Let the production function beQ = K0.®L0.2Solow's assumptions areK = sQ – 6KThe symbols s represents a (constant) marginal propensity to save, n, a (constant) rate of growthof labor and 8 constant depreciation rate.(a) Derive the fundamental equation of Solow growth model for given production function.(b) Sketch graph of with k on the vertical axis and k on the horizontal taken = 0.01, s = 0.3, 8 = 0.1.

Solow Model of growth depicts the long term equilibrium level steady state which an economy attains…

Answered: Let the production function be Q =…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Describe how, if at all, each of the following developments affects the break-even and actual investment line in the diagram for the Solow growth model: (a) The rate of depreciation falls. (b) The rate of technological progress rises. (c) The production function is Cobb-Douglas, f(k) = ka, and capital's share, a, rises. (d) Workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before.
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4. Consider the following endogenous growth model: a representative household's life-time utility function is given as: pe C(t)!-o – 1 -dt. 1- 0 The production function is: Y (t) = AK(t)ª Hp(t)'-a where Hp(t) denotes human capital used in production. Human capital accumulation equation is: Н() — ВНE() — 6H(), where HE(t) is human capital devoted to education. In total we have HE(t) + Hp(t) H(t). Denote the fraction of human capital allocated to production by ø(t). Please go as far as you can to characterize the balanced growth path of the economy.
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Assume the production function takes the general form: Y=Z*F (K,L,A)where all marginal products are positive.Which 3 of the following statements are correct?a. If A is fixed, then population growth acts as a drag on growth of output per person.b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that populationgrowth will always reverse the impact of technological improvements.c. Both rises in z and rises in K/L (capital intensity) will boost output per worker.d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), orboth.
If the current capital stock per person in South Korea is greater than the current capital stock per person in China and total factor productivity is the same in both countries, according to the Solow model: O a. China initially will grow slower than South Korea, but each will have the same steady state Ob. China initially will grow faster than South Korea, but each will have the same steady state О с. Both South Korea and China initially will grow at the same rate and have the same steady state O d. China initially will grow faster than South Korea and will have a lower steady state О . China initially will grow faster than South Korea and will have a higher steady state
how to do all parts?
Consider the Solow model with Cobb-Douglas production function with productivity parameter A, exponents on capital equal to 1/4, and exponent on labor equal to 3/4. Derive the MPL funcion as a function of K, L and constant A Note: xa is the same as x power a O (3/4) A(K/L) 0.25 O(1/4) A(L/KY0.76 O (1/4) A(KML)+0.75 O (3/4) A(UK) 0 25
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.
In class we argued that if people could accumulate human as well as physical capital, the production function would look like the “AK” production function. • (a) If the production function is AK and the savings rate is constant at rate “s”, and the rates of depreciation and populati on growth are δ and n respectively, what would the growth rate of the economy be? • (b) What would be the macroeconomic consequences of decreasing the savings rate in this economy? • (c) What would be the consequences of an increase in fertility in this economy? • (d) Would the consequences of decreasing fertility be UNAMBIGUOUSLY GOOD? • (e) Can human capital grow without bounds? Explain why or why not (make sure you discuss the physical nature of human capital). • (f) What is the growth rate of the economy (in the absence of technological progress) if human capital cannot grow without bounds?
Consider the Solow growth model with labor growth and no technology growth, i.e., n = 0, x = 0. Output is created by a Cobb-Douglas produc- n0,x tion function combining Labor, Lt, and capital, Kt, such that output, Y+is given by Y₁ = A+ KL Yt 1-a For a given time t, Given a level of Capital, and Investment, It, and a depreciation rate of capital, 8, the level of capital at time t+1 is given by the following law of motion of capital K++1 = Kt - 8Kt + It The labor growth rate in this economy is n = 2%, depreciation is 8 = 4%, the savings rate is s = 25%, and a = 0.3. Initial levels of capital, labor and technology are Ko = 10, Lo = 5, Ao = 1 respectively. The economy is assumed to be closed with no government spending. What is the value for capital per worker at time t = 1? (a) 2.22 (b) 2.57 (c)1.78 (d) 1.82
A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?

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