Exercise 4. (16 points) Consider a consumer with a utility function U(x,y) = x05 + 4y05. a) Compute the expression of the consumer's MRS as a function of x and y. Page 2 b) Along an indifference curve, as x goes to zero and y increases, what happens to the consumer's /MRS/? Will this consumer ever choose to spend all of his budget on y only? c) Along an indifference curve, as y goes to zero and z increases, what happens to the consumer's /MRS/? Will this consumer ever choose to spend all of his budget on x only? d) Call px the price of X, py the price of Y and M the consumer's cash endowment and write the consumer's utility maximization problem. e) Write the expression of the consumer's Lagrangian function. f) Write the first order conditions for the constrained utility maximization problem. g) Solve the first order conditions and find the expression of the consumer's optimal amounts x* and y* as functions of px, py and W