Consider an economy with a Cobb-Douglass production function Y = A1-«KªN1-a Where TFP, A, grows at a rate of g per year and population grows at a rate of п рer year. 1. Derive an expression for the production function per effective worker f(k) = Yt in terms of the ratio of capital per effective worker ki AtNt
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- 3. Consider the Basic Solow growth model with a Cobb-Douglas production function and no technological change for the economy china. In this island economy, capital’s share α= 0.3, the annual depreciation rate on capital δ = 0.08 and the annual population growth rate n = 0.02. Suppose that this is the year 2017, and the economy is in the steady-state with GDP (Y) = 200 bananas, and capital stock K = 400 bananas. [Feel free to use any form of exponentiation that works best for you] Project the equilibrium level of GDP for 2050. Calculate the market value of fixed capital (K) in 2050 on a gross basis. Using the steady-state conditions, solve for the saving rate (s*) that is consistent with a stable steady-state.3. An economy described by the Augmented Solow growth model has the following production function with populationgrowth (1+n) and technological growth (1+z):y =p(k)(a) Solve for the steady-state values of capital per capita and output as a function of s, n, z, and δ.(b) A developed country has a saving rate of 28 percent and a population growth rate of 1 percent per year. A lessdeveloped country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In bothcountries, g = 0.02 and d = 0.04. Find the steady-state value of y for each country.(c) What policies might the less developed country pursue to raise its level of income? Graphically demonstrate howyour advised policy would increase income per capita (y).8 Suppose we are considering a Solow Model without technology progress. Population growth rate=0.03 The capital accumulation is sY-dK s=0.1, d=0.02 Please calculate the capital per capita under the steady state. A. 2 B. 4 C. 6 D. 8 E. 16 F. None of the above
- A Solow Growth Economy with production function Y=K¹/²(AL)¹/² has a savings rate of 24 percent, a depreciation rate of 2 percent, labour force growth of 1 percent and technological progress improving at 3 percent per year. Provide a labelled diagram to illustrate and quantify the determination of equilibrium output per effective worker and capital per effective worker.Consider the following Solow diagram, indicating two sep-arate savings rates, 0.2 and 0.4: Suppose the savings rate is 0.2. At the steady state, what is capital per worker? What is output per worker? How much is saved per worker? Suppose the population growth rate is equal to the depreciationrate. Solve for n and d.Assume that the economy’s production function is Cobb Douglas so per-capita output is ? = k^α, where k is per-capita capital. Using the Solow growth model, explain the impact of the loss of capital on the growth rate of per-capita output in the years following the disaster.
- Based on article "Technology and economic growth: From Robert Solow to Paul Romer" by Rui Zhao, Solow mentioned technology (At) and capital per unit of effective labor (Kt) have a significant influence on a country's ability to “catch-up” or “converge” to a steady-state level (K*). Using the central equation of the Solow model, discuss the influence of At and Kt on country's ability to grow and move to a steady-state level (K*).Suppose we started out at the steady state capital stock in the basic Solow growth model (see graph a few questions ago). If there subsequently were an increase in the demand for loanable funds due to more favorable tax treatment of business investment, ceteris paribus (i.e., holding other factors constant, including no shift in the supply of loanable funds), then as we move to the new steady state over time we would expect to see Group of answer choices A) economic growth rates turn negative as we move toward the new steady state and the nation’s capital stock to decrease from its current level. B) economic growth rates turn positive as we move toward the new steady state and the nation’s capital stock to decrease from its current level. C) economic growth rates turn positive as we move toward the new steady state and the nation’s capital stock to grow from its current level. D) economic growth rates turn negative as we move toward the new steady state and the nation’s…Derive the equilibrium law of motion for capital per worker in the Solow growth model (equation 7-19). State which equation you start with, and the operation you perform at each step. 2. Graph this equation in the space of capital tomorrow on the y-axis and capital today on the x-axis, and explain how you identify the steady-state level of capital per capita from the graph
- Assuming a country’s economy maintains an 8% rate of growth, young adults starting at age 20 would see the average standard of living in their country more than double by the time they had reached age __________. Question options: a) 30 b) 60 c) 50 d) 40 Country Alpha and Country Beta initially have the same real GDP per capita. Country Alpha experiences no economic growth, while CountryBeta grows at a sustained rate of 5 percent. In 14 years, Country Alpha’s GDP will be approximately _________ that of Country Beta. Question options: a) triple b) double c) one-half d) one-fourthSuppose that the production function is Y= 10(K)1/4 (L)3/4 and capital lasts for an average of 50 years so that 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate, s =0.128, calculate the steady-state level of capital per worker, output per worker, consumption per worker, saving and investment per worker and depreciation per worker.If the population growth rate increases by 5% and the depreciation rate decreases by 5%, what happens to the steady-state, per-worker consumption in Solow's exogenous growth model?