Answer to Question #225731 in Economics of Enterprise for elda

Question #225731

. 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.

1
Expert's answer
2021-08-13T13:57:55-0400

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\u00d7Quantity\\\\=9\u00d7200\\\\=1800"

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

"TC=200+Q+0.02Q^2\\\\=200+200+0.02\u00d7200^2\\\\=1200"

Profit is calculated by subtracting total cost from total revenue.

"Profit=TR\u2212TC\\\\=1800\u22121200\\\\=600"

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



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