Econ402_Solutions_Set4

# Econ402_Solutions_Set4 - Economics 402 Winter 2009 Problem...

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Economics 402, Winter 2009 Problem Set 4 (60 Raw Points) Suggested Solutions 1 Labor Supply (20 Raw Points) The Nobel Prize winning economist, Ed Prescott, published in 2004 (in the Minneapolis Federal Reserve Bank Quarterly Review, 28(1), pp. 2-13) the following table: Period Country Labor Supply Tax Rates 1993-1996 Germany 19.3 0.59 France 17.5 0.59 Italy 16.5 0.64 USA 25.9 0.40 Labor supply is measured in weekly hours worked per prime aged person. Also, notice that tax rates are not lump sum taxes, but rather (more realistically) income tax rates, so that for every unit of real wage, w , the households on net receive (1 - τ ) w in their pockets. 1) In the consumption-leisure choice diagram, can you explain the difference between European and US labor supply through differences in the income tax rates? (10) In this problem, I will assume that non-labor income, π , and lump-sum taxes, T are both zero 1 . Adding income taxes, τ , and initially taking income taxes to be fixed at τ 1 , the static consumption-leisure utility maximization problem becomes: max c,l U ( c, l ) s.t. l + N s = h c = (1 - τ 1 ) wN s We can reduce the two constraints to one through plugging the first constraint into the second through N s , yielding the single equation budget constraint c = (1 - τ 1 ) wh - (1 - τ 1 ) wl From the above equation, we can see that the slope of the budget line is - (1 - τ 1 ) w , the c -axis intercept is (1 - τ ) wh , and the l -axis intercept is h . Finally, the optimal consumption bundle lies at the point where the indifference curve, I 1 is tangent (assuming an interior solution) to the budget line, as shown in Figure 1. Now suppose that τ increases to τ 2 > τ 1 . The tax change lowers the c -axis intercept from (1 - τ 1 ) wh to (1 - τ 2 ) wh and lowers the slope from - (1 - τ 1 ) to - (1 - τ 2 ), effectively rotating 2 the budget line in towards the origin. The new tangency point lies on a lower indifference curve, I 2 , and consumption is unambiguously lower. Whether leisure increases, decreases, or remains the same, however, depends on the households relative preferences towards consumption and leisure. 1 This assumption will make no difference on the qualitative results. 2 Note that this is not a shift in the budget line since the l -axis intercept does not change. 1

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Figure 1: The Optimal Consumption-Leisure Choice The amibguity lies within the competing income and subsitution effects. As the hourly take home wage decreases in the tax rate, the return to working an extra hour (i.e. the opportunity cost of leisure) is lower; therefore, the household has incentive to substitute out of work (and extra consumption) and into leisure. However, as the tax rate increases, the households net income falls, leaving it less wealthy, and giving it incentive to work more to try and offset some of the decrease in wealth. Whether leisure increases or decreases depends on whether the substituion or income effect dominates.
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