FinalExam - ANUMEHA YADAV CRP 512 FINAL EXAM 11 December...

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ANUMEHA YADAV CRP 512 FINAL EXAM 11 December 2007 1. Giant Products, Inc., is a monopolist whose marginal cost of production function is given by P = 10 + 2Q. Demand for the company’s products is Q = 200-2P. A. What price will the monopolist charge? B. What profits will the monopolist earn? C. What will the consumer surplus and the deadweight loss be? D. How will the monopolist’s price and profits change if a tax of $15 per unit is imposed. E. What is the deadweight burden of the tax. Solution: A. Given marginal cost P = 10 + 2Q And demand function Q = 200 – 2P Then inverse demand will P = 100 - .5Q The marginal revenue function has the same intercept as the inverse demand function but is twice as steep, thus MR = 100 – Q To find the monopolist’s profit maximizing level of output, we set MR =MC Thus 100 – Q = 10+ 2Q Or 3Q = 90 Or Q = 30 Thus this is the profit maximizing quantity And substituting Q=30 in the demand function, P = 100 - .5 * 30 Or P = 85 Thus the monopolist will charge $85.
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B. The profit she will make will be [85 – (10+2Q] * 30 = [85 – (10+2*30)] *30 = (85-70)*30 = 15*30 = 450 Thus the monopolist will make a profit of $450. C. Here the consumer surplus when P = 85 and Q = 30 will be the area of the upper shaded triangle = ½ * 30 *15 = 225 Thus consumer surplus will be $225. To calculate the deadweight loss, We will set P = marginal cost Here marginal cost is P =10+2Q = 10 + 2*30 = $70 Substituting this in the original demand function, Q = 200 – 2*70 = 200- 140 = 60 Then deadweight loss will be the area of the lower shaded triangle whose base is between 30 and 60 on the x axis as shown in the figure DWL = ½ * 15*30 = 225. Deadweight loss will be $225. D. Given marginal cost is P =10+2Q = 10 + 2*30 = $70 With a tax of $15, the marginal cost becomes $85. Setting MC = MR, 85 = 100 – Q Or Q = 15 Plugging this into the inverse demand function, P= 100 - .5*15 = 92.5 Thus after the tax, the monopolist will charge $92.5.
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Profit will be [92.5 – marginal cost] * 15 = [92.5 – 85)]*15 = 7.5*15 = 112.5 Profit will be $ 112.5 after the tax. E . To calculate the deadweight burden of the tax we need to calculate how the deadweight loss changes after the tax is imposed. To calculate the DWL after the tax, we will set P = 85 (70+15) in the demand function. Then Q = 200 -2P = 200 – 2 *85 = 30 Then base of the triangle that shows the DWL = 30-15 = 15 And height of this triangle = 92.5 – 85 = 7.5 Then area = ½ *15*7.5 = 56.25 Thus after the tax is imposed the DWL will be $56.25.
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