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Final+Answer+Key - EEP 100 Spring 2010 Final Answers 1(9...

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EEP 100 Spring 2010 Final Answers May 14, 2010 1.(9 points) With the end of the Cold War the U.S. government decided to °downsize± the military. Along with a pink slip, the government o/ered ex-military personnel their choice of $8,000 a year for 30 years or a lump sum payment of $50,000 immediately. The lump-sum option was chosen by 92% of enlisted personnel and 51% of o¢ cers (Warner and Pleeter, 2001). Assuming that all these individuals expect to live at least 30 years, what is the break-even personal discount rate at which someone would be indi/erent between the two options? What can you conclude about the relative size of the personal discount rates of the enlisted personnel and of the o¢ cers? (Hint: You may treat 30 years as being essentially °forever.±) Answer: (a). Suppose the break-even personal discount rate is r*, then we have: 30 X t =1 8000 (1 + r ° ) t = 50000 Using the hint, we can write the left-hand-side as: 1 X t =1 8000 (1 + r ° ) t = 8000 1 X t =1 1 (1 + r ° ) t = 8000 1 r ° Therefore we have: 8000 1 r ° = 50000 ) r ° = 8000 50000 = 0 : 16 = 16% i.e. the break-even personal discount rate is 16%. (b). From the present value formula, we can see that one²s present value of the ³rst option will be smaller than $50,000 if one²s personal discount rate is greater than r*. Since the lump-sum option was chosen by 92% of enlisted personnel but only 51% of o¢ cers, therefore 92% of enlisted personnel and 51% of o¢ cers should have personal discount rates greater than 16%. 1
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2.(9 points) A monopoly has a marginal cost of zero and faces two groups of consumers. At ³rst, the monopoly could not prevent resales between groups, so it maximized its pro³t by charging everyone the same price, p = $5. No one from the ³rst group chose to purchase. Now the monopoly can prevent resales, so it decides to price discriminate. Will total output expand? Why or why not? What happens to pro³t and consumer surplus? Answer: When the monopoly could not prevent resales, since no one from the ³rst group (denoted by group 1 afterwards) chose to purchase at p = $5, then there is no resales from group 2 to group 1 because the price is higher than the choke price of the demand (or the greatest willingness-to-pay) of group 1. Now when the monopoly can prevent resales, it will use multi-market price discrimination. Since the marginal cost is zero, then the equilibrium price and quantity of group 2 won²t change after the price discrimination. Since now there will be another price (lower than $5) for group 1, the new equilibrium quantity of group 1 will be positive. Therefore, the total output will expand after the price discrimination. More- over, after the price discrimination, since the cost curves, demand functions, or equilibrium price and quantity won²t change, and the new equilibrium quantity of group 1 will be positive, therefore the monopoly²s pro³t will increase and consumer surplus will also increase due to the additional quantity purchased by group 1.
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