Econ_102A_PS6_Answer

Econ_102A_PS6_Answer - exactly that much. iii) How much...

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Problem Set 6 1. Suppose that the market demand curve is given by Q=100-P. Also, the firms’ technology is given by Q=f(K,L)=KL ½ . The rental rate on capital is $10/unit and the wage is $25. The firm utilizes 5 units of capital in the short run. The market structure is perfectly competitive. i) Write down the total cost function and total variable cost function. What are the fixed costs? TC = wL + rK = 25L + 50 but L=(Q^2)/25 TC=Q^2 + 50. Variable Costs = Q^2 Fixed Costs = capital expenditure = 50 ii) Derive the marginal cost function. If the price prevailing in the market is $50, how many units will the firm sell? How many firms are in the industry? MC= dTC/dQ = 2Q. If P=50, then the profit maximizing condition is P=MC or 50=2Q => Q=25 units supplied by each firm. But if P=50, total market demand is Q=100-P = 100-50 = 50 units total demanded in the market. Thus, if one firm produces 25 units and total market demand is 50 units, we will need 2 firms to supply a total of 50 units to the consumers demanding
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Unformatted text preview: exactly that much. iii) How much profit does each firm make? Profit = TR- TC Profit = P*Q [(Q^2)+50] P=50, Q=25 and substitute into above equation. iv) What is the value of the consumer and producer surpluses in this equilibrium? CS=(100-50)*(50)/2 = (50^2)/2 ; PS = (50)(50)/2 = (50^2)/2 2. Now suppose that the rest of the producers leave the market so that only one is left to monopolize the market. The market demand curve is the same as in #1. i) What is the marginal revenue function? MR=100-2Q ii) What how many units will the monopoly sell? What price will they charge? Set MR=MC 100-2Q=2Q Q=25. If Q=25, then P=100-Q=100-25=75. iii) How much profit will the monopoly make? What is the new consumer surplus? Profit = TR- TC Profit = P*Q [(Q^2)+50] P=75, Q=25 and substitute into above equation. CS=(100-75)*(25)/2 = (25^2)/2 iv) What is the deadweight loss due to monopolization? DWL= (75-50)(50-25)/2= (25^2)/2...
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Econ_102A_PS6_Answer - exactly that much. iii) How much...

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