ECO 303 Problem Set 31. A closed economy has the following Cobb-Douglas production function_5=6F (K; L) = K 1=6 (EL) . The depreciation rate is 1% and the saving rate is48%. The economy is in a steady state, where the population decreases at arate 1%, while real GDP per capita grows at a rate 1.5%.(a) Find the growth rates of the following variables:(i) the e¤ective labor force, EL(ii) the ratio of labor to capital, L=K(iii) the labor income, wL(iv) the ratio of the real rental rate to the real wage, r=w(b) If total capital K is 64 million this year, â¦nd real GDP next year.(c) By how many percentage points should the government change the savingrate so that the economy may converge to the golden rule steady state (use a â+âfor an increase and a â â for a decrease)? How would the current generationfeel about the change?2. A closed economy has two factors of production: capital and labor. Theproduction function is known to exhibit constant returns to scale. The capitalstock is about 3 times one yearâs real GDP. Approximately 10% of GDP is usedto replace depreciating capital. Labor income is 85% of real GDP. Real GDPgrows at an average rate of 3% per year. Assume the economy is at a steadystate.(a) Is the capital per e¤ective worker lower or larger than it would have beenin the golden rule steady state? [To receive points on this question, you need toshow me your calculations](b) [growth accounting] If the population grows at a rate 1% per year, â¦ndwhat portion of output growth is due to:(i) an increase in capital;(ii) an increase in labor;(iii) an increase in total factor productivity.3. A closed economy has a production function: Y = K 1=3 L2=3 , where Kdenotes machines and L denotes workers. The population grows at a rate 2%per year and there is no technological progress. The depreciation rate is 3%.The saving rate, s, depends on the level of capital per worker, k, as follows:8<><> 10 There are three steady states with k > 0: a low-income stable steady state,a middle unstable steady state, an a high-income stable steady state. Capitalper worker in the middle unstable steady state is 6.8661.1 (a) Find output per worker in the low-income stable steady state(b) Find output per worker in the high-income stable steady state(c) Assume the economy is in the low-income stable steady state. A donoris discussing a development aid in the form of a large-scale capital investment.What is the minimum integer amount of machines per worker that the donorshould provide so that the economy could escape the poverty trap and eventuallyconverge to the high-income stable steady state? [In answering the question,assume there are no leakages, transaction costs, or any other frictions.]4. Consider a closed economy and use graphical analysis to illustrate howthe equilibrium output, price level, and interest rate would be a¤ected in theshort run and over time by:(a) a substantial increase in credit card usage (absent any policy response)(b) a stock market crash (absent any policy response)(i) What can the government do to stabilize output?(c) an exogenous increase in the price of oil (absent any policy response)(i) What can the Fed do to stabilize the interest rate?5. Consider a closed economy where: I = 150M=P = Y C = 50 + 0:8(Y T )G = 50; T = 100;10r, where r is measured in percent10r , where r is measured in percentM = 1; 000; P = 2 (a) Assume that government spending G decreases by 10% and tax revenueT decreases by 4%(i) Calculate the corresponding horizontal shift in the IS curve.(ii) Calculate the resulting change in the equilibrium income and theresulting change in the equilibrium interest rate.(iii) How would the price level evolve over time (increase, decrease, orremain the same)?(b) Assume that government spending and tax revenue are as before: G = 50and T = 100, but the Fed increases money supply M by 10%.(i) Calculate the vertical shift in the LM curve.(ii) Find the short-run equilibrium income and interest rate.(iii) How would the price evolve over time (increase, decrease, or remainthe same)? 2