Question

1. Cali and David both collect stamps (x) and fancy spoons (y). They have the following preferences and endowments.

U_c (x, y) = x_c.y_c²

ω_c = (10, 5.2)

U_D (x, y) = x_D. y_D

ω_D = (14, 6.8)

1. Write down the resource constraints and draw an Edgeworth box that shows the set of feasible allocations.

2. Label the current allocation inside the box. How much utility does each person have?

3. Show that the current allocation of stamps and fancy spoons is not efficient. (Hint: Define the contract curve, or the set of Pareto optimal allocations.)

4. Show that the following allocation would make both Cali and David better off compared to the original allocation. Is it possible to make any further pareto improvements?

ω_c = (6,8)

ω_D = (16, 6)

2. Suppose the economy consists of two individuals, Ariel and Brad, who consume two goods, ? and ?, with the following preferences and initial endowments.

U_A (x, y) = x_A. y_A

ω_A = (4, 2)

U_B (x, y) = x_B. y_B

ω_B = (2, 3)

1. In an Edgeworth Box label the initial endowment, draw an indifference curve through the initial endowment for each individual, and shade the region of allocations that would be a Pareto improvement to the initial endowment.
2. Derive an equation to describe the set of Pareto-optimal allocations, and draw it in the Edgeworth Box.

3. Define the competitive equilibrium allocation [(x_A, y_A), (X_B, y_B)] and price ratio P_X/P_Y. (Remember that without loss of generality, you may set P₁ ≡ 1.)

4. Find a set of transfers, ?_? and ?_?, where ?_A + ?_? = 0, such that the competitive equilibrium becomes [(1, 1), (5, 4)].

Answer 1

Pareto dominates. At the same time consider the point P,S that is showing inefficient allocation. Because Cali's better off and David's worse off.