Consider the following utility functions and utility levels:

1. U(x,y) = 2x + y, U = 8 U = 10
2. U(x,y)= (x²y), U = 18 U = 36
3. U(x,y) = min(2x,y) U = 2 U = 4

a. Draw the indifference curves that correspond to the two utility levels indicated for each utility function. (I only need help with 3)

b. Define the MRS_Yx . For each of the three utility functions, find the MRS_Yx. Note that MU_x=2 and MU_y=1 when U(x,y) = 2x + y; MU_x =2xy and MU_y= x²when U(x,y) = x²y.

Is the MRS a function? If it is, what is it a function of?

c. Suppose U^A(x,y) = 2x+y and A currently has consumption bundle (4,4). Suppose that U^B(x,y) = x²y and has consumption bundle (2,4). What is the maximum B is willing to give up for more X? Why? What is the minimum A is willing to accept to give up y? Why? Could they make a voluntary trade and what is the range of the terms of trade would be?