QUESTION 2 Suppose that an economy's production function is y-ALO.5g0.3y0.7, where Y is output, A is total factor productivity, L is land, K is capital and N is labor. However, we make a mistake and assume that it is given by y-AKO3N0.7. In other words, we do not take into account that landL matters. If K and N do not change, but L grows by 19.9%, what would we estimate the growth rate of A to be (approximately, in percent terms)? (Submit your answer with up to two decimals, i.e., 10.22 for 10.22% and 11.44 for 11442%.)
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- Economics, physical capital represents the uildings or machines used by a business to produce product. The marginal product of physical capital presents the rate of change of output product with spect to physical capital (informally, if you increase e size of your factory a little, how much more Foduct can you create?). articular model tells us that the output product Y is given, a function of capital K, by Y = AKªL'-a ere A is a constant, L is units of labor (assumed to be stant), and a is a constant between 0 and 1. Determine marginal product of physical capital predicted by this del. ned with CamScanneras Figure 11-1 D Real GDP per hour worked, YIL v $40 IC 8 T 1 60 Production function, Production function, Production function, Capital per hour worked, KIL Refer to Figure 11-1. Diminishing marginal returns is illustrated in the per-worker production function in the figure above by a movement from Production function 1 to Production function 2 from Production function 2 to Production function 1. from Production function 1 to Production function 3. up along any of the production functionsIn any Econorry the production function | 1-x is y=Ka L!-xnfinity Derive ss level of output per and capital per worker. vyorker
- Assume that a country's production function is Y= AKº³Lº7. The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Capital is paid its marginal product. a. What is the marginal product of capital in this situation? (Hint: The marginal product of capital may be computed using calculus by differentiating the production function and using the capital-output ratio or by using the fact that capital's share equals MPK multiplied by K divided by Y.) b. If the economy is in a steady state, what must be the saving rate? (Hint: The saving rate multiplied by Y must provide for gross growth of (8 + n + g)K, where 8 is the depreciation rate.) c. If the economy decides to achieve the Golden Rule level of capital and actually reaches it, what will be the marginal product of capital? d. What must the saving rate be to achieve the Golden Rule level of capital?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=1/3.1. 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.
- The graph below shows three production functions. PFO shows the current production function for the economy, and capital per worker is currently (K/L)o; thus ouput per worker is (Y/L)o. Suppose that there is a decrease in capital per worker. Which of the points on the graph could show the new capital per worker and output per worker? A. 3 O C. 1 Click to select your answer. B. 2 D. 4 Real GDP per hour worked, Y/L (Y/L)o 2 0 3 (K/L)o Capital per hour worked, K/L PF1 PF0 PF₂Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker? Only D, other option answeredAssume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker?
- 3. What are the 2 variables that the Production Function is analyzing/graphing? Why does the production function diminish over time?1. O LounchPad • Country A and country B both have the production function Y = F(K, L) = K/³L²/3. a. Does this production function have constant returns to scale? Explain. b. What is the per-worker production function, y = f(k)? c. Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per work- er for each country. Then find the steady-state levels of income per worker and consumption per worker. d. Suppose that both countries start off with a capital stock per worker of 1. What are the levels of income per worker and consumption per worker?2. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress. (a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (c) Find the long-run growth rate of output per worker. Now the economy has the following production function:Yt = 3Kt but savings rate, depreciation rate, and population remain the same. (d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt (e) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy…