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Difficulty: MediumPerfect Competition: Price and Output Determination in Short and Long Run

A firm operating in a perfectly competitive market sells its product at a constant price of P=$30P = \$30. The firm's short-run marginal cost function is given by MC=2Q+10MC = 2Q + 10, where QQ is the quantity produced. Assuming the firm maximizes profit, what is the total revenue earned by the firm at equilibrium?

  1. $300\$300Answer
  2. B
    $150\$150
  3. C
    $200\$200
  4. D
    $600\$600

Answer

$300\$300
In perfect competition, the firm is a price taker, so price equals marginal revenue (P=MR=$30P = MR = \$30). Setting MR=MCMR = MC gives 30=2Q+1030 = 2Q + 10, which solves to Q=10Q = 10 units. Multiplying output by the price yields total revenue of $300\$300.

Step-by-Step Solution

1
Determine Marginal Revenue (MR)
MR=P=$30MR = P = \$30
In a perfectly competitive market, price is constant and equal to marginal revenue.
2
Set profit-maximization condition MR = MC to solve for equilibrium quantity (Q)
30=2Q+10⇒2Q=20⇒Q=1030 = 2Q + 10 \Rightarrow 2Q = 20 \Rightarrow Q = 10 units
Profit is maximized where marginal revenue equals marginal cost.
3
Calculate Total Revenue (TR)
TR=P×Q=$30×10=$300TR = P \times Q = \$30 \times 10 = \$300
Total revenue is the product of market price and equilibrium output.

Key Concept

Short-run Profit Maximization under Perfect Competition
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Topics

Perfect Competition: Price and Output Determination in Short and Long Run

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