The cheese business in Lake Fon-du-lac, Wisconsin, is a competitive industry.All cheese manufacturers have the cost function C = Q² + 4, while demand for cheese in the town is given by Q_d = 120 - P.The long-run equilibrium number of firms in this industry is

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To find the long-run equilibrium number of firms in the industry, we need to use the formula: LRAC = P = MC. In this case, LRAC (long-run average cost) is given by CF1S1/QS1, which simplifies to F1F1F10 + (4S1/QS1). Setting this equal to demand, we get: P = 120 - QS1/58 (where 58 is the number of firms in the industry). To find where LRAC = P = MC, we need to substitute P into the LRAC equation and solve for S1/QS1. Substituting, we get: F1F1F10 + (4S1/QS1) = 120 - QS1/58. Simplifying, we get: 4S1/QS1 + QS1/58 = 120 - F1F1F10. Rearranging, we get: S1/QS1 = (58/4)(120 - F1F1F10) - 58 = 435 - 14.5F1F1F1. This expression tells us the minimum value of S1/QS1 required for LRAC = P = MC to hold, given the number of firms in the industry. Since S1/QS1 must be positive, we can solve for the maximum number of firms by setting S1/QS1 = 0: 0 = 435 - 14.5F1F1F1, which gives F1F1F1 = 30. Therefore, the maximum number of firms is 58 (the closest even number to 30*2).

The Cheese Business in Lake Fon-Du-Lac, Wisconsin, Is a Competitive