Question 36 W Suppose that Y, VN, VK, and N1-N₂ (1+(Y/N, -yJ/y] where y, is the subsistence level of income. Assume that K,- 64 for all t. No - 36 and y, - 1. The aggregate output period 0 is O 16/9 O 4/3 01 O none of the others
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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.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.asap Suppose the economy's production function is Y = AKO.3NO.7. If K=2000, N = 100, and A = 1, then Y=246. If K and N both rise by 20%, and A is unchanged, by how much does Y increase?
- Show that, when using a traditional economic production function,doubling our population can double our output if capital stocks alsodouble. Use the production function: Q = AK L , where A representstechnology in an economy, K capital, and L labor. Double K and L andshow that Q also doubles, assuming α=β=1/2. Now show that, when we incorporate natural capital into thediscussion, doubling the population does not increase output in thesame way (since natural capital cannot also grow). Use theproduction function: Q = AK L N , where N is natural capital. DoubleK and L and show that Q less than doubles, assuming α=β=γ=1/3.Exercise 2: Growth and developmentCountries 1 and 2 have the production function: Yt = AiKαt L1−αt , where country 1 hasTotal Factor Productivity (TFP) of A1 = 25, country 2 has TFP A2 = 100, and α = 0.35for both. In the two countries population is constant and there is no technological progress.Every year capital depreciates by 6% in both countries. Country 1 saves 40% of output, andcountry 2 saves 20%.a) Write down the function of production per unit of labor. Suppose the two countriesstart with an initial capital stock (per unit of labor) of 500, what are the initial income andconsumption per unit of labor in both countries?b) Determine their steady state levels of capital, income and consumption per unit oflabor.c) Determine the difference in their steady state level of income per unit of labor, andhow much of that difference is due to differences in TFP and how much is due to differencesin capital per unit of labor.d) Suppose now that country 2 suddenly has access to the country 1…Productivity is generally measured as: O output per year. O nominal output over time. O real output over time. O output per worker. A
- One of your clients, a mining company with operations in the Democratic Republic of Congo and Zambia, is concerned withthe current macroeconomic environment’s impact on their operations. Among their worries is the slowdown in global growth, which is expected to moderate from 5.9 in 2021 to 4.4 percent in 2022—half a percentage point lower for 2022 than in the October World Economic Outlook.You are required to critically discuss some of the major factors that drove the global growth trajectoryi) Pre-Covid-19 pandemic ii) at the height of the pandemic iii) going into 2022 and beyond.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 double5) Suppose, Nepal was in general equilibrium before COVID-19. Explain the effect of increase in labor supply due to returnee’s migrants. Assume that everything else has not changed at all. Use IS-LM-FE model to answer.
- 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?TheeconomyofGhana ismadeupofthreesectorsnamelyAgriculture,Industryand Se rvice s. The se thre e sectors contribute to the national output. For de cade s prior to the 2000s, the Agricultural sector contributed the most to the national output. Sadly, in recent years however, the sector has been the least contributor to national output. Trends in production of major food crops such as maize, rice and sorghum show that on-farm productivity has stagnated and the exploitable difference between the actual and the potential output of most ofthe crops (yield gap) has widened. Low and inadequate levelsofusageofproductivityenhancingtechnologiessuchasqualityseeds of improved varieties and fertilizer, thin extension services and weak market linkages contributes to the poor agricultural performance. It was against this background that theNPP-led government implemented one of her flagship programmes “Planting for Food and Jobs”. The programme is primarily aimed at making subsidized improved seeds and…3. Suppose that we have a Solow model with one twist. The twist is that thereis a government. Each period, the government consumes a fraction of output,sG. Hence, the aggregate resource constraint is:Yt = Ct + It + Gt.Where Gt = sGYt. Define private output as Ypt = Yt − Gt. Suppose thatinvestment is a constant fraction, s, of private output (consumption is then1 − s times private output). Otherwise the model is the same as in the text.104(a) Re-derive the central equation of the Solow model under this setup.(b) Suppose that the economy initially sits in a steady state. Suppose thatthere is an increase in sG that is expected to last forever. Graphicallyanalyze how this will affect the steady state value of the capital stockper worker. Plot out a graph showing how the capital stock per workerwill be affected in a dynamic sense