Island Neighbors: Consider two remote, but neighborly, nations, the Isle of Sand and the Glass Islands. Both economies have similar demographics and technology (n, A, Zt , and z), but the Isle of Sand has a larger initial population Nt and a higher level of depreciation δ. Both economies can be represented by Cobb Douglas production functions, and their initial savings rate s is the same. Consider the following situation: Hurricane winds visit the virus, and wipe out half of the capital stock on both the Island of Sand and the Glass Islands. As a result, people on the Island of Sand start saving at twice their initial rate. People on the Glass Islands invent a new way to store their capital, so their depreciation decreases. (a) Characterize the initial steady state equilibrium in both countries, graphically and in algebraic expressions. Which country is initially better off? (b) Demonstrate graphically what happens to both economies after the hurricane. What are the changes to total output, total capital, income per capita, capital per capita, consumption, investment, the rental rate of capital, and wages? Trace out dynamics and explain the effects. Be sure to clearly explain the timing of the hurricane and the change insavings/depreciation. (c) Which economy has a higher capital stock per effective unit of labor? Which economy has a higher total output? Which economy has a higher capital stock per worker? (d) Use your answers above to report on the effects of the hurricane to a government agency deciding whether to give foreign aid to one of the Isle of Sand or the Glass Islands. Which economy should the foreign government help? How should the foreign government help that economy?
Island Neighbors: Consider two remote, but neighborly, nations, the Isle of Sand and the Glass Islands. Both economies have similar demographics and technology (n, A, Zt , and z), but the Isle of Sand has a larger initial population Nt and a higher level of
of Sand start saving at twice their initial rate. People on the Glass Islands invent a new way to store their capital, so their depreciation decreases.
(a) Characterize the initial steady state equilibrium in both countries, graphically and in algebraic expressions. Which country is initially better off?
(b) Demonstrate graphically what happens to both economies after the hurricane. What are the changes to total output, total capital, income per capita, capital per capita, consumption, investment, the rental rate of capital, and wages? Trace out dynamics and explain the effects. Be sure to clearly explain the timing of the hurricane and the change insavings/depreciation.
(c) Which economy has a higher capital stock per effective unit of labor? Which economy has a higher total output? Which economy has a higher capital stock per worker?
(d) Use your answers above to report on the effects of the hurricane to a government agency deciding whether to give foreign aid to one of the Isle of Sand or the Glass Islands. Which economy should the foreign government help? How should the foreign government help that economy?
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