Equilibrium price ratio
Find the equilibrium price ratio and allocations for the following utility functions and endowments
1. U A(x, y) = x 1/3y 2/3 U B(x, y) = x 2/3y 1/3 e A x = 100, eA y = 100, eB x = 100, eB y = 100
2. Same as 1 except both consumers increase endowment of x to 200 (e A x = e B x = 200)
3. Same as 1 except both consumers increase endowment of y to 200 (e A y = e B y = 200)
4. Same as 1 except consumer A’s endowment of both goods increases to 200 (e A x = e A y = 200)
5. Same as 1 except consumer A’s endowment of both goods increases to 200 (e B x = e B y = 200)
6. Compare the price ratios you got in 2-5 to the price in 1. Come up with an economic intuition for why they changed in the direction they did.
7. U A(x, y) = 2x + y U B(x, y) = 2x + 5y e A x = 100, eA y = 100, eB x = 100, eB y = 100 (hint: each consumer will only consume one type of good in equilibrium. Why? Can you guess which good each consumer will consume?)
8. U A(x, y) = x 1/2y 1/2 U B(x, y) = x 1/4y 3/4 U C(x, y) = x 3/4y 1/4 e A x = 100, eA y = 100, eB x = 100, eB y = 100, eC x = 100, eC y = 100 (hint: There are three consumers in this economy, but the same definitions hold. All consumers must be maximizing utility and markets must clear.)
