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Zorluk: ZorPerfect Competition: Price and Output Determination in Short and Long Run

A firm operating in a perfectly competitive market faces a constant market equilibrium price of P=$60P = \$60. The firm's short-run total cost function is given by TC=Q2+20Q+100TC = Q^2 + 20Q + 100, where QQ represents output in units, resulting in a marginal cost function of MC=2Q+20MC = 2Q + 20. What is the total short-run economic profit earned by this firm at its profit-maximizing output level?

  1. $300Cevap
  2. B
    $200
  3. C
    $400
  4. D
    $15

Cevap

The firm earns a total short-run economic profit of $300.
Under perfect competition, a firm maximizes profit by producing where price equals marginal revenue and marginal cost (P=MR=MCP = MR = MC). At P=$60P = \$60, setting 60=2Q+2060 = 2Q + 20 yields Q=20Q = 20. At Q=20Q = 20, Total Revenue is TR=60×20=$1,200TR = 60 \times 20 = \$1,200 and Total Cost is TC=202+20(20)+100=$900TC = 20^2 + 20(20) + 100 = \$900. Total short-run economic profit is TR−TC=$1,200−$900=$300TR - TC = \$1,200 - \$900 = \$300.

Adım Adım Çözüm

1
Determine the profit-maximizing output level
Output Q = 20 units
Under perfect competition, marginal revenue equals market price (MR=P=$60MR = P = \$60). Setting MR=MCMR = MC gives 60=2Q+2060 = 2Q + 20, which simplifies to 2Q=402Q = 40 or Q=20Q = 20 units.
2
Calculate total revenue (TR)
TR = $1,200
TR=P×Q=60×20=$1,200TR = P \times Q = 60 \times 20 = \$1,200.
3
Calculate total cost (TC)
TC = $900
TC=(20)2+20(20)+100=400+400+100=$900TC = (20)^2 + 20(20) + 100 = 400 + 400 + 100 = \$900.
4
Compute total economic profit (π)
Profit = $300
π=TR−TC=$1,200−$900=$300\pi = TR - TC = \$1,200 - \$900 = \$300.

Anahtar Kavram

Short-run profit maximization under perfect competition occurs where Price (Marginal Revenue) equals Marginal Cost (P = MC). Total economic profit is Total Revenue minus Total Cost.
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Perfect Competition: Price and Output Determination in Short and Long Run

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