Question

Assume several identical firms have the short run production function Q= √40L and pay a wage of 10 for each unit of labor employed. Fixed costs for each firm are 100 . The market demand for the good is Qₔ = 100,000−.25P. How many firms are in the industry in the long run?

Answer 1

To find the number of firms in the industry in the long run, we need to find the price at which the market demand equals the quantity produced at the bottom of the long-run average cost curve. Using the market demand curve and the short-run production function, we can solve for the price, quantity, and number of firms in the long run.

Step-by-step explanation:

In the long run, the number of firms in an industry is determined by the intersection of the market demand curve and the long-run average cost curve. In this case, the market demand curve is given by Qₔ = 100,000 − 0.25P, and the long-run average cost curve is determined by the short-run production function Q = √(40L). To find the number of firms in the long run, we need to find the price at which the market demand equals the quantity produced at the bottom of the long-run average cost curve. Substituting the short-run production function into the market demand curve, we get P = 400 - 0.01Q. Setting Q equal to the production quantity at the bottom of the long-run average cost curve, Q = √(40L), we can solve for L. Then, substituting L back into Q = √(40L), we can find the quantity produced at the bottom of the long-run average cost curve. Finally, by substituting this quantity into the market demand curve, we can solve for P. The number of firms in the long run is then given by the total market demand divided by the quantity produced by each firm.