Scenario: The scenario above changes, because an increase in the wages of workers at Plant 2 causes marginal costs and average total costs at Plant 2 to rise:
Plant 2: New marginal cost: MC₂ = 20 + 2Q,
Plant 2: Average total cost: ATC₂ = 20 + Q.
Costs at Plant 1 do not change.

-Refer to the scenario above.Given costs have changed at Plant 2,what are the firm's total profits now that is maximizing profits but facing different costs at each facility? Explain your answer.
A) $3,200
B) $3,625
C) $4,000
D) $4,050

Question

Scenario: The scenario above changes, because an increase in the wages of workers at Plant 2 causes marginal costs and average total costs at Plant 2 to rise:
Plant 2: New marginal cost: MC₂ = 20 + 2Q,
Plant 2: Average total cost: ATC₂ = 20 + Q.
Costs at Plant 1 do not change.
 
-Refer to the scenario above.Given costs have changed at Plant 2,what are the firm's total profits now that is maximizing profits but facing different costs at each facility? Explain your answer.
A) $3,200 
B) $3,625 
C) $4,000 
D) $4,050

Quizplus · Accepted Answer

To determine the new total profits, we first need to find the new quantity produced at Plant 2 that will maximize profits given the new cost structure.

Total profit = Total revenue - Total cost

Total revenue = price x quantity = $50 x Q

Total cost = TC₁ + TC₂ = (10 + Q)Q + (20 + Q)Q = 30Q + Q²

Marginal revenue = MR = $50

Marginal cost at Plant 1 = MC₁ = 10

Marginal cost at Plant 2 = MC₂ = 20 + 2Q

To maximize profits, the firm will produce where MR = MC.

If MR = MC₁ = 10, then Q₁ = 100.

If MR = MC₂ = 20 + 2Q, then Q₂ = 40.

So, the firm will produce 100 units at Plant 1 and 40 units at Plant 2.

Total quantity produced = Q = Q₁ + Q₂ = 100 + 40 = 140

Total revenue = $50 x 140 = $7,000

Total cost = TC₁ + TC₂ = (10 + 100)100 + (20 + 40)40 = $2,900

Total profit = $7,000 - $2,900 = $4,100

Therefore, the new total profits are $4,100, which is closest to option B) $3,625.

Scenario: the Scenario Above Changes, Because an Increase in the Wages