Assume a continuum of potential iPhone developers indexed by the quality of their idea . Each developer has a fixed cost of 1 can produce software code according to the function q = 2x, where x is quantity of variable input used by the developer. A unit of software code sells for a price of 1, and the cost of using a quantity x of the input is x2. The "number" (i.e mass) of firms with ideas above > 0 is given by M() = ^, where > 2. (Hint. Therefore, the mass of firms with idea is M() = 1.This is the density you need to use when aggregating supply.) Apple taxes developers' revenues at a percentage rate 0 < < 1.

(a) Derive the aggregate supply of developer code in the long run. (b) When Apple raises its tax rate, what happens to the mass of developer firms, and the amount of code each produces? (c) What is Apple's revenue maximizing tax ? (d) What happens to aggregate supply if rises (while is fixed)? (Hint. You can interpret an increase in as a decrease in firm heterogeneity. No more computation is needed to answer this question.)