A poultry farm operates in a perfectly competitive market where the market price per crate… — JAMB UTME

A poultry farm operates in a perfectly competitive market where the market price per crate of eggs is $\text{N}70$ . The farm's short-run total cost function is $TC = 2Q^2 + 10Q + 200$ , where $Q$ is the quantity of crates produced and $TC$ is the total cost in Naira. What is the maximum economic profit, in Naira, realized by the farm?

Answer: 250 Naira

Answer

The maximum economic profit realized by the farm is 250 Naira.

In a perfectly competitive market, the firm is a price taker so marginal revenue equals market price (

MR = P = 70

). Equating marginal revenue to marginal cost (

MC = 4Q + 10

) gives an equilibrium output of

Q = 15

units. Substituting

Q = 15

into Total Revenue (

TR = 70 \times 15 = 1050

) and Total Cost (

TC = 2(15)^2 + 10(15) + 200 = 800

) yields an economic profit of

1050 - 800 = \text{N}250

Step-by-Step Solution

Derive the Marginal Cost equation from Total Cost

MC = 4Q + 10

Marginal Cost represents the rate of change of Total Cost with respect to output.

Equate Marginal Revenue (which equals price in perfect competition) to Marginal Cost

70 = 4Q + 10 \implies Q = 15

units

A price-taking firm maximizes profit where price equals marginal cost (

P = MC

Calculate Total Revenue at optimal output level

TR = 70 \times 15 = \text{N}1050

Total revenue is the product of price per unit and total output sold.

Calculate Total Cost at optimal output level

TC = 2(15)^2 + 10(15) + 200 = \text{N}800

Substitute optimal output into the total cost function.

Subtract Total Cost from Total Revenue to find economic profit

\text{Profit} = 1050 - 800 = \text{N}250

Economic profit is the surplus remaining after deducting total explicit and fixed cost from total revenue.

Key Concept

Profit Maximization in Perfect Competition

Estimated Time:1m 30s

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