Unformatted text preview: Economics 3010
Fall 2009 Professor Daniel Benjamin
Cornell University Problem Set 4 This problem set is due in section on Friday, October 2. Please collect your answers into a stapled packet, and write your own name and your TA’s name on the front of each packet, as well as your netID and the time of the section you usually attend. 0. (Aplia) Please do the assigned problems on the Aplia website. These problems are due at 11:45pm on Thursday, October 1. 1. (Slutsky equation: The law of demand) In his book, The Armchair Economist: Economics & Everyday Life (1993, pp.6‐7), the economist Steven Landsburg writes: Will the invention of a better birth control technique reduce the number of unwanted pregnancies? Not necessarily – the invention reduces the ‘price’ of sexual intercourse (unwanted pregnancies being a component of that price) and thereby induces people to engage in more of it. The percentage of sexual encounters that lead to pregnancy goes down, the number of sexual encounters goes up, and the number of unwanted pregnancies can go either down or up. Illustrate in a budget constraint / indifference curve diagram an individual’s tradeoff between number of sexual encounters (measured in units of quality, where higher risk of unwanted pregnancy represents a lower quality encounter) and all other uses of time. Show what happens to the budget constraint when the price of sexual encounters falls. What will happen to the individual’s consumption of sexual encounters if the number of sexual encounters is a normal good? Can we make a confident prediction if it is an inferior good? Which assumption seems more reasonable to you? What data could you look at to test whether the number of sexual encounters is normal or inferior (for a typical individual)? 2. (Buying and Selling: An advantage of owning your house) (a) First we’ll consider the case of someone who rents her home. Write down her budget constraint for housing services versus all other goods. (This is the standard budget constraint you are used to.) Show in a diagram what happens when the price of housing services goes up. Use the principle of revealed preference to argue that if the price of housing services goes up (i.e., her rent goes up), then she is worse off, assuming that she was consuming a positive amount of housing services before the price change. (b) Now suppose that she owns her home instead of renting it, and her endowment is her currently optimal mix of housing services and all other goods. Write down her budget constraint, and illustrate it in a diagram. Draw an indifference curve that is tangent to her budget constraint at her endowment. 1 (c) In the diagram, illustrate how the budget line rotates when the price of housing services goes up. How will she change her consumption bundle? Is she better off or worse off? Now illustrate how the budget line rotates when the price of housing services goes down. How will she change her consumption bundle? Is she better off or worse off? (d) How is it possible that the consumer is better off, regardless of whether the price of housing services goes up or down?! 3. (Consumer’s surplus: The case of Cobb‐Douglas utility) [ You can find solutions to some parts of this question in the appendix to ch. 14, and other parts closely follow an example in ch. 14.8. Feel free to use what you learn from those parts of the textbook in writing up your answer, but try the problem first with the textbook closed, and make sure you write up solutions in your own words. ] (a) Consider a household’s choice between charitable giving (Good 1) and all other goods (Good 2). Suppose we observe that expenditure on charitable giving across households is a constant fraction α of household income and does not depend on the prices of other goods. Hence a household’s demand function is x1*(p1, p2, m) = αm/p1, where m is the household’s income, and p1 is the “price” of charitable giving (the number of dollars you have to contribute to the charity per dollar that gets transferred to poor people). Suppose the price p1 falls from p to q<p (perhaps because the charity becomes more efficient at converting contributions to charitable transfers or because the government increases the tax deduction on charitable giving). Explain why the increase in consumer’s surplus is ∫t[p,q] (am/ t) dt. Illustrate on a demand curve. Calculate the increase in consumer’s surplus in terms of p, q, a, and m. (b) Consumer’s surplus has the advantage that it can be calculated directly from the observed demand function, but it is only an approximate measure of welfare (except in the case of quasi‐linear utility, when it is an exact measure). However, you showed in the last problem set that Cobb‐Douglas preferences generate this demand function. So in this case, we can infer from the demand function that the underlying utility function is Cobb‐Douglas. We can use that fact to calculate exact measures of the change in welfare: equivalent variation and compensating variation. Assume that m = $100,000, a = 0.02, p = $1.50, and q = $1.30. What is the change in consumer’s surplus, equivalent variation, and compensating variation? Show that the change in consumer’s surplus is in between the equivalent variation and the compensating variation. 2 ...
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