A typical Silicon Valley firm produces output of chips y using a cost function c(y), which exhibits increasing marginal costs. Of the chips it produces, a fraction 1 - a are defective and cannot be sold. Working chips can be sold at a price p and the chip market is highly competitive.
(a) Calculate the derivative of profits with respect to a and its sign.
(b) Calculate the derivative of output with respect to a and its sign.
(c) Suppose that there are n identical chip producers, let D(p) be the demand function, and let p(a) be the competitive equilibrium price. Calculate (dplda) and its sign.