Classical Growth theory predicts that O aggregate income always returns to the subsistence income O log run population will be constant O long run income per capita always returns to the subsistence income O aggregate output always returns to the subsistence income
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- 1. Country A and B both have the production functionY = F (K, L) = K ½L ½or Y = K0.5 L0.5 a) What is the per-worker production function, y= f (k)? Please make sure to write specificfunctional form of the per-worker production function. b) Assume that neither country experiences population growth nor technological progressand that 4 percent of capital depreciates each year. Assume further that country A saves 24percent of output each year and country B saves 16 percent of output each year. Using youranswer from part a) and the steady-state condition, find the steady-state level of capital perworker for each country. Then find the steady-state levels of income per worker for eachcountry and steady-state level of consumption per worker for each country.Farmland is a developing country with the following production function:Y = 24L2/3K1/3with Y = Output levelL = Quantity of laborK = Quantity of machinesa. Find the real rate of return for labor. Show your calculation. b. Suppose Farmland is granted some extra machines for production.How would this affect the real rate of return for labor? Explain by using theresult in (a).y=zk^2/3 For this economy, derive the competitive equilibrium, and derive the equation that solves for a steady state capital stock per worker.
- Exercise 4: Growth and capital over-accumulationSuppose two countries, A and B, with the same production function Y = KαL1−α. Thevalue of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%.a) Show that with price-taking firms the share of labor must be 1 − α.b) Compute the stock of capital, output and consumption per unit of labor in the steadystate if the savings rates were 25% for country A and 35% for country B.c) Compare both economies to the Golden Rule.d) Explain what would happen to both countries if suddenly their savings rate becamethe Golden Rule savings rate.Suppose an economy begins in steady state. By what proportion does per capita GDP change in the long run in reponse to each of the following changes? Production function is Y=AK^1/3L^2/3 a. Investment rate doubles b. depreciation rate falls by 10% c. Productivity level rises by 10% d. Earthquake destrys 75% of the capital stock e. Generous immigration policy lead the population to doublePlease the answer correct please ASAP Don't answer by pen paper please. he golden rule level of capital refers to: Question 19Answer a. the level of capital that maximises output per worker. b. the level of capital that maximises the standard of living. c. the level of capital that maximises the level of output in the steady state. d. the level of capital that maximises consumption per worker. e. the level of capital that maximises consumption per worker in the steady state.
- Suppose an economy begins in steady state. By what proportion does per capita GDP change in the long run in reponse to each of the following changes? Production function is Y=AK^1/3L^2/3 d. Earthquake destrys 75% of the capital stock e. Generous immigration policy lead the population to double Fast answerConsider an economy with a Cobb-Douglas production function with α = 1/3 that begins in steady state with a growth rate of technological progress of g of 2 percent. Consider what happens when g increases to 3 percent. (a) What is the growth rate of output per worker before the change? What happens to this growth rate in the long run? (b) Perform a growth accounting exercise for the economy, decomposing the growth rate in output per capita into components contributed by capital per capita growth and technology growth. What is the contribution of the change in g to output per capita growth according to this formula? (c) In what sense is the growth accounting result in part b producing a misleading picture of this experiment? Explain why this is the case.Assume there is a second economy ( country B ) with everything identical to country A except for the rate of population growth , which is 2 percent . Answer the following questions for country B. Assume both countries start a k = 0 , which country grows more in the short run ( before steady state is reached ) , as given by the rate of growth of output per worker ? ( hint : the further away from steady state , the faster the growth towards it ). O. Country A O. Same for both O. Country B
- Assume that Economyland’s production function is Y = F (K, L) = K 0.5 L 0.5Where Y is output level, K is the amount of capital input, and L is the amount of laborinput. a) What is the per-worker production function, y= f (k) for Economyland? b) Assume that 10 percent of capital depreciates each year and savings rate is 20 percent,find the steady-state level of capital per worker for Economyland. Then find the steady-state levelof income per worker and steady-state level of consumption per worker. c) Is it possible to save too much? Why?Suppose that total capital and labour both increase by the Suppose that total capital and labour both increase by the same percentage amount so that the amount of capital per worker k does not change. Writing the production function in per-worker terms, y = f(k), requires that this increase in capital and labour must not change the amount of output produced per worker y. Use the growth accounting equation to show that equal percentage increases in capital and labour will leave output per worker unaffected only if aK + aN = 1. Suppose that total capital and labour both increase by theIn macroeconomics, the connection from inputs to outputs forthe entire economy is called _______________. a)physical capital b)a production function c)human capital d)an aggregateproduction function
