A firm operating in a perfectly competitive market faces a constant market equilibrium pri… — JAMB UTME

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

$300Answer
B
$200
C
$400
D
$15

Answer

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 = MC

). At

P = \$60

, setting

60 = 2Q + 20

yields

Q = 20

. At

Q = 20

, Total Revenue is

TR = 60 \times 20 = \$1,200

and Total Cost is

TC = 20^2 + 20(20) + 100 = \$900

. Total short-run economic profit is

TR - TC = \$1,200 - \$900 = \$300

Step-by-Step Solution

Determine the profit-maximizing output level

Output Q = 20 units

Under perfect competition, marginal revenue equals market price (

MR = P = \$60

). Setting

MR = MC

gives

60 = 2Q + 20

, which simplifies to

2Q = 40

Q = 20

units.

Calculate total revenue (TR)

TR = $1,200

TR = P \times Q = 60 \times 20 = \$1,200

Calculate total cost (TC)

TC = $900

TC = (20)^2 + 20(20) + 100 = 400 + 400 + 100 = \$900

Compute total economic profit (π)

Profit = $300

\pi = TR - TC = \$1,200 - \$900 = \$300

Key Concept

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.

Estimated Time:2m 0s

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