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.
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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
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- 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.Using the Solow model diagram, illustrate what happens to the steady-state capital per worker and output per worker and output per worker when a country faces a positive technology stock.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…
- Consider the following Solow growth model in which households save a constant fraction of their income. Let N be the population (also the labor force) in the current period. Assume that the population follows N′ = (1+n)N where N′ is the population in the future period, and n is the net population growth rate. Assume that the output is produced according to the production function Y = zF(K, N), where z is the total factor productivity, K is capital stock, and F(K, N) exhibits constant returns to scale. Capital depreciates at the rate d where 0 < d < 1. The capital stock changes over time according to K′ = (1 − d)K + I where I is the investment level. (a) Derive the equation that determines the future capital-per-worker in competitive equilibrium. Here is some additional information for parts (5b), (5c), and (5d). Suppose that the economy is initially in steady state, and experiences a natural disaster (e.g. the recent quake and tsunami in Japan in 2011) that destroys some of 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 the Solow model. Using suitable diagrams, compare the different dynamics for the levels and growth rates of capital per capita and output per capita following: (a) a new wave of immigration, (b) an increase in the saving rate, (c) a one-shot foreign investment which increase the size of the available stock of capital, (d) an important technological advance.
- 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.Which of the following is an incorrect statement about the variable ‘s’ in the Solow Growth Model? a.s is the fraction of income that is saved b.s is an exogenous factor c.s is referred to as saving per worker d.s determines how income is allocated between consumption and investmentDraw a well labeled graph that illustrates the steady state of the solow model with population growth. Use the graph to find what happens to steady state capital per worker and income per worker in response to each of the following exogenous changes D. A one time permanent improvement in technology increases the amount of output that can be produced from any given amount of capital and labor. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
- Income per person exceeds $ 25,000 in many countries but it is below $ 1,000 per person in many other countries. Based on the Solow growth model, suggest at least four possible explanations for this gap in living standards.Suppose a country has a capital-output ratio equal to 10, a savings rate equal to 20% of GDP, capital that lasts on average 100 years and population growth of 1% per year. If we assume the country is at its steady state and production is given by the Solow model with labor augmenting technological change, so Y = Kª(Ex L)¹-a, then the growth rate of technology as measured by the growth rate of efficiency workers is 3% 1% 4% 0% 2%The Solow model without exogenous productivity growth predicts that rich countries with more capital will grow faster than poor countries with less capital, assuming other economic conditions are equal. Is this statement true or false? Explain.