Midterm2prep_ans - Chapter 11 Perfectly Competitive Market...

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Chapter 11 Perfectly Competitive Market. Question 2: Setting price P = 10 equal to marginal cost (SMC) = 2 + 4Q, solve for quantity: 10 = 2 + 4Q, or Q = 2 units. The fixed cost that leads to zero economic profit is calculated by solving = PQ VC - FC = 0 or (10)(2) 6*2 - FC = 0 for FC = $8. Question 3: Short run supply = MCi . We have MC i = 4 + Q i , and hence Q i = MC i 4. Q i = Q = MC i 4000, or Q = 1000 MC 4000. For profit maximization, MC = P, and so Q = 1000 P 4000, which means that industry supply is given by P = 4 + 0.001Q. Hence short run equilibrium Q occurs where 4 + 0.001Q = 10 0.002Q. With 0.003Q = 6, we have Q = 2000 units, and P = $6/unit. 10 6 4 2000 S D Q P Consumer surplus Producer surplus Consumer surplus = area of upper triangle = (10 6)(2000)/2 = $4000. Producer surplus = area of lower triangle = (6 4)(2000)/2 = $2000. Total loss of surplus = $6000. Question 4: In the long run, if the aflatoxin problem persists, we would expect both demand and supply to become more elastic, as consumers found substitutes for peanut butter and peanut farmers shifted into other crops. Hence the long run loss of both consumer and producer surplus should be lower. Question 5: Since P = SMC > AVC, we know that the firm should continue at its current level of output (call it Q 0 ) in the short run. Is the firm making economic profits? Since LMC = 12 > min LAC = 10, we know that the firm is producing to the right of its long run cost-minimizing level, that LAC is rising, and therefore that 10 < LAC(Q 0 ) < 12. Since SMC ≠ LMC, LAC(Q 0 ) < SAC(Q 0 ), and hence P = MC < SAC. Therefore the firm is incurring losses in the short run, and in the long run it should shift to a smaller size of plant (in fact, the size that minimizes LAC at Q*), as shown in the following diagram.
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12 LAC LMC SAC SMC AVC 10 8 $/Q Q Q* Q 0 Question 6: Long-run equilibrium price for this industry will occur at the minimum value of LAC. LAC = LTC/Q = Q 2 10Q + 36. Minimum LAC occurs with dLAC/dQ = 2Q 10 = 0, which solves for Q = 5 units per firm. At Q = 5, LAC = 25 50 + 36 = $11/unit. Question 12: a) MC = ∆VC/∆Q = w∆L/∆Q = w/MP L . Similarly, AVC = wL/Q = w/AP L . So when MP L = AP L , it follows that MC = AVC. b) Since the firm is perfectly competitive, its output price is equal to marginal cost, which here is equal to AVC. Hence all of the firm's revenue is paid out to workers, leaving nothing to cover its fixed costs. If the firm stays open in the short run, its loss will be equal to its fixed capital costs of $40/day, which is the same loss it would suffer if it were to shut down. So the firm will be indifferent between shutting down and remaining open in the short run.
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