Scenario: A small firm manufactures maple baseball bats in two small production facilities, with the following marginal cost and average total cost equations:
Plant 1: Marginal cost: MC₁ = 10 + 2Q,
Plant 1: Average total cost: ATC₁ = 10 + Q.
Plant 2: Marginal cost: MC₂ = 10 + 2Q,
Plant 2: Average total cost: ATC₂ = 10 + Q.

-Refer to the scenario above.Now suppose the plant is sold to a new owner with an undergraduate degree in economics and an MBA in finance.The new owner plans to follow the profit-maximizing rule (produce the level of output at which Marginal Cost = Price)rather than equalize production across both plants.Under this new guidance,production levels at each firm are ________.Explain your answer.
A) Produce 45 units of output at Plant 1 and shut down Plant 2
B) Produce 45 units of output at Plant 1 and produce 40 units of output at Plant 2
C) Produce 45 units of output at Plant 1 and produce 45 units of output at Plant 2
D) Produce 40 units of output at Plant 1 and 40 units of output at Plant 2

Question

Scenario: A small firm manufactures maple baseball bats in two small production facilities, with the following marginal cost and average total cost equations:
Plant 1: Marginal cost: MC₁ = 10 + 2Q,
Plant 1: Average total cost: ATC₁ = 10 + Q.
Plant 2: Marginal cost: MC₂ = 10 + 2Q,
Plant 2: Average total cost: ATC₂ = 10 + Q.
 
-Refer to the scenario above.Now suppose the plant is sold to a new owner with an undergraduate degree in economics and an MBA in finance.The new owner plans to follow the profit-maximizing rule (produce the level of output at which Marginal Cost = Price)rather than equalize production across both plants.Under this new guidance,production levels at each firm are ________.Explain your answer.
A) Produce 45 units of output at Plant 1 and shut down Plant 2 
B) Produce 45 units of output at Plant 1 and produce 40 units of output at Plant 2 
C) Produce 45 units of output at Plant 1 and produce 45 units of output at Plant 2 
D) Produce 40 units of output at Plant 1 and 40 units of output at Plant 2

Quizplus · Accepted Answer

The profit-maximizing rule states that a firm should produce the quantity of output at which its marginal cost equals the price it receives. In this scenario, we do not have information about the market price of maple baseball bats. Therefore, we cannot determine the exact level of output at which the firm should produce to maximize profits. However, given the marginal cost equations, we can determine the optimal production levels for each plant. 
The marginal cost equations for both plants are MC₁ = 10 + 2Q and MC₂ = 10 + 2Q. Setting both equations equal to the unknown market price P, we get P = 10 + 2Q for both plants. Equating these two equations, we get
10 + 2Q = 10 + 2Q
Simplifying, we get Q = Q, which means that the production levels for both plants should be the same. Therefore, the optimal production levels for both plants are when they produce 45 units of output each, and the answer is C.

Scenario: a Small Firm Manufactures Maple Baseball Bats in Two