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 pa, po, pp 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 xn units of commodity n is denoted by the vector (x 1, x 2, … , xn). • Commodity prices are p 1, p 2, … , pn. • When is a consumption bundle (x 1, … , xn) affordable at given prices p 1, …, pn? • We usually deal with 2 commodities.

Budget Constraints • The consumer’s budget set is the set of all affordable bundles; x 1 ³ 0, … , xn ³ 0 and p 1 x 1 + … + 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?

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. 05 p. • 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?

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?

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.