Consider a consumer with the following utility function u(x, y) = x + y where the price of x is p and the price of y is one and income is M.

a. Write down the consumer's constrained maximization problem.

b. Find the consumer's inverse demand function. (You may assume there are no corner solutions.)

c. Suppose that the consumer is purchasing 16 units of the good. What is his marginal benefit of consuming the 16th unit of the good?

d. Suppose that the market price is $0.10. What is his consumer surplus from consuming the 16th unit of the good?