Asked by Alexandre Al Mokhtari on Jul 05, 2024
Verified
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 Qd 120 P.The long-run equilibrium number of firms in this industry is
A) 29.
B) 58.
C) 56.
D) 120.
E) 59.
Cost Function
An equation that calculates the total cost incurred by a company to produce a specific quantity of a good or service.
Long-run Equilibrium
A market condition where all factors of production and inputs can be varied, allowing firms to enter or exit the market, ultimately resulting in no economic profit for any firm.
Demand
The amount of a product or service that buyers are ready and able to buy at different price levels over a certain timeframe.
- Familiarize yourself with the interplay between production functions, costs of inputs, and the supply curves in different sectors during short-term and long-term spans.
- Investigate the role of cost functions in determining the number of firms in an industry.
Verified Answer
PV
Parakh VijayJul 06, 2024
Final Answer :
B
Explanation :
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 + (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: + (4S1/QS1) = 120 - QS1/58. Simplifying, we get: 4S1/QS1 + QS1/58 = 120 - . Rearranging, we get: S1/QS1 = (58/4)(120 - ) - 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).
Learning Objectives
- Familiarize yourself with the interplay between production functions, costs of inputs, and the supply curves in different sectors during short-term and long-term spans.
- Investigate the role of cost functions in determining the number of firms in an industry.