Assume that in the Solow model the aggregate production function takes the Cobb-Douglas form: Y = 8K“ (AL)" 1-a where Y is output, K is capital input, L is labour input, and A is the level of labour- augmenting technical progress. Capital grows through investment but also decays due to wear and tear at a constant rate per period. Assume that A is growing at the exogenous rate g, that L is growing at the exogenous raten, and that households save a constant proportion s of their income. There is perfect competition in the markets for output and the inputs. a. Find the steady-state level of output per unit of labour in terms of A and the parameters of the model. What is the growth rate of total factor productivity (TFP) in terms of the parameters of the model? b. Find the steady state level of the capital-output ratio (k/y) in terms of the parameters of the model. c. Write down an expression for consumption per effective labour (c*) in the long run and show how

Assume that in the Solow model the aggregate production function takes the Cobb-Douglas form: Y = 8K“ (AL)" 1-a where Y is output, K is capital input, L is labour input, and A is the level of labour- augmenting technical progress. Capital grows through investment but also decays due to wear and tear at a constant rate per period. Assume that A is growing at the exogenous rate g, that L is growing at the exogenous raten, and that households save a constant proportion s of their income. There is perfect competition in the markets for output and the inputs. a. Find the steady-state level of output per unit of labour in terms of A and the parameters of the model. What is the growth rate of total factor productivity (TFP) in terms of the parameters of the model? b. Find the steady state level of the capital-output ratio (k/y) in terms of the parameters of the model. c. Write down an expression for consumption per effective labour (c*) in the long run and show how

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(b) Assume that the production function for an economy in the Solow Growth Model is given by: Y = K 1/3 (L x E) 2/3 (where Y = Total output; K = Capital stock; L = Labour force; E = advances in technology, which are measured as improvements in the efficiency of labour). The savings rate in the economy is 0.4, the depreciation rate is 0.1, the growth in the labour force is 0.05 and technology advances at a rate of 0.05 (each of these changes relate to a given time period). Calculate the steady state capital stock per efficiency unit of labour (k*).
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 a Solow model with a constant returns to scale Cobb - Douglas production function without technological progress. Use standard notation as in the Lecture. a. Construct a Solow graph in (Y/N) - (K/N ) space with capital per worker and output per worker in equilibrium such that the steady state capital stock per worker is in fact the consumption maximising one. Label all curves and equilibrium points.
Consider an AK model of endogenous growth. If the aggregate production function is given by Y=1.5K and the depreciation rate is 17.5%: What is the minimum savings rate such that this economy will experience growth in the long run?
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Question 3 Suppose that the production function is given by: Y = 0.5 K0.3 N0.7 where Y is aggregate output, K is aggregate capital and N is the number of workers (labour). a) In the context of the Solow model, derive the steady-state levels of capital per worker, output per worker and consumption per worker in terms of the saving rate, s, and the depreciation rate, 6. Show clearly your calculations and workings. b) Graphically show and explain the effect of a fall of the saving rate on steady state output, capital and consumption per worker.
Could you please please answer question d and e.
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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1. Consider an economy that operates under competitive markets and meets the assumptions of the Solow model. The production function is given as follows: Y(t) = K (t) 0.3 (A(t)L(t)) ⁰.7 Assume a saving rate of 15%, labor force growth rate of 2% and depreciation rate of 5% and effectiveness of labor growth rate of 8%. a. Show that the production function exhibit constant return to scale? b. Derive the production function for output per capita. c. Derive the production function for output per effective unit of labor. d. Find equilibrium real wage as a function of capital per unit of effective labor and effectiveness of labor. e. Find equilibrium real rental price of capital as a function of capital per unit of effective labor and effectiveness of labor. f. Solve for steady state level of capital per unit of effective labor. g. Find steady state level of output per unit of effective labor. h. Find growth rate of output and output per worker on the balanced growth path. i. Which one would…
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