A 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 − α 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 α and its sign.
b) Calculate the derivative of output with respect to α and its sign.
c) Suppose that there are n identical chip producers. Let D(p) be the demand function, and let p(α) be the competitive equilibrium price. Calculate dp/dαand its sign.