Question

Solow-Romer Model 2. Let the production function for output be 11/2 YA,K/2L2 Compared to the model described in the Chapter 6 Appendix, the exponent on capital has been increased from 1/3 to 1/2 above and decreased on labor from 2/3 to 1/2 to preserve constant returns to scale in objects. All of the other assumptions from lecture and/or from the Chapter 6 Appendix are the same What is the growth rate of output per worker along a balanced growth path? Explain why it is different from the model considered in the Appendix of Chapter 6. Solve for the level of output per worker along a balanced growth path. Explain how and why this solution differs from what is presented in the Chapter 6 Appendix. Suppose that there is a one-time sudden and permanent increase in the savings rate (5). Illustrate the impact of this on a ratio scale diagram and briefly explain what happens to the level and growth rate of output per worker (and output per capita), both initially and in the long-run. A. B. C.

Answer 1

Answer: solow - Romer modeli Given, Yt = Atkits Le @) Growth rate of output per coxxor along a balanced groot pathi Is The General Expression denied for the growth in output per capita is : guide t o where [ = work fore 2 = Exponent ī = research share o from the model describe in Chapter 6: The exponent on capital has been increased from 1/3 to 1/2 and labor is desdeased from 213 to 1/2 to maintain Constant returs to scale in objects. Therefore, the growth rate of output per capita is given as

eo for chapter 6 Appendix As the capital's share of income ! 974 = ETE CHJ - 317 · Similarly from Capital's share of income 1/2, the groenth rate of output per capita is given as, zīł. 9y* = =QZĪT Hence as per the calculations we notic that growth rate is higher for bigger capital share. This we can say that with a larger capital share. the output per workers is increased which leads to greater capital a cumulation . Hence Capital share of income 1/2 has greater output per worker than that of capital Shase of income 1/3.

(B level of output per worker along a balanced growth pathi . Explanation: l. In the Romer model the growth rate of output, was equal to z/s; however in splow somer model the growth rate 18 1.95 times fagter. " The reason behind this is an increase in the ideas leads to an increase in the productivity which increases Capital Stock, which in turns leads to further growth of output. . Now the output per worker also increased as new ideas raises the output per work or in the economy through uniqueness of it . Also in solow model, if the investment rate is creates the level of output per worker will increase by the square asoot of the investmentrade.

do yt / N = (slgen + D)"? Att sly (k-1) In not shell, bith Solow and somes model are continue to hold in the combined model, but the long term grocoth is contributed to the non rivalry of ideas. © If there is sudden one time permanent increase in savings rate (5) then impact of this 18; . A one time increase in savings rate will change the level of output by not the growth rate of output: * In the short con, growth rate of output per worker increases but in the long run growth rate desturme back per worker will to old level. But the level of outpert be higher than the old level. - o-