Convergence

The Solow model has two basic equations: y = k α (1) ∆k = sy − (n + δ)k (2) where y is output per labor, k is capital per labor, s is the savings rate, δ is the rate of depreciation, and n is the rate of population growth. Note that the second equation is just a simplification of the law of motion (1 + n) kt+1 = syt + (1 − δ) kt (1) [2 points] In words, explain what equations (1) and (2) mean in economic terms. (2) [1 point] Now find an expression for the steady-state values of y and k. [Hint: write y in terms of k in equation (2) and set ∆k to zero.] (3) [2 points] Explain why this is a steady state. If you lived in this economy, what would it look like? In other words, describe what happens when the economy is on the balanced growth path. (4) The following statements are true or false. Say which, then explain why. (a) [3 points] Suppose you know both countries have the same underlying parameters α, s, n, δ. If country A is growing faster than country B, then we know A is poorer than B. (b) [3 points] If A is growing faster than B, then we we know that it has a higher savings rate than B. Assume that both countries have the same k at this point and the same n and δ. (c) [3 points] Suppose A has faster population growth than B. Then, in the steady state, A will be poorer than B in per-capita terms. Assume that both countries have the same sand δ. (d) [3 points] Everything else—s, n, δ—being equal, if α is greater in A than in B, it means A will be wealthier per capita in the steady state. (e) [4 points] Suppose that country A has positive population growth and B has negative population growth. Explain what the Solow model implies about these two countries. Then think about what reality might tell us. Explain the limitations of the simple Solow model this comparison implies. You can assume that these countries have the same s and δ. (5) [4 points] Suppose there are two countries in a Solow world. One is much wealthier than the other. If it were possible for the rich country to invest in the poor, what would happen? Use the model to describe this. [Hint: returns to investment are higher when the marginal product of capital is higher. Which country has higher marginal product of capital?] 1 Economics 308 Prof. Artunç Spring 2018 II. Solow and Conditional Convergence [10 points] In this section, assume we are in a Solow world where each country has different parameters. We don’t know which parameters are different. (1) More true/false and explain: (a) [2 points] In country A, the absolute amount of investment is greater each year than in country B. This must mean that B is wealthier than A. (b) [4 points] Suppose we know that A and B will converge to different steady states, but we do not know anything more than that. If we see A growing faster than B, what can we conclude? What other information might allow us to say something more? (2) [4 points] Now use these models to structure an understanding of the following sets of facts. (i) The U.S. had per-capita income similar to that of Britain in 1800. By 1930, the U.S. per capita income was much higher than Britain’s. (ii) In 1820, German per-capita income was much lower than that of Britain. By the late 1920s, German incomes were higher. Today they are about the same again. (iii) The U.S. growth has always been “low but steady,” about 2 percent per year without much deviation from that.