5. Consider the Solow growth model learnt in the class where output is given by Cobb-Douglas production function as Y, = A, K; L; and capital accumulation is given by: AK, = 5 Y; – d K,where s is the constant savings rate and d is the depreciation rate. a) Mathematically solve for the steady state level of capital. How does the steady state level related to the savings rate (s) and the depreciation rate (d). b) What is the steady state level of capital, if saving rate (s) = 10%, depreciation rate (d) = 5%, A̟ = 2 and ī = 1.5?

5. Consider the Solow growth model learnt in the class where output is given by Cobb-Douglas production function as Y, = A, K; L; and capital accumulation is given by: AK, = 5 Y; – d K,where s is the constant savings rate and d is the depreciation rate. a) Mathematically solve for the steady state level of capital. How does the steady state level related to the savings rate (s) and the depreciation rate (d). b) What is the steady state level of capital, if saving rate (s) = 10%, depreciation rate (d) = 5%, A̟ = 2 and ī = 1.5?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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i need part C,D,E,F,G In the Solow growth model, output Y is produced using capital K and labour L.Assume the production function is Y =√K√L, which has total factor productivityconstant over time. The change over time in the capital stock is ∆K = I−δK, whereI is investment and δ is the depreciation rate. The labour force L is constant overtime. Investment I is equal to saving S, which is a fraction s of income.Let k = K/L and y = Y/L denote capital per worker and output per worker. In thisquestion, assume that δ = 1. Capital can be used for production and generates anincome for its owner before it depreciates.(a) Show that y =√k and ∆k = s√k − k, and solve for the steady-statevalues of k and y where ∆k = 0.(b) Using a diagram, explain intuitively why there is a steady statewhere growth in output per worker is zero, and why the economy convergesto this steady state in the long run.Total consumption divided by the number of workers is given by c = (1 − s)y.(c) Using your answer…
2) Assume that two countries are identical in every respect, except Country A initially has more capital per worker than Country B (i.e. they have the same saving rate (s), labor supply growth rate (n), depreciation rate (d), total factor productivity (A), and elasticity of output with respect to capital (a)). A) According to the Solow model, which country has greater income per worker initially? B) According to the Solow model, which country will grow faster in the short-run? What about the long-run? Explain your answer. C) Compare Country A’s steady-state output per worker with Country B’s in the Solow model. Explain.
QUESTION 1 (10 marks) Consider the Solow growth model without population growth or technological change. The parameters of the model are given by s = 0.2 (savings rate) and δ = 0.05 (depreciation rate). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. a. Rewrite production function per-worker terms. b. Find the steady-state level of the capital stock, kss
Consider the basic Solow model. Assume that Country A has a production function as following. Y = A√K Where A represents the technology available in the country and & the aggregate capital. Let the national saving rate be equal to 30%, s = 0.3. Also, assume that capital depreciates at a constant rate of 3%, delta = 0.03. a) For this question, assume A = 1. According to the basic Solow model we learned in class, what is the steady state level of capital and output?
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 = K^a(EL)^(1 – a), then the growth rate of technology as measured by the growth rate of efficiency workers is 0% 1% 3% 2% 4%
Identify two assumptions of the basic Solow Growth Model. b. Why are these assumptions important in supporting the Solow Model? c. You are given the following information about an economy.Y = C + IY = F(K, L) The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns.s = saving rate (assume this is constant) per yearδ= depreciation rate (assume this is a constant) per yeary = Y/Lk = K/Lk* = steady state of capital per worker (K/L) and sf(k) < δk.i. What is sf(k)? ii. What is δk? iii. Interpret the meaning of sf(k) < δk? iv. Graphically illustrate sf(k), δk, and k*. Indicate on your graph where sf(k) < δk. v. Explain what happens in this economy when sf(k) < δk.
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.
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?
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.
Please aid in answering the underlined questions in BOLD Question 4:a. Identify two assumptions of the basic Solow Growth Model. b. Why are these assumptions important in supporting the Solow Model? c. You are given the following information about an economy.Y = C + IY = F(K, L)The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns.s = saving rate (assume this is constant) per yearδ= depreciation rate (assume this is a constant) per yeary = Y/Lk = K/Lk* = steady state of capital per worker (K/L) and sf(k) < δk.i. What is sf(k)? ii. What is δk?iii. Interpret the meaning of sf(k) < δk? iv. Graphically illustrate sf(k), δk, and k*. Indicate on your graph where sf(k) < δk.v. Explain what happens in this economy when sf(k) < δk.
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 validity and ability of the Solow Growth Model in explaining the long-term growth of a country has been tested empirically.(a) In the Solow Growth Model we are introduced to the concept of the Golden Rule; optimum level of saving and capital formation to support growth. Is this Golden Rule concept proven empirically?(b) From what we have learned from the Solow Growth Model, describe some policies that can improve a country's economic growth rate.