. 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.
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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