Boğaziçi University-Department of Economics

Boğaziçi University-Department of Economics EC203 Microeconomics I- Levent Yıldıran PS6

1. (Chp31) In a two-person, two-good exchange economy, both consumers have quasi- linear utility functions, linear in good 2. If quantities of good 1 are measured horizontally and quantities of good 2 are measured vertically in the Edgeworth box, what will be set of pareto optimal allocations?

2. (Chp31) A small economy has only two consumers, Pitogoras and Socrates. Pitogoras’ utility function is U (x, y) = x + 12y 1/2. Socrates’s utility function is U (x, y) = x + 3y. Given that Pitagoras is endowed with 6 units of x and 3 units of y, how much y does Pitogoras consume in order to attain the pareto optimal allocation?

3. (Chp31) Tayfun and Banu both consume the same goods in a pure exchange economy. Tayfun is originally endowed with 18 units of good 1 and 14 units of good 2. Banu is originally endowed with 16 units of good 1 and 3 units of good 2. They 1/3 2/3 both have the utility function U(x ,x ) = x1 x2 . If we let good 1 to be a numeraire good (so that we take p1 = 1) then what will be the equilibrium price of good 2?

4. (Chp31) Consumer A and Consumer B consume only two goods, x and y. They can trade only with each other and there is no production. The total endowment of good x, equals to the total endowment of good y. A’s utility function is U (x, y) = min{x, y}and B’s utility function is U (x, y) = max{x, y}. In an Edgeworth box both for A and B, what will be set of Pareto optimal allocations?

5. (Chp31) Erkuts’s utility function is U (a, b) = min{a,2b}. Hayri’s utility function is U(a,b)= a + 2b. Erkut has initially 12 units of a and no b. Hayri has 12 units of b and no a. In this economy show the competitive equilibrium on the Edgeworth box.

6. (Chp31) Murat has a utility function U(m,j) = max{3m,j} and Ceren has a utility function U(m,j) = 2m+j. Murat is initially endowed with 4 units of milk and 2 units of juice. Ceren is initially endowed with 4 units of milk and 6 units of juice. Show the initial endowment point and Pareto optimal allocations on an Edgeworth box.