

2.9 The Effect of Various Policy Changes

2.10 What Happens to Labor Supply in Response to Such a

Policy Change?

2.11 A Different Preference Function

2.12 Summary of Labor Supply Effects

2.13 Recap of Relevant Concepts

2.13.1 Social Welfare



2.13.2 Demand Curves

2.14 Elasticity of Demand

2.14.1 Perfectly Inelastic

2.14.2 Perfectly Elastic

2.15 Production & Cost Function

2.16 Profit Maximization

2.17 Equilibrium: Aggregate Demand

2.18 Equilibrium: Aggregate Supply

2.19 Competitive Equilibrium

2.20 Competitive Equilibrium Maximizes Social Efficiency

2.21 Equilibrium and Social Welfare

2.21.1 Competitive Equilibrium Maximizes Social Efficiency

2.21.2 The Role of Equity

2.21.3 Welfare Maximization

2.22 Welfare Implication of Benefit Reduction



Module 2

Lecture 3

Topics

2.1 TOOLS OF PUBLIC ECONOMICS

Suppose that you are a member of the economic advisory board of the PM and the PM

must decide on the amount of cash transfer that is to be made to the NREGS program.

The chief economic advisor believes that by providing cash to very low income families,

it only encourages them to stay at home rather than go to work. To provide incentives to

these people the government must cut back on the cash benefits. The PM disagrees; he

thinks that poor families who are at home in villages are incapable of finding a job that

pays them high enough to encourage them to work. So if the state cuts the cash benefits it

will only penalize these poor households. You being a researcher are being asked to

inform this debate by assessing the degree to which cutting cash benefits to low income

families will encourage them to work by evaluating the cut.

Such an evaluation would require you to use both theoretical and empirical tools

of economics.

Theoretical tools are a set of tools used to understand economic decision making.

They are primarily graphical and mathematical.

Empirical tools allow you to examine the theory with data.

First we would discuss a few theoretical tools derived from microeconomics that

are most commonly used in public policy analysis. Theoretical Tools: Recap of

utility maximization.

2.2 CONSTRAINED UTILITY MAXIMIZATION

Constrained utility maximization: individuals have well defined utility functions.

In modeling preferences, we do not impose any budget constraint. Simply ask

what people prefer, ignoring what they can afford.



Assumption0: Individuals prefer higher

Indifference Curves:

10th

pizza is not as good as 1st.

But having the 10th

pizza is better than not

having it

Figure 3.1

Higher salary in Kanpur is

enough to compensate him for a

city life in Bombay.

But he may prefer Gurgaon to

either: the salary is higher than in

Bombay but city (how urban) is

more fun than Kanpur.

Figure 3.2

Constrained utility maximization: all decisions are made in order to maximize the

well-being of the individual, subject to his available resources.

Recall that Marginal utility is defined as the additional increment to utility from

consuming an additional unit of a good.

Diminishing marginal utility means each additional unit makes the individual

less happy than the previous unit.

Let us consider 2 goods M and C and the utility function , , the

marginal utility is:

Non Satiation

Convexity of preferences



2.3 MARGINAL RATES OF SUBSTITUTION

Figure 3.3

The individual is willing to give up fewer C to get more M when she has more M

than less.

Figure 3.4

Moving from point A to point B along indifference curve we have:

Loss in utility from less

Gain in utility from more

Since he is on the same Indifference Curve (IC), loss = gain, so that total utility is

constant

How much C she is willing to give up for an additional unit of

M. This is defined as the marginal rate of substitution (MRS).



Relationship between MRS and marginal utility is given by.

i.e. the MRS shows how relative Marginal utilities evolve

over the IC. Moving from left to right

=> and .

Slope of the indifference curve is called the Marginal rate of substitution and is the rate at

which consumer is willing to trade off the two goods.

Is MRS constant along the IC?

MRS is diminishing (in absolute terms) as we move along an indifference curve.

This means that an individual is willing to give up fewer units of C to get more M when

she has more M (bundle B in Fig 3.4) than when she has less M (bundle A in fig 3.4).

2.4 CONSTRAINED UTILITY MAXIMIZATION:

BUDGET CONSTRAINTS

Budget constraint: The budget constraint is a representation of the combination

of goods the consumer can afford to buy with a given income.

Where,

– Y = Income level

– PM = Price of movie

– PC = Price of CD

Thus, the total amount spent must equal income, assuming no saving or borrowing.

The slope of the budget constraint is:

Optimization Problem :

What is the highest IC that an individual can reach given a budget constraint?

The individual chooses the bundle of goods that gives the highest utility, subject

to the budget constraint.

At the optimum: slope of the indifference curve equals the slope of the budget

constraint.



The benefit of her consuming another M is

the MRS, the rate at which she is willing to

trade C for M. The cost to her of making

this trade is the price ratio, the rate at

which the market allows her to trade C for

M. Thus the optimal choice is one at which

Figure 3.5

Thus, the marginal rate of substitution equals the ratio of prices:

One way to demonstrate that 1 is

optimal choice is to show that she is

worse off with any others choice.

At 2,

She is willing to

give up more C for 1 unit of M than

what the market is charging for an

additional unit of M (the rel. price of

M).

She can make herself better off by

C & M & move from 2 to 1. Key

result so far .

Figure 3.6

She is worse off at any other point on the indifference curve.

2. 5 SUBSTITUTION EFFECTS AND INCOME EFFECTS

Consider an, Increase in the price of M, PM .

A change in price consists of two effects:

– Substitution effect–change in consumption due to change in relative

prices, holding utility constant.

– Income effect–change in consumption due to feeling “poorer” after price

increase.



Figure 3.7

In Fig 3.7 as , Budget constraint becomes steeper. Let the budget

constraint shift from AB to AD.

relative price of is more expensive now.

Moreover real income falls.

Suppose government provides subsidy to compensate for the in

If we keep utility level constant the individual is on the same level of

indifference curve. Only the slope of the budget constraint changes. Decline in

is due to Substitution effect.

As you move along indifference curve (1-1’), for same level of utilities, is

relatively more expensive. Hence is relatively cheaper. Hence . You

substitute more expensive M by cheaper C.

This effect of a price change is called a Substitution Effect.

is going to another indifference curve with new slope of Budget constraint

relative price is same as EF but income falls .

further as we move from . This change is purely due to a

change in real income and hence constitutes the income effect.

Movement along indifference curve =Substitution Effect

Movement from indifference curve = Income Effect.

Lecture 3 Public Economics

Documents

Transcript of Lecture 3 Public Economics