In Problem 4, suppose that each firm has the cost function c(y) = y² + 9 for y 0 and c(0) = 0. With industry demand given by D(p) = 51 - p, the equilibrium price and equilibrium number of firms in the industry (in that order) will be

Question

In Problem 4, suppose that each firm has the cost function c(y) = y² + 9 for y > 0 and c(0) = 0. With industry demand given by D(p) = 51 - p, the equilibrium price and equilibrium number of firms in the industry (in that order) will be

Quizplus · Accepted Answer

First, we can find the equilibrium price by setting the industry demand equal to the industry supply: Qd = Qs 51 - p = 15y p = 51 - 15y Next, we need to find the equilibrium number of firms. We can do this by finding the minimum point on the long-run average cost curve, which occurs where marginal cost equals average cost. Using the cost function given in the problem, we can find the marginal cost: MC(y) = ² + 9 And the average cost: AC(y) = y² + 9/y Setting MC equal to AC and solving for y, we get: ² + 9 = ²/y + 9/y^2 Simplifying, we get: ²y + 9 = ² + 9y Solving for y, we get: y = ²/2 Plugging in the values given in the problem, we get: y = 3/2 Finally, we can plug this value of y into the equilibrium price equation we found earlier to get: p = 51 - 15y = 51 - 15(3/2) = $6 So the equilibrium price is $6 and the equilibrium number of firms is 15. Therefore, the answer is D.

In Problem 4, Suppose That Each Firm Has the Cost