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(alpha) 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 alpha and its sign.

c. suppose there are n identical chip producers, let D(p) be the demand function and let p(a) be the competitive equilibrium price. Calculate (dp/da) and its sign