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A firm’s profit function is given by  π(q) = TR(q)-C(q) where TR is Total Revenue and C...

A firm’s profit function is given by  π(q) = TR(q)-C(q) where TR is Total Revenue and C is total cost. If the profit function is π(q)=200q - (120+25q+25q^2), what is the output q , that maximizes the firm’s profit? What is the firm’s revenue, variable cost, and profit? Should the firm operate or shut down in the short run? (Hint: What is the condition for profit maximization?)

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Answer #1

Answer:

Condition for profit maximization = when MR = MC

1. Output

From TR we can derive MR

TR = 200Q

MR = 200

From TC we can derive MC

TC = 120 + 25Q + 25Q^2

MC = 25 + 50Q

For profit maximizing quantity MR = MC

200 = 25 + 50Q

175 = 50Q

Q = 175/50

Q = 3.5 units is output


2. Revenue

TR = 200Q

TR = 200 * 3.5

TR = $700 is total revenue

3. Variable cost

TVC = 25q+25q^2

TVC = 25(3.5) + 25 (3.5)^2

TVC = 87.5 + 306.25

TVC = $393.75‬

4. Profit/loss

Profit = TR - TFC - TVC

Profit = 700 - 120 - 393.75

Profit = $186.25‬

5. Operate or Shut down

Price or ( Total revenu ) > ATC or ( Total variable cost )

Thus firm should operate

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