Consider a two person (1 and 2), two good (A

Consider a two person (1 and 2), two good (A and B) exchange economy. Social welfare for the economy is: W=U₁+U₂.

a. Draw social indifference curves for the economy in question. What is the rate at which society is willing to trade one person’s welfare for another?

b. Suppose that person 1’s utility function is U₁=A+2B and person 2’s utility function is U₂=3A+B. Suppose that each person is endowed with 15 units of goods A and B (making a total of 30 units in the economy). Determine the optimal allocation in the economy, under the condition that both individuals receive at least as much utility as their endowed consumption bundle.
The marginal utilities for person 1 are: MU_A=1, MU_B=2. The marginal utilities for person 2 are: MU_A=3, MU_B=1.

c. Suppose social welfare is now characterized as: W=min(U₁,U₂), re-do part B. Describe how the optimal allocations change and why.