【正文】 n the steady state, Δk = sf(k) – (δ + n + g)k = 0. Hence, sAkα = (δ + n + g)k, or, after rearranging: . Plugging into the perworker production function from part (a) gives . Thus, the ratio of steadystate ine per worker in Richland to Poorland is c. If α equals 1/3, then Richland should be 41/2, or two times, richer than Poorland. d. If = 16, then it must be the case that , which in turn requires that α equals 2/3. Hence, if the Cobb–Douglas production function puts 2/3 of the weight on capital and only 1/3 on labor, then we can explain a 16fold difference in levels of ine per worker. One way to justify this might be to think about capital more broadly to include human capital—which must also be accumulated through investment, much in the way one accumulates physical capital.6. How do differences in education across countries affect the Solow model? Education is one factor affecting the efficiency of labor, which we denoted by E. (Other factors affecting the efficiency of labor include levels of health, skill, and knowledge.) Since country 1 has a more highly educated labor force than country 2, each worker in country 1 is more efficient. That is, E1 E2. We will assume that both countries are in steady state. a. In the Solow growth model, the rate of growth of total ine is equal to n + g, which is independent of the work force’s level of education. The two countries will, thus, have the same rate of growth of total ine because they have the same rate of population growth and the same rate of technological progress. b. Because both countries have the same saving rate, the same population growth rate, and the same rate of technological progress, we know that the two countries will converge to the same steadystate level of capital per effective worker k*. This is shown in Figure 91. Hence, output per effective worker in the steady state, which is y* = f(k*), is the same in both countries. But y* = Y/(L 180。 (K/Y). In the steady state, we know from part (a) that the capital–output ratio K/Y is constant. We also know from the hint that the MPK is a function of k, which is constant in the steady state。Answers to Textbook Questions and ProblemsCHAPTER 9Economic Growth II: Technology, Empirics, and PolicyQuestions for Review1. In the Solow model, we find that only technological progress can affect the steadystate rate of growth in ine per worker. Growth in the capital stock (through high saving) has no effect on the steadystate growth rate of ine per worker。 E (or LE), where L is the number of workers, and E measures the efficiency of each worker. To find output per effective worker y, divide total output by the number of effective workers: b. To solve for the steadystate value of y as a function of s, n, g, and δ, we begin with the equation for the change in the capital stock in the steady state: Δk = sf(k) – (δ + n + g)k = 0. The production function can also be rewritten as y2 = k. Plugging this production function into the equation for the change in the capital stock, we find that in the steady state: sy – (δ + n + g)y2 = 0. Solving this, we find the steadystate value of y: y* = s/(δ + n + g). c. The question provides us with the following information about each country: Atlantis: s = Xanadu: s = n = n = g = g = δ = δ = Using the equation for y* that we derived in part (a), we can calculate the steadystate values of y for each country. Developed country: y* = ( + + ) = 4 Lessdeveloped country: y* = ( + + ) = 12. a. In the steady state, capital per effective worker is constant, and this leads to a constant level of output per effective worker. Given that the growth rate of output per effective worker is zero, this means the growth rate of output is equal to the growth rate of effective workers (LE). We know labor grows at the rate of population growth n and the efficiency of labor (E) grows at rate g. Therefore, output grows at rate n+g. Given output grows at rate n+g and labor grows at rate n, output per worker must grow at rate g. This follows from the rule that the growth rate of Y/L is equal to the growth rate of Y minus the growth rate of L. b. First find the output per effective worker production function by dividing both sides of the production function by the number of effective workers LE: To solve for capital per effective worker, we start with the steady state condition: Δk = sf(k) – (δ + n + g)k = 0. Now substitute in the given parameter values and solve for capital per effective worker (k): =(++)k k23=4 k=8. Substitute the value for k back into the per effective worker production function to find output per effective worker is equal to 2. The marginal product of capital is given by MPK=13k23 . Substitute