Question

. Suppose the short run market price a competitive firm faces is Birr 9 and the total cost of the firm is: TC = 200 + Q + 0.02Q 2  (A) Calculate the short run equilibrium output and profit of the firm.

Answer 1

A firm in the competitive market will produce output up to a level where the marginal revenue is equal to the marginal cost. The marginal revenue of a competitive firm is equal to the market price. Marginal cost can be calculated as the derivative of the total cost function.

$MR=\frac{dTC}{dQ}\\\frac{d(200+Q+0.02Q^2)}{dQ}\\MR=1+0.04Q$

The market price is Birr 9. Therefore the marginal revenue is also Birr 9. Equating marginal revenue and marginal cost gives the equilibrium quantity.

$MC=MR\\1+0.04Q=9\\0.04Q=8\\Q=\frac{8}{0.04}\\=200$

The total revenue is the product of price and quantity.

$TR=Price×Quantity\\=9×200\\=1800$

Total cost is calculated by substituting the quantity in the total cost function.

$TC=200+Q+0.02Q^2\\=200+200+0.02×200^2\\=1200$

Profit is calculated by subtracting total cost from total revenue.

$Profit=TR−TC\\=1800−1200\\=600$

Therefore the equilibrium output is 200 units and the profit is Birr 600.