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.Given the quantity of bats each facility produces under the new owner's advice to maximize profits by producing until Marginal Cost = Price at each facility,what are the firm's profits? Compare your answer to the profits made under the old owner.
A) $2,025
B) $3,625
C) $4,000
D) $4,050

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.Given the quantity of bats each facility produces under the new owner's advice to maximize profits by producing until Marginal Cost = Price at each facility,what are the firm's profits? Compare your answer to the profits made under the old owner.
A) $2,025 
B) $3,625 
C) $4,000 
D) $4,050

Quizplus · Accepted Answer

To find the optimal quantity of bats produced by each plant, we need to set the marginal cost equal to the price. Let's assume that the market price for each baseball bat is $20.

For Plant 1:
MC₁ = P
10 + 2Q₁ = 20
2Q₁ = 10
Q₁ = 5

For Plant 2:
MC₂ = P
10 + 2Q₂ = 20
2Q₂ = 10
Q₂ = 5

So, each plant should produce 5 baseball bats to maximize profits.

To find the firm's profits, we need to calculate the total revenue and total cost.

Total revenue = Price x Quantity
= 20 x (5 + 5)
= $200

Total cost = Total variable cost + Total fixed cost

For Plant 1:
Total variable cost₁ = MC₁ x Q₁
= (10 + 2Q₁) x Q₁
= (10 + 2(5)) x 5
= $75

Total fixed cost₁ = ATC₁ x Q₁
= (10 + 5) x 5
= $75

Total cost₁ = Total variable cost₁ + Total fixed cost₁
= $75 + $75
= $150

For Plant 2:
Total variable cost₂ = MC₂ x Q₂
= (10 + 2Q₂) x Q₂
= (10 + 2(5)) x 5
= $75

Total fixed cost₂ = ATC₂ x Q₂
= (10 + 5) x 5
= $75

Total cost₂ = Total variable cost₂ + Total fixed cost₂
= $75 + $75
= $150

Total cost = Total cost₁ + Total cost₂
= $150 + $150
= $300

Therefore, the firm's profits are:
Total revenue - Total cost
= $200 - $300
= -$100

Under the old owner, the firm's profits were $2,000. So, the new owner's strategy of producing until Marginal Cost = Price has resulted in a decrease in profits.

Scenario: a Small Firm Manufactures Maple Baseball Bats in Two