Consider two individuals  M and F who must split 20 units of good X and 10 units of good Y. Suppose we can represent M's preference with the utility function

Um =X^{^2}mYm and Fs preference with the utility

Uf = min{Xf, 2Yf}

Where Xm and Xf indicate their X consumption, while Ym and Yf indicate their Y consumption

a) Derive the MRS for M

b) Interpret F's utility function

c) Find and graph the contract curve

d) What is the ratio of the price of X to the Price of Y in competitive equilibrium?

e) To which allocation will M and F trade? Indicate this outcome clearly in your graph