24 Jun CONSIDER A SOLOW MODEL WITH POPULATION GROWTH BUT NO TECHNOLOGY GROWTH
1. Derive the steady-state condition in terms of the equilibrium capital stock per person, k ∗ , starting from the law of motion for total capital, in a Solow model with positive population growth. 2. Consider a Solow model with population growth but no technology growth, Y = F(K, L). Explain what happens to the steady-state and transition path for income per worker when a war destroys both a large chunk of the population and a large chunk of the capital stock. 3. Take two countries with different values of all parameters in the Solow model. Contrast and compare the long-run convergence of these two countries with and without technological progress. 4. Explain, in words, the golden rule condition for capital in the Solow model with and without population growth (no technology growth). 5. In the Solow model, is there any link between saving and technological progress? Does this make sense? 6. Numerically, solve for equilibrium in a Solow model with a production function Y = K0.3L 0.7 and parameters s = 0.2, δ = 0.08, η = 0.02. Should public policy try to encourage more or less saving here? Why? 7. (Ch.5 Review) Consider some small open economy with fixed factors of production, given as follows: • Y = C + I + G + NX • Y = F(K, L), G = G, T = T are all fixed. • I = I(r), C = C(r), NX = NX() That is, a world where consumption/savings, not just investment, depends on the interest rate. Why might savings increase or decrease with the interest rate? Show whether or not savings equals investment in this economy. Explain what happens when the government makes regulatory changes to increase household saving.
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