9. Buying and Selling - Solutions

9. Buying and Selling - Solutions - Chapter 9 NAME Buying...

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Chapter 9 NAME Buying and Selling Introduction. In previous chapters, we studied the behavior of con- sumers who start out without owning any goods, but who had some money with which to buy goods. In this chapter, the consumer has an initial en- dowment , which is the bundle of goods the consumer owns before any trades are made. A consumer can trade away from his initial endowment by selling one good and buying the other. The techniques that you have already learned will serve you well here. To Fnd out how much a consumer demands at given prices, you Fnd his budget line and then Fnd a point of tangency between his budget line and an indi±erence curve. To determine a budget line for a consumer who is trading from an initial endowment and who has no source of income other than his initial endowment, notice two things. ²irst, the initial endowment must lie on the consumer’s budget line .Th i si st ruebecau se , no matter what the prices are, the consumer can always a±ord his initial endowment. Second, if the prices are p 1 and p 2 , the slope of the budget line must be p 1 /p 2 . This is true, since for every unit of good 1 the consumer gives up, he can get exactly p 1 /p 2 units of good 2. Therefore if you know the prices and you know the consumer’s initial endowment, then you can always write an equation for the consumer’s budget line. After all, if you know one point on a line and you know its slope, you can either draw the line or write down its equation. Once you have the budget equation, you can Fnd the bundle the consumer chooses, using the same methods you learned in Chapter 5. Example: A peasant consumes only rice and Fsh. He grows some rice and some Fsh, but not necessarily in the same proportion in which he wants to consume them. Suppose that if he makes no trades, he will have 20 units of rice and 5 units of Fsh. The price of rice is 1 yuan per unit, and the price of Fsh is 2 yuan per unit. The value of the peasant’s endowment is (1 × 20) + (2 × 5) = 30. Therefore the peasant can consume any bundle ( R, F ) such that (1 × R )+(2 × F ) = 30. Perhaps the most interesting application of trading from an initial endowment is the theory of labor supply. To study labor supply, we consider the behavior of a consumer who is choosing between leisure and other goods. The only thing that is at all new or “tricky” is Fnding the appropriate budget constraint for the problem at hand. To study labor supply, we think of the consumer as having an initial endowment of leisure, some of which he may trade away for goods. In most applications we set the price of “other goods” at 1. The wage rate is the price of leisure. The role that is played by income in the ordinary consumer-good model is now played by “full income.” A worker’s full income is the income she would have if she chose to take no leisure.
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112 BUYING AND SELLING (Ch. 9) Example: Sherwin has 18 hours a day which he divides between labor and leisure. He can work as many hours a day as he wishes for a wage of $5 per hour. He also receives a pension that gives him $10 a day whether he
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9. Buying and Selling - Solutions - Chapter 9 NAME Buying...

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