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1. Suppose an earthquake destroys part of a nation’s capital stock, but does not kill off any people. Use the Solow model without technological change to describe the effect of this event on the country’s total output and its per capita output over time. Assume prior to this event the economy was on its steady state path.
2. Suppose a war destroys part of a nation’s population but not its capital stock, (say on account of a neutron bomb being deployed). Use the Solow model without technological change to show the effect of this event on the country’s total output and per capita output over time. Assume prior to this event the economy was on its steady state path.
3. Assume a Solow growth model economy with no exogenous technological change is initially at a steady state. Suppose there is a permanent decrease in the population growth rate, say on account of the spread of AIDS – a major current problem in Sub-Sahara Africa. Show graphically the path of the economy’s capital and output per capita over time following this event.
4. Take the Solow model without technological change. Assume there is a government that taxes consumer’s income at the tax rate τ. The government uses the tax receipts to buy some of output. Assume that individuals save a fixed fraction, s, of their after tax income so St =s(1-τ)Yt. (In this case, the government spending, g = τY). Show graphically that an increase in the tax rate will lower the steady state capital stock of an economy. Solve algebraically for the steady state capital stock.
5. Now assume that the government imposes a lump-sum tax, T, and just uses the receipts to buy goods (so that g = T). With a lump-sum tax, consumers have an after tax disposable income equal to Y-T. Consequently, saving St = s(Y-T). Show graphically that there are 2 steady states it the lump sum tax is not too big, or 0 steady states if the lump sum tax is large. a. Provide some intuition for why there are two steady states in the case of a small lump sum tax. b. For the case, where there are 2 steady states, show graphically how the transitional dynamics for this economy are. Namely, suppose you start to the left of the low steady state capital stock, what happens? What about to the right?
6. Suppose total National Savings, St, is St= sYt – hKt. The extra term -hKt reflects the idea that when wealth (as measured by the capital stock) is higher, savings is lower, (i.e., wealthier people have less need to save for the future). Assume that production is given by the Solow model without technological change. Solve algebraically for the steady state capital stock. Show graphically how the steady state capital stock compares for an economy with h= 0 and another with h>0.
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