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Principles of Economics: Short-run Firm Equilibrium PROFIT MAXIMIZATION Profit = Total Revenue (P*Q) Total Costs Accountants calculate Profit as operating Profit = Total Revenue Operating Costs = Total Revenue Variable Costs (in economic terminology) (Operating Profit = Producer Surplus in economic terminology) Accountants compare this operating profit with Capital to find the rate of return on capital Economics calculate Economic Profit from all costs, including the cost of capital calculated as the opportunity cost of Capital. Definition: Economic Profit = Total Revenue (Variable Costs + Fixed Costs) Definition: Normal Profit = Opportunity Cost of Capital 0 Economic Profit = Normal Profit since it includes the Opportunity Cost of Capital Economic Loss => Economic Profit < 0 (less than the Opportunity Cost of Capital) Economic Profit => Economic Profit > 0 (greater than the Opportunity Cost of Capital) Short-run Profit Maximization => Find the output that maximizes Profit (TR TC) => (TR TC)/q = 0 [d(TR TC)/dq = 0] => TR/q TC/q = 0 [dTR/dq - dTC/dq = 0] => MR = MC [More formally: Profit = TR TC = PQ (wL + rK) (w = wage rate and r = opportunity cost of Capital) Profit Maximization => (PQ wL rK)/ Q = 0 P + QP/Q wL/Q = 0 - 1 - Principles of Economics: Short-run Firm Equilibrium P + QP/Q = MC since wL/Q = MC MR = MC for all firms since P + QP/Q = MR] Marginal Revenue equal to Marginal Cost gives the profit maximizing output but this expression also includes the loss minimizing output if the price is below Average Cost. (There is one exception to this rule as we will see). E.g. Suppose that the following functions describe the Variable Cost and Fixed Cost of a competitive firm VC = q 59q + 1315q FC = 2000 This cubic function gives the correct shape for the Marginal Cost function but we will eventually work only with more quadratic Variable Cost functions. Note that a change in quantity changes Variable Cost but has no effect on Fixed Cost. Total Cost is the sum of both functions. Suppose further that the firms Total Revenue function is TR = 1000q 2q . TC = q3 - 59q +1315q +2000; TR = 1000q - 2q $000 60 Max (TR - TC) => Max Profit 50 40 TR Slope TR = Slope TC => MR = MC TC 30 20 10 0 0 10 20 30 q* 40 50 MaxProfit Quantity Total Economic Profit is the difference between the Total Revenue and Total Cost functions as shown in the diagram below. Total Economic Profit is greatest at the output where Total Revenue Total Cost is greatest. This occurs where the slopes of the two functions are equal, or - 2 - Principles of Economics: Short-run Firm Equilibrium when Marginal Revenue equals Marginal Cost since these are the slopes of Total Revenue and Total Cost respectively. The diagram below shows Economic Profit as a function of q for this firm. Total Profit = 1000q - 2q - (q- 59q +1315q +2000) $000 15 Total Profit (TR - TC) 10 5 0 -5 0 10 20 30 q* 40 50 Quantity MaxProfit Comparison Marginal Revenue and Marginal Cost shows the maximum profit output more clearly than comparison of Total Revenue and Total Cost. Marginal Revenue = 1000 4q Marginal Cost = 3q - 118q + 1315 2 MC = 3q - 118q +1315;MR = 1000 - 4q $s 3500 3000 MC 2500 2000 1500 1000 500 MR 0 0 10 20 30 q* 40 50 Quantity MaxProfit - 3 -
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