1. Budget Constraints ECO61 Udayan Roy Fall 2008

2. Prices, quantities, and expenditures P X is the price of good X – It is measured in dollars per unit of good X – The consumer pays this price no matter what quantity she buys. – That is, there are no quantity discounts and there is no rationing X is also the quantity of good X that is purchased by the consumer – It is measured in units of good X per unit of time P X  X = P X X is the consumer’s expenditure on good X

3. Budget constraint Assume a world with only two consumer goods, X and Y Total expenditure = P X X + P Y Y M is the consumer’s income or budget The consumer cannot spend more than her budget allows P X X + P Y Y ≤ M is the consumer’s budget constraint

4. “More-is-better” implies budget exhaustion A rational consumer will spend every penny available. P X X + P Y Y ≤ M becomes P X X + P Y Y = M Here’s an example:

5. Saving The budget constraint P X X + P Y Y = M does not imply that saving is being ignored. We saw earlier that, to an economist, “food delivered now” and “food delivered in the future” are different goods The former could be our good X and the latter could be good Y Then P Y Y would represent saving for the future.

6. Saving You may pay today for something that will be delivered at some date in the future. – For example, you may pay Long Island University today for courses you plan to take in 2015 – You may pay today to reserve hotel rooms in London for the 2012 Olympics – You may pay today for the future delivery of the National Geographic magazine These purchases are the same as saving for the future.

7. Budget constraint algebra

8. If X = 0, then Y = M/P Y – This is the maximum amount of good Y that the consumer can buy Similarly, the maximum amount of good X that the consumer can buy is M/P X If the consumer’s income (M) increases, both maximums will increase by the same proportion

9. Budget Constraint: Graph P S S + P B B = M is the budget constraint It can be graphed into the budget line:

10. Budget constraint algebra If X increases by one unit, then Y must decrease by P X /P Y units – This is at the heart of the consumer’s tradeoff – P X /P Y is also called the relative price of good X (in units of good Y)

11. Budget Constraint Consider Lisa, who buys only burritos (B) and pizza (Z) – If p Z = $1, p B = $2, and M = $50, then:

12. Possible Allocations of Lisa’s Budget Between Burritos and Pizza Lisa’s budget is $50. Burritos are $2 each and pizzas are $1 each.

13. Budget Constraint: graph  From previous slide we have that if: –p Z = $1, p B = $2, and M = $50, then the budget constraint, L 1, is: B, Bur r itos per semester Opportunity set 50 = M / p Z L 1 25 = M/p B 20 10 030 Z, Pizzas per semester a b c d Amount of Burritos consumed if all income is allocated for Burritos. Amount of Pizza consumed if all income is allocated for Pizza.

14. The Slope of the Budget Constraint We have seen that the budget constraint for Lisa is given by the following equation: – The slope of the budget line is the rate at which Lisa can trade burritos for pizza in the marketplace Slope =  B/  Z

15. Changes in the Budget Constraint: An increase in the Price of Pizzas. B, Bur r itos per semester Loss 50 p Z = $1 p Z = $2 25 0 Z, Pizzas per semester B = M PBPB - P Z = $1 PBPB Z If the price of Pizza doubles, (increases from $1 to $2) the slope of the budget line increases This area represents the bundles she can no longer afford $2 Slope = -$1/$2 = -0.5 Slope = -$2/$2 = -1

16. How taxes affect the budget constraint A tax of T Z dollars per pizza has the effect of raising the price paid by the buyer from P Z to P Z + T Z. Therefore, the effect is essentially the same as in the previous slide

17. Changes in the Budget Constraint: Increase in Income ( M ) Gain M = $100 M = $50 0 B = $50 PBPB - PZPZ PBPB Z If Lisa’s income increases by $50 the budget line shifts to the right (with the same slope!) $100 This area represents the new consumption bundles she can now afford 10050 Z, Pizzas per semester B, Burritos per semester 50 25

18. Solved Problem A government rations water, setting a quota on how much a consumer can purchase. If a consumer can afford to buy 12 thousand gallons a month but the government restricts purchases to no more than 10 thousand gallons a month, how does the consumer’s opportunity set change?

19. Solved Problem

20. Income in the budget constraint We have seen that the consumer’s budget is affected by her income (M) Therefore, the consumer’s choices (of X and Y) are affected by her income But it has been implied that income (M) is not affected by the consumer’s choices (of X and Y) This is not always true: the consumer’s choices (of X and Y) may affect her income (M)

21. Income in the budget constraint It is also implicit in my discussion of the budget constraint that income (M) is not affected by prices (of X and Y) This is not always true: the prices of goods (P X and P Y ) may affect income (M)

22. Leisure and consumption Y, Goods per d a y Time constraint H 2 H 1 240 N 2 N 1 0 H,Work hours per day N, Leisure hours per day The price of leisure (N) is the wage (w) that is lost (24w + M * ) /P Y When w/P Y decreases, the budget constraint rotates down Consumption with non- labor income (M * /P Y ) Slope = -w/P Y

23. Leisure and consumption II: M * = 0 Y, Goods per d a y H 2 H 1 240 N 2 N 1 0 H,Work hours per day N, Leisure hours per day The price of leisure (N) is the wage (w) that is lost 24w /P Y When w/P Y decreases, the budget constraint rotates down Slope = -w/P Y 24w/w = 24

24. Progressive income tax Now we have a 20% income tax, but only on income in excess of Y 0. Y, Goods per d a y H 2 H 1 240 N 2 N 1 0 H,Work hours per day N, Leisure hours per day 24w  (1-0.20) /P Y Slope = -w/P Y 24w/w = 24 Slope = -w  (1-0.20)/P Y Y0Y0

25. Income is affected by choices Other examples where consumers’ choices affect their incomes – How much we save today will affect our future interest income – How much we spend today on which asset (stocks, bonds, college courses) will affect our future incomes