negative.
4. In the case described in the preceding question, would the government be paying out more or less than it received in tax revenues? 8.4. They are receiving tx’ in revenues and paying out tx, so they are losing money.
5. In this case would the consumers be better o? or worse o? if the tax with rebate based on original consumption were in e?ect?
8.5. Since their old consumption is a?ordable, the consumers would have to be at least as well-o?. This happens because the government is giving them back more money than they are losing due to the higher price of gasoline.
9 Buying and Selling
1. If a consumer’s net demands are (5,?3) and her endowment is (4,4), what are her gross demands? 9.1. Her gross demands are (9,1).
2. The prices are (p1,p2) = (2 ,3), and the consumer is currently consuming (x1,x2) = (4 ,4). There is a perfect market for the two goods in which they can be bought and sold costlessly. Will the consumer necessarily prefer consuming the bundle (y1,y2) = (3 ,5)? Will she
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necessarily prefer having the bundle (y1,y2)?
9.2. The bundle (y1,y2) = (3 ,5) costs more than the bundle (4,4) at the current prices. The consumer will not necessarily prefer consuming this bundle, but would certainly prefer to own it, since she could sell it and purchase a bundle that she would prefer.
3. The prices are (p1,p2) = (2 ,3), and the consumer is currently consuming (x1,x2) = (4 ,4). Now the prices change to (q1,q2) = (2 ,4). Could the consumer be better o? under these new prices?
9.3. Sure. It depends on whether she was a net buyer or a net seller of the good that became more expensive.
4. The U.S. currently imports about half of the petroleum that it uses. The rest of its needs are met by domestic production. Could the price of oil rise so much that the U.S. would be made better o?? 9.4. Yes, but only if the U.S. switched to being a net exporter of oil.
5. Suppose that by some miracle the number of hours in the day increased from 24 to 30 hours (with luck this would happen shortly before exam week). How would this a?ect the budget constraint? 9.5. The new budget line would shift outward and remain parallel to the old one, since the increase in the number of hours in the day is a pure
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endowment e?ect.
6. If leisure is an inferior good, what can you say about the slope of the labor supply curve?
9.6. The slope will be positive.
10 Intertemporal Choice
1. How much is $1 million to be delivered 20 years in the future worth today if the interest rate is 20 percent?
10.1. According to Table 10.1, $1 20 years from now is worth 3 cents today at a 20 percent interest rate. Thus $1 million is worth .03×1,000,000 = $30,000 today.
2. As the interest rate rises, does the intertemporal budget constraint be- come steeper or ?atter?
10.2. The slope of the intertemporal budget constraint is equal to ?(1+r). Thus as r increases the slope becomes more negative (steeper).
3. Would the assumption that goods are perfect substitutes be valid in a study of intertemporal food purchases?
10.3. If goods are perfect substitutes, then consumers will only purchase the cheaper good. In the case of intertemporal food purchases, this implies that consumers only buy food in one period, which may not be
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very realistic.
4. A consumer, who is initially a lender, remains a lender even after a decline in interest rates. Is this consumer better o? or worse o? after the change in interest rates? If the consumer becomes a borrower after the change is he better o? or worse o??
10.4. In order to remain a lender after the change in interest rates, the consumer must be choosing a point that he could have chosen under the old interest rates, but decided not to. Thus the consumer must be worse o?. If the consumer becomes a borrower after the change, then he is choosing a previously unavailable point that cannot be compared to the initial point (since the initial point is no longer available under the new budget constraint), and therefore the change in the consumer’s welfare is unknown.
5. What is the present value of $100 one year from now if the interest rate is 10%? What is the present value if the interest rate is 5%? 10.5. At an interest rate of 10%, the present value of $100 is $90.91. At a rate of 5% the present value is $95.24.
11 Asset Markets
1. Suppose asset A can be sold for $11 next period. If assets similar to A are paying a rate of return of 10%, what must be asset A’s current
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price?
11.1. Asset A must be selling for 11/(1 + 0.10) = $10.
2. A house, which you could rent for $10,000 a year and sell for $110,000 a year from now, can be purchased for $100,000. What is the rate of return on this house?
11.2. The rate of return is equal to (10,000 + 10,000)/100,000 = 20%.
3. The payments of certain types of bonds (e.g., municipal bonds) are not taxable. If similar taxable bonds are paying 10% and everyone faces a marginal tax rate of 40%, what rate of return must the nontaxable bonds pay?
11.3. We know that the rate of return on the nontaxable bonds, r, must be such that (1?t)rt = r, therefore (1?0.40)*0.10 =0 .06 = r.
4. Suppose that a scarce resource, facing a constant demand, will be exhausted in 10 years. If an alternative resource will be available at a price of $40 and if the interest rate is 10%, what must the price of the scarce resource be today?
11.4. The price today must be 40/(1 +0 .10)^10 = $15.42.
12 Uncertainty
1. How can one reach the consumption points to the left of the
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