profit maximization.doc

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) => Δ(TR – TC)/Δq = 0 [d(TR – TC)/dq = 0] => ΔTR/Δq – ΔTC/Δq = 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 => Δ(PQ – wL – rK)/ ΔQ = 0 → P + QΔP/ΔQ – wΔL/ΔQ = 0 - 1 - Principles of Economics: Short-run Firm Equilibrium → P + QΔP/ΔQ = MC since wΔL/ΔQ = MC → MR = MC for all firms since P + QΔP/ΔQ = 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 3 2 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 firm’s Total Revenue function is TR = 1000q – 2q . 3 2 2 TC = q - 59q +1315q +2000; TR = 1000q - 2q 60 $000 Max (TR - TC) => Max Profit 50 TR 40 Slope TR = Slope TC => MR = MC TC 30 20 10 0 0 10 20 30 q* 40 50 Quantity Max Profit 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. 2 3 2 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 Max Profit Quantity Comparison Marginal Revenue and Marginal Cost shows the maximum profit output more clearly than comparison of Total Revenue and Total Cost. 2 Marginal Revenue = 1000 – 4q Marginal Cost = 3q - 118q + 1315 - 3 - Principles of Economics: Short-run Firm Equilibrium MC = 3q 2 - 118q +1315; MR = 1000 - 4q 3500 $s 3000 MC 2500 2000 1500 1000 MR 500 0 0 10 20 30 q* 40 50 Max Profit Quantity Maximum Profit => MR = MC => q = 35 NOTE: Marginal Revenue > Marginal Cost => Revenue from the last unit produced is greater than cost of the last unit produced => Produce this unit and increase production Marginal Revenue < Marginal Cost => Revenue from the last unit produced is less than the cost of the last unit produced => Do not produce this unit and decrease production Marginal Revenue = Marginal Cost => Profit Maximization => Short-run equilibrium for the firm Most firms would not consciously apply the Marginal Revenue = Marginal Cost rule for Maximum Profit but they would follow it in practice. SHORT-RUN COMPETITIVE EQUILIBRIUM (Profit Maximization): MC = MR - 4 - Principles of Economics: Short-run Firm Equilibrium Recall that competition implies price-taking. This means that a firm chooses the quantity that maximizes profit for a given price. Competition in an industry usually implies: 1. Many sellers (firms). (This limits the ability of any firm to influence price) 2. Homogeneous (identical) products. (This allows firms to compete with each other) Firms (such as beer producers) try to distinguish their products to avoid competition. 3. No barriers to entry or exit. (This prevents firms from raising prices above competitive prices) Definition: Perfect Competition is competition where all firms in an industry have identical cost functions. The assumption that all firms have identical cost functions virtually ensures competition since no firm has a cost advantage to influence price. It doesn’t always apply in the real world (though more often than is immediately apparent as we will see) so economists have another less restricted definition of competition Definition: Pure Competition occurs where firms have different cost functions in an industry but there are no barriers to entry and price taking occurs. We will assume perfect competition in this course for simplicity. Price-taking implies that Marginal Revenue for the firm equals the Price of the commodity. Competitive Firm Equilibrium => P = MC Since competition (‘price taking’) => P = MR and equilibrium => MR = MC Short-run Profit Maximization for a Competitive Firm: Given Price (P), the firm chooses the quantity supplied to maximize profit - 5 - Principles of Economics: Short-run Firm Equilibrium => P = MC (since P = MR and MR = MC) => Economic Profit = P*q – Total Cost or = P*q – (Average Cost)q = (P – AC)q (P –C)q is most convenient for graphical analysis while P*q – Total Cost is usually most convenient for numerical analysis. We now analyze firm response to various prices: P > AC, P = AC, AVC < P < AC, and P < AVC to clarify identification of competitive firm equilibrium quantity supplied and economic profit or loss. This review will also indicate the Supply function of the competitive firm. E.g. VC = q + 5q + 400 FC = 500 MC = 2q + 5 Quantity VC TC MC AVC AFC AC Economic Profit 0 400 900 -900 5 450 950 15 90 100 190 -875 10 550 1050 25 55 50 105 -800 15 700 1200 35 46.66 33.33 80 -675 20 900 1400 45 45 25 70 -500 25 1150 1650 55 46 20 66 -275 30 1450 1950 65 48.33 16.66 65 0 35 1800 2300 75 50.76 14.7 65.47 325 40 2200 2700 85 55 12.5 67.5 700 45 2650 3150 95 58.88 11.11 70 1125 50 3150 3650 105 63 10 73 1600 1. P > AC => Economic Profit 2 e.g. P = 85 => q = 40 at P = MC => Economic Profit = 85*40 – (40 + 5*40 + 900) = +700 - 6 - Principles of Economics: Short-run Firm Equilibrium VC = q + 5q + 400, FC = 500, MC = 2q + 5 140 120 MC 100 85 Po 80 Economic Profit AC 60 AVC 40 20 0 0 10 20 30 40 50 Quantity 2. P = AC (‘Break even output) P = AC => MC = AC since the firm produces at P = MC => P = min AC since MC = AC at minimum AC => 0 Economic Profit since P = AC This price is called the Breakeven Price since the firm makes a Normal Profit E.g. P = 65 (see calculation in previous lecture) => q = 30 from P = MC => Economic Profit = 85*30 – (30 + 5*30 + 900) = 0 VC = q + 5q + 400, FC = 500, MC = 2q + 5 140 120 MC 100 80 AC 65 60 Po AVC 40 20 0 0 10 20 30 40 50 Quantity 3. AVC < P < AC - 7 - Principles of Economics: Short-run Firm Equilibrium If Price is less than Average Cost, the firm makes an Economic Loss since price is insufficient for the firm to make a Normal Profit. The firm will still produce, however, at P = MC, provided that Price is greater than minimum Average Variable Cost. The reasoning is that the firm’s other option of shutting down and producing nothing results in a loss equal to the amount of the Fixed Cost, which is bigger than the Economic Loss if Price is greater than minimum Average Variable Cost. The firm is making an accounting profit on operating costs (variable costs) so that there is some return to capital; the problem is that the return gives less than the average rate of profit. E.g. P = $55 2 => q = 25 from 55 = 2q + 5 => Economic Profit = 55*25 – (25 + 5*25 + 900) = -275 The firm does produce 25 for an economic loss of 275 because shutting down would entail no output and an economic loss equal to the Fixed Cost of 500. 2 VC = q + 5q + 400, FC = 500, MC = 2q + 5 140 120