= For the purpose of this question you can assume NO population growth NOR technology growth...
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= For the purpose of this question you can assume NO population growth NOR technology growth (namely, you should solve the question with n = 0 and x = 0). Assume that Lo 1 and A0 = 1. Consider a version of the Solow model with a Government, which can be either a Good or Bad government. The law of motion for aggregate capital in the Solow model is given by K+1 = (1-8)K++ It, where I, is total investment in this economy. Private investment is: I = SYD where YP is disposable income, given by: YP = Y-G. Assume that G = TY, with r (0, 1) is a parameter that captures how much the government extracts resources from private households. The goal of this question is to show that Government expenditures can be good or bad for GDP, depending on their uses. a. (5 points, easy) Provide an expression for Investment I, only as a function of total income Y, (as opposed to YP) (hint: replace YP in the private investment equation). Replace investment in the law of motion for capital and find that K+1 b. (10 points, moderate) For this question assume that (18) K+s (Y-G). Y = KL-a Use your equation for investment to write the law of motion for capital per worker obtained from the previous equation. Assume that all the proceeds from G are spent in corrupt activities, like paying for the yachts of government cronies and their friends. Find an expression for steady state GDP. Argue that increases in 7 act like reductions in the economy's savings rate. What happens in governments with a lot of corruption, where r is almost one? c. (10 points, easy) Now suppose we have a good government and that G, is invested in good uses. In particular, assume that the production of goods is now boosted by government spending. You can think of this spending as infrastructure that improves productivity (roads, ports, etc). Assume that the production function is now: YG KL(-a) The idea is that 1-y is the parameter that governs the decreasing returns to scale to government expenditures on GDP, as if it where an input like capital or labor. Substitute G = TY, into the equation above. Show that GDP can be re-written as: Y =KL(-a) d. (10 points, harder) Using the steps you've learned in class to obtain the steady-state in the standard Solow model, find steady state output in this version. Assume that y=0.5. How does the steady state level of capital and output depend on 7? Compare 7 = 0, 7 = 0.5, and 7=1. When is GDP the highest? e.(5 points, moderate) What do you learn from this exercise? When are governments bad for GDP? And which are the best governments? Is 7 = 1 a good idea, even though the government's resources are put to good use? = For the purpose of this question you can assume NO population growth NOR technology growth (namely, you should solve the question with n = 0 and x = 0). Assume that Lo 1 and A0 = 1. Consider a version of the Solow model with a Government, which can be either a Good or Bad government. The law of motion for aggregate capital in the Solow model is given by K+1 = (1-8)K++ It, where I, is total investment in this economy. Private investment is: I = SYD where YP is disposable income, given by: YP = Y-G. Assume that G = TY, with r (0, 1) is a parameter that captures how much the government extracts resources from private households. The goal of this question is to show that Government expenditures can be good or bad for GDP, depending on their uses. a. (5 points, easy) Provide an expression for Investment I, only as a function of total income Y, (as opposed to YP) (hint: replace YP in the private investment equation). Replace investment in the law of motion for capital and find that K+1 b. (10 points, moderate) For this question assume that (18) K+s (Y-G). Y = KL-a Use your equation for investment to write the law of motion for capital per worker obtained from the previous equation. Assume that all the proceeds from G are spent in corrupt activities, like paying for the yachts of government cronies and their friends. Find an expression for steady state GDP. Argue that increases in 7 act like reductions in the economy's savings rate. What happens in governments with a lot of corruption, where r is almost one? c. (10 points, easy) Now suppose we have a good government and that G, is invested in good uses. In particular, assume that the production of goods is now boosted by government spending. You can think of this spending as infrastructure that improves productivity (roads, ports, etc). Assume that the production function is now: YG KL(-a) The idea is that 1-y is the parameter that governs the decreasing returns to scale to government expenditures on GDP, as if it where an input like capital or labor. Substitute G = TY, into the equation above. Show that GDP can be re-written as: Y =KL(-a) d. (10 points, harder) Using the steps you've learned in class to obtain the steady-state in the standard Solow model, find steady state output in this version. Assume that y=0.5. How does the steady state level of capital and output depend on 7? Compare 7 = 0, 7 = 0.5, and 7=1. When is GDP the highest? e.(5 points, moderate) What do you learn from this exercise? When are governments bad for GDP? And which are the best governments? Is 7 = 1 a good idea, even though the government's resources are put to good use?
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a To express investment It only as a function of total income Yt we substitute YtD into the private investment equation YtD Yt Gt YtD Yt Yt substituti... View the full answer
Related Book For
Economics of Strategy
ISBN: 978-1118319185
6th edition
Authors: David Besanko, David Dranove, Mark Shanley, Scott Schaefer
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