Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKªL²-a 1. Use the production function to compute output per capita, y =Y /L, as a function of capital per person, k = K/L. 2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps. Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 8= 0.1 and n =0.01. You do not know the value of A. 3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k.
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- Hello, please help me to solve these questions.Consider the Solow growth model with technological progress at the rate g, population growth at the rate n, and capital depreciation rate at the rate δ. The savings rate is denoted by s and the production function is given by:Y = Kα (AL)1-α , 0 < α < 1.Y is aggregate output, K is aggregate capital, L is aggregate labour, A is technology and AL is effective labour. (a) Let ݇k = K/AL which denotes capital per unit of effective labour. Obtain the production function in terms of capital per unit of effective labour. Explain the properties this production function satisfies. (b) Derive the key equation that governs the evolution of capital per unit of effective labour in this Solow model. Provide the steady state value of capital and output in per unit of effective labour terms. What are the growth rates of capital per unit of labour and output per unit of labour in the steady state? (c) Analyse the effect of a decrease in the…In the Solow growth model, suppose that the per-worker production function is given by y=zk2/3 . The saving rate is s, depreciation rate is d, and population growth rate is n. Calculate the per capita capital (k) and output per worker (y) in the steady state.Consider a numerical example using the Solow Growth Model, for 2 countries.Country A: d=0.1, s=0.3, n=0.01, z=1, F(K,L)=K0.3N0.7 Country B: d=0.1, s=0.2, n=0.01, z=1.5, F(K,L)=K0.4N0.6Which Country has a higher level of GDP per capita in steady state? Country A Country B Not enough information
- Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience and that there is labor-augmenting technological progress, with a production function Y =F(K,bN) where b denotes the number of units of "human capital" per worker, and bN is "efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1 + f ) b, where f is the growth rate in human capital. (c) In the real world, we usually consider education level as a proxy to human capital. To examine the theory, what suggestions can you make to growth economists? What are factors other than education can you think of that contribute to human capital?Assume there is no population and technology grows at a constant rate of g. Graphically illustrate and explain the effects of a reduction in the saving rate on the Solow-Swan growth model and increase in technological growth. In your graph, clearly label all curves and equilibria. Explain what will happen to each of the following over time: capital per effective worker, output per effective worker, and consumption per effective worker.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
- Assume that an economy is described by the Solow model in the long run. The rate of population growth in this economy is n technological growth is g rates of total GDP, GDP per worker, and GDP per effective worker? 0.01 and the rate of 0.02. What are the long-run (steady state) growth rates of total GDP, GDP per worker, and GDP per effective worker?This question is about the Solow model. For 2 countries, 1 and 2 which has the same rate of population growth and depreciation and the same saving rate, and are in initial steady state, their capital have equal importance for production for both countries with the same value of α = 1/2 a. In the initial steady state, country 1 has 2 times the output per capita to country 2 because of its greater productivity A. Please use the steady-state equation to find the ratio of the 2 countries’ ratio of productivity and explain it. b. Find the 2 countries’ ratio of capital per capita and explain it. c. Please explain in detail if the capital owners in country 1 are motivated to move their capital from country 1 which is capital abundant, to country 2 which is more capital scarce? Hint: the 2 countries’ payment per unit of capital d. Does workers in country 2 motivated to immigrate to country 1? Please explain from the perspective of the 2 countries’ wages.The Solow Growth Model is an exogenous model of economic growth that analyzes changes in the level of output in an economy over time as a result of changes in the population growth rate, the savings rate, and the rate of technological progress. Consider the Solow model. a) Explain using a graph why there is a poverty trap in this model b)Describe how an economy such as one characterized by this model may break out of a poverty trap.
- Consider our graph of the basic Solow growth model. On the graph above: y represents real output (or income) per worker; y=F(k) is the production function; k is the capital stock per worker; s is the savings rate; δ is the rate of depreciation of capital; ‘i’ represents business investment (purchases of capital) per worker); ‘LF’ stands for Loanable Funds. (For purposed of intuition, think of capital as ‘machines.’) If we started out with a capital (per worker) stock lower than the steady-state stock ( , above), we would expect to see which of the following happen over time? Group of answer choices A) Positive growth rates while the capital stock increases. B) Negative growth rates while the capital stock increases. C) Negative growth rates while the capital stock decreases. D) Positive growth rates while the capital stock stays less than the steady-state level. E) Positive growth rates while the capital stock decreases.“The Solow model shows that the higher the rate of population growth, the higher the steady-state levels of capital per worker and output per worker because more population means more worker so more output”. Do you agree with the statement? Graphically explain,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…