Suppose Va is a person's willingness to pay for good A,Vb is a person's willingness to pay for good B. Va is uniformly distributed between 0 and 10 across the population,Vb is uniformly distributed between 0 and 15 across the population. There are only two products A and B. Each person buys at most one unit of A. There are altogether N persons in the population (N is a very large number) .

a) Suppose the company is only allowed to do component pricing. Find an expression for the percentages of population that buys A only, B only, and both.

b) Calculate the optimal prices under component pricing.

c) Calculate the optimal prices under pure bundling

d) Calculate the average consumer surplus under component pricing and under pure bundling.