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Managerial Economics Profit Max for a Competitive Firm

Managerial Economics Profit Max for a Competitive Firm. Suppose that the manager of a firm operating in a competitive market has estimated the firm’s average variable cost function to be AVC = 10  0.03Q + 0.00005Q 2 Total fixed cost is $600.

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Managerial Economics Profit Max for a Competitive Firm

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  1. Managerial Economics Profit Max for a Competitive Firm Suppose that the manager of a firm operating in a competitive market has estimated the firm’s average variable cost function to be AVC = 10  0.03Q + 0.00005Q2 Total fixed cost is $600. What is the corresponding marginal cost function? At what output is AVC at its minimum? What is the minimum value for AVC? If the forecasted price of the firm’s output is $10 per unit: d. How much output will the firm produce in the short run? How much profit ( loss) will the firm earn? If the forecasted price is $5 per unit: f. How much output will the firm produce in the short run? g. How much profit ( loss) will the firm earn? Dr. C. Chen

  2. Managerial Economics Profit Max for a Competitive Firm Suppose that the manager of a firm operating in a competitive market has estimated the firm’s average variable cost function to be AVC = 10  0.03Q + 0.00005Q2 Total fixed cost is $600. a. What is the corresponding marginal cost function? The relationship b/w AVC and SMC can be summarized as AVC = a + bQ + cQ2 SMC = a + 2bQ + 3cQ2 So, SMC = 10 0.06Q + 0.00015Q2 At what output is AVC at its minimum? The minimum of AVC occurs at Q = b/2c =  ( 0.03)/2(0.00005) = 300 What is the minimum value for AVC? The minimum AVC = 10  0.03(300) + 0.00005(300)2 = $5.5 Dr. C. Chen

  3. Managerial Economics Profit Max for a Competitive Firm Suppose that the manager of a firm operating in a competitive market has estimated the firm’s average variable cost function to be AVC = 10  0.03Q + 0.00005Q2 Total fixed cost is $600. If the forecasted price of the firm’s output is $10 per unit: How much output will the firm produce in the short run? Because the price $10 is higher than the minimum AVC (Answer c), the firm will continue to operate. The profit-maximizing output occurs when P=MC. Given the answer in a for MC = 10 0.06Q + 0.00015Q2 =10 = P , we solve the quadratic function as 0.00015Q2 0.06Q = 0; 0.00015Q(Q  400) = 0 Q* = 400 (0 will not be the solution) How much profit (loss) will the firm earn? At Q*=400, TR = P*Q=$10*400 = $4,000; TC = TVC + TFC = AVC*Q + TFC = $[10  0.03(400) + 0.00005(400)2]*400 + $600 = $3,000 The profit = TR  TC = $4,000  $3,000 = $1,000 Dr. C. Chen

  4. Managerial Economics Profit Max for a Competitive Firm Suppose that the manager of a firm operating in a competitive market has estimated the firm’s average variable cost function to be AVC = 10  0.03Q + 0.00005Q2 Total fixed cost is $600. If the forecasted price is $5 per unit: How much output will the firm produce in the short run? Because the price, $5, is less than the minimum AVC, $5.5 (derived in question c), the firm will shutdown in the short run. The output Q* = 0. How much profit (loss) will the firm earn? Once shutting down, the firm still needs to pay for the fixed costs, $600, in the short run. So, the largest possible loss in the short run is the fixed cost. Dr. C. Chen

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