325_PracticePS2_Soln - Department of Economics University...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Practice Problem Set 2 Suggested Solutions Professor Sanjay Chugh Spring 2011 1. Interaction of Consumption Tax and Wage Tax. One basic idea of President Bush’s economic advisers throughout his administration had been to move the U.S. further away from a system of investment taxes (which we will discuss later in the course) and more towards a system of consumption taxes . Discussion of a federal consumption tax, which would essentially be a national sales tax, has again emerged in recent policy discussions. Here, you will modify the basic consumption-leisure framework to include both a proportional wage tax (which we will now denote by n t , where, as before, 0 1 n t ) as well as a proportional consumption tax (which we will denote by c t , where 0 1 c t ). A proportional consumption tax means that for every dollar on the price tags of items the consumer buys, the consumer must pay (1 ) c t ² dollars. Throughout the following, suppose that economic policy has no effect on wages or prices (that is, the nominal wage W and the price of consumption P are constant throughout). a. Construct the budget constraint in this modified version of the consumption- leisure model. Briefly explain economically how this budget constraint differs from that in the standard consumption-leisure model we have studied in class. Solution: The representative agent’s net income from working is now given by (1 ) n Yt W n ³ ´´ , where n t is the labor tax rate and the other notation is the same as in Chapter 2. He spends all of this income on consumption, which now costs ) c Pt ´² dollars per unit (inclusive of the consumption tax). Using the fact that 168 nl ³ in the weekly model, equating the representative agent’s labor income with his expenditures on consumption gives us ) ) (168 ) cn c t W l ´² ´ ³ ´ ´ ³ . If we multiply out the right-hand-side of this expression and then move the term involving the labor tax rate to the left-hand-side we obtain ) ) 168 (1 ) n c t W l t W ´² ´²³ ´ ´ ´³ ´ . Then, solving this last expression for c , we arrive at
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2 168 (1 ) (1 ) ) ) nn cc tW cl tP ± ²± ² ³ ±³ ± . This last expression can now readily be graphed with consumption on the vertical axis and leisure on the horizontal axis. As in the standard model, the horizontal intercept is 168 l . However, the slope is now ) ) n c ² ± ² ³ ± . Clearly, however, if we set the consumption tax rate to zero, we recover the budget constraint in our standard consumption-leisure model – indeed, the model we studied in Chapter 2 is simply a special case of the model here. The reason the budget constraint differs here from the standard model is simple: the consumption tax is yet another tax for the consumer to take account of when making his choices about consumption and leisure.
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325_PracticePS2_Soln - Department of Economics University...

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