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problem+set+6+solutions-1 - Econ 1 Fall 2010 University of...

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Econ 1, Fall 2010 Problem Set 6 Solutions University of California, Berkeley Page 1 of 9 Problem Set #6 Solutions 1. Recall the rule of 72 (see the solutions for Problem Set 1), and recall that sustainable annual consumption spending per capita in the United States today is about $30,000 a year. In those scenarios in which global warming does not fully destabilize the climate or world politics, in which technological change continues at its present pace, in which the world population peaks at 10 billion around 2050, and in which we avoid blowing all of ourselves up with nuclear weapons, we are looking forward to a per capita GDP and consumption growth rate in the rich regions of the world of about 1.8% per year for the foreseeable future. Suppose that these scenarios turn out to be true: a. What will be the level of consumption per capita in the United States in 2090? g2784g2779 g2778.g2785 =g2781g2777 _ Thus consumption spending per capita per year in the United States will be expected to double in 40 years. In 80 years it will double twice, so under these assumptions it will be: g2779 g2779 ∙($g2780g2777,g2777g2777g2777) = $120,000/year b. What will be the level of consumption per capita in the United States in 2210? Since g2779g2777g2777 g2781g2777 = g2782 , over 200 years consumption spending per capita per year in the United States will be expected to double five times, so in 2210 its level will be expected to be: g2779 g2782 ∙($g2780g2777,g2777g2777g2777) = $960,000/year c. What do you think life would be like in a society as rich as this scenario suggests that the United States will be by 2210? Your guess is probably as good as anyone’s. This is indeed the realm of pure speculation. Could anyone from 1810 have begun to envision the world of 2010? It might be expected that a great many members of society would be willing to trade income for greater amounts of leisure time, implying that recreation, tourism, and entertainment would be much more important parts of the economy. More pessimistically, it may be that a large share of income will need to be devoted to mitigating the effects of climate change.
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Econ 1, Fall 2010 Problem Set 6 Solutions University of California, Berkeley Page 2 of 9 2. Consider a monopoly seller of tickets to classic Japanese movies. The cost of showing the movie to an extra customer is zero. The quantity demanded for tickets is given by: Q D = 1500 - 100 P , where Q D is the number of tickets that will sell at price P and where P is given in dollars. Note that Q D = 1500 – 100 P P = 15 – 0.01 Q D . a. What is the price that the monopolist should charge if it wants to maximize profits? For any firm profit is maximized where marginal revenue equals marginal cost: g2169g2174=g2169g2159 . Total revenue is price times quantity sold: g2176g2174=g2172∙g2173 g2160 =g3435g2778g2782 g2777 . g2777g2778g2173 g2160 g3439∙g2173 g2160 =g2778g2782g2173 g2160 −g2777.g2777g2778g2173 g2160 g2779 Marginal revenue is the derivative of total revenue: g2169g2174= g2186g2176g2174 g2186g2173 g2160 =g2778g2782−g2777.g2777g2779g2173 g2160 Marginal revenue equals marginal cost (zero in this case) where: g2778g2782−g2777.g2777g2779g2173 g2160 =g2777 g2173 g2160 =g2784g2782g2777 The profit-maximizing quantity is 750. Given this, the price the monopolist will charge is given by the demand curve: g2172=g2778g2782 g2777 .
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