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Difficulty: HardMonopolistic Competition: Features, Product Differentiation, and Equilibrium

A firm operating under monopolistic competition faces an inverse demand function P=120−4QP = 120 - 4Q and a marginal revenue function MR=120−8QMR = 120 - 8Q, where PP is price in Naira and QQ is quantity of output. Its total cost function is TC=200+20Q+Q2TC = 200 + 20Q + Q^2 and its marginal cost function is MC=20+2QMC = 20 + 2Q. What is the firm's maximum short-run economic profit in Naira?

Answer: 300 Naira

Answer

The firm's maximum short-run economic profit is 300 Naira.
The profit-maximizing condition for a monopolistically competitive firm is MR=MCMR = MC. Setting 120−8Q=20+2Q120 - 8Q = 20 + 2Q yields Q=10Q = 10 units. Substituting Q=10Q = 10 into the demand function gives a price of 8080 Naira, producing Total Revenue of 800800 Naira (80×1080 \times 10). Substituting Q=10Q = 10 into the Total Cost function yields 500500 Naira (200+200+100200 + 200 + 100). Short-run economic profit is TR−TC=800−500=300TR - TC = 800 - 500 = 300 Naira.

Step-by-Step Solution

1
Equate Marginal Revenue (MR) to Marginal Cost (MC) to find the profit-maximizing output
120−8Q=20+2Q  ⟹  10Q=100  ⟹  Q=10120 - 8Q = 20 + 2Q \implies 10Q = 100 \implies Q = 10 units
Like all imperfectly competitive firms, a monopolistically competitive firm maximizes profit at the output level where marginal revenue equals marginal cost.
2
Determine the price using the demand curve at the optimal output level
P=120−4(10)=80P = 120 - 4(10) = 80 Naira
The demand curve indicates the maximum price per unit consumers are willing to pay for 10 units.
3
Calculate Total Revenue (TR) and Total Cost (TC)
TR=80×10=800TR = 80 \times 10 = 800 Naira and TC=200+20(10)+102=500TC = 200 + 20(10) + 10^2 = 500 Naira
Total revenue is price multiplied by quantity produced, while total cost is evaluated directly from the given total cost equation.
4
Subtract Total Cost from Total Revenue to determine short-run economic profit
Economic profit =800−500=300= 800 - 500 = 300 Naira
Economic profit represents the excess of total revenue over total economic cost in the short run.

Key Concept

Short-Run Profit Maximization in Monopolistic Competition
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Topics

Monopolistic Competition: Features, Product Differentiation, and Equilibrium

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