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# ECON201PSet4Answers - WELLESLEY COLLEGE DEPARTMENT OF...

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WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS ECONOMICS 201-03 JOHNSON Answers to Problem Set #4 I. P&R, page 550, #2: This problem was interpreted two different ways by you, so I'm offering answers to "both" ways. Method #1: The government's program guarantees you \$5000 worth of income whether you work or not. One might then assume that working for anything less than \$10,000 pre-tax (which would be less than \$5000 after-tat' given the 50% tax rate in the problem) is silly because the government would guarantee you \$5000 if you stayed at home all day. So, for example, if your after-tax pay is \$2000, the government would give you \$3000 to guarantee you the \$5000. BUT, if you also received the full \$5000 if you didn't work for \$2000, you'd have MORE leisure for the same amount of income, clearly a BETTER situation for you in terms of utility. Thus, the budget constraint would have a flat part, reflecting the fact that "work" up to the point of \$5000 after-tax income would not make you better off. See graph below. Only when your after-tax income rises above \$5000 would the budget constraint assume its "usual" shape. Note if you were to draw indifference curves in the diagram below, the individual would never be at the inner "kink" in this case, meaning that labor supply almost assuredly falls in this case, relative to the case in which the government does not offer this guarantee. 2-Lt

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Method #2: The government guarantee amounts to giving everyone \$5000 on top of what they would earn by working. This is probably not in the spirit of the program, but we can consider it as a possibility anyway. In the diagram below, then, the budget constraint shifts out (up) by \$5000 worth of AOG's, and the kink here relates to the point at which the tax rate changes from 50% to something different. We've assumed that the tax rate falls (just because income tax rates for monies earned at the lower end of the income scale are not as high as 50%), but you could also assume that tax rate for earned income above \$10,000 is higher than 50% -- making your diagram look a bit different from ours below. We've also made the same assumption in the diagram above as well. Note the parallel nature of the shift here for the person working for earned income between 0 and \$5000 after- tax. That pure income effect along that portion of the budget constraint would also predict a rise in leisure, ceteris paribus, and therefore again a fall in labor supply.
2. Here, we can appeal to simple consumer theory to explain why, in the face of rising real wages in both Europe and the U.S. over the past 30-40 years, Europeans have responded by working less and American workers have responded by not altering their hours worked much at all. With a bit of a refresher from our labor/leisure model, let's review both the S.E. and the I.E. of a rising real wage according to economists' models of consumption vs. leisure and preferences between the two: Substitution Effect: An increase in the real wage RAISES the opportunity cost price of leisure and lowers the relative price of consumption. Thus, the S.E.

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