Consumer Theory Consumers choose the best bundles of goods they can afford. 1.Can afford – Budget constraints. 2.“Best” – according to preferences. Why is it useful? 1.Predict behavior changes. 2.Policy analysis.

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.

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 p a, p o, p p and income is m. What can one buy?

Budget Constraints A consumption bundle containing x 1 units of commodity 1, x 2 units of commodity 2 and so on up to x n units of commodity n is denoted by the vector (x 1, x 2, …, x n ). Commodity prices are p 1, p 2, …, p n. When is a consumption bundle (x 1, …, x n ) affordable at given prices p 1, …, p n ? We usually deal with 2 commodities.

Budget Constraints The consumer’s budget set is the set of all affordable bundles; x 1  0, …, x n  0 and p 1 x 1 + … + p n x n  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?

Budget Constraints For n = 2 and x 1 on the horizontal axis, the constraint’s slope is -p 1 /p 2. What does it mean? Increasing x 1 by 1 must reduce x 2 by p 1 /p 2 This is the opportunity cost. The budget constraint and budget set depend upon prices and income. What happens as prices or income change? Does inflation hurt us?

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 of t 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.

The Food Stamp Program Food stamps are coupons that can be legally exchanged only for food. How does a commodity-specific gift such as a food stamp alter a family’s budget constraint?

The Food Stamp Program Suppose m = £100, p F = £1 and the price of “other goods” is p G = £1. The budget constraint is then F + 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?

Fun Budget Constraints 1.Quantity Discounts: Suppose p 2 is constant at £1 but that p 1 =£2 for 0  x 1  20 and p 1 =£1 for x 1 >20. 2.Try drawing a 3-d budget constraint. (p 1 =p 2 =p 3 =1, m=3) 3.Coke machine doesn’t 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.