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Consumer Theory

Consumers choose the best bundles of

goods they can afford.

1. Can affordBudget constraints.

2. Best according to preferences.

Why is it useful?

1. Predict behavior changes.

2. Policy analysis.

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Consumption Choice Sets

A consumption choice set is the collection

of all consumption choices available to the

consumer. What constrains consumption choice?

Budgetary, time and other resource limitations.

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Fruity Example

You are going to the grocery. You buy 2 apples, 3

oranges, and 4 pears. Apples and Oranges cost 1

each and a pear is 2. How much do you spend? If you have 10 to spend, what can you buy?

Prices of apples, oranges, and pears are

represented by pa, po, pp and income is m. What

can one buy?

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Budget Constraints

A consumption bundle containing x1 units of

commodity 1, x2 units of commodity 2 and so on

up to xn units of commodity n is denoted by thevector (x1, x2, , xn).

Commodity prices are p1, p2, , pn.

When is a consumption bundle(x1, , xn) affordable at given prices p1, , pn?

We usually deal with 2 commodities.

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Budget Constraints

The consumers budget set is the set of all

affordable bundles;

x1

0, , xn

0 and p1x1+ + pnxn

m

The budget constraint is the upper boundary

of the budget set.

Draw budget set for general two goods. What is affordable, just affordable, not

affordable?

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Budget Constraints

For n = 2 and x1 on the horizontal axis, theconstraints slope is -p1/p2. What does it

mean?

Increasing x1 by 1 must reduce x2 by p1/p2

This is the opportunity cost.

The budget constraint and budget set

depend upon prices and income. Whathappens as prices or income change?

Does inflation hurt us?

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Ad Valorem Sales Taxes

An ad valorem sales tax levied at a rate of 5%

increases all prices by 5%, from p to (1+0.05)p =

1.05p.

An ad valorem sales tax levied at a rate oft

increases all prices by tp from p to (1+t)p. A uniform sales tax is applied uniformly to all

commodities.

Write the new budget constraint. Can the government replace this with an income

tax? (Sort of like old betting tax)

Subsidies are opposite of a tax (1-s)p.

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The Food Stamp Program

Food stamps are coupons that can be legally

exchanged only for food.

How does a commodity-specific gift such asa food stamp alter a familys budget

constraint?

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The Food Stamp Program

Suppose m = 100, pF = 1 and the price of

other goods is pG = 1.

The budget constraint is thenF + G =100.

What is budget set after 40 food stamps are

issued? What if food stamps can be traded on the

black market for .50?

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Budget with Rationing

What does the budget look like if we ration

good 1?

What happens if we tax all goods purchased

above the ration at rate t?

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Fun Budget Constraints

1. Quantity Discounts: Suppose p2 isconstant at 1 but that p1=2 for 0 x1

20 and p1=1 for x1>20.

2. Try drawing a 3-d budget constraint.(p1=p2=p3=1, m=3)

3. Coke machine doesnt give change. Candy

machine does. Must buy Candy with Coke,but Coke with Candy.

4. Negative Prices: one hour of work gives

3, can of Beer is 1. Have 5 already.