Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK¹/2 H¹/4L1¹/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (a) Express output per person, y=Y/L, as a function of capital per person, k =K/L. (b) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (c) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. (d) Suppose first that sA

Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK¹/2 H¹/4L1¹/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (a) Express output per person, y=Y/L, as a function of capital per person, k =K/L. (b) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (c) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. (d) Suppose first that sA

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Problem 1. Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, 8, and a population growth rate, n. The production function is given by Y = AK + BK³3/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb- Douglas production function. • (i) Does this production function exhibit constant returns to scale? Explain why. (ii) Does it exhibit diminishing returns to physical capital? Explain why. • (ii) Express output per person, y =- as a function of capital per person, k =. • (iv) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (v) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. • (vi) Suppose first that sA 8 + n. Draw the savings and depreciation curves, making sure to label the steady state level of capital(if it exists). Under these circumstances,…
Problem 1. Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, 8, and a population growth rate, n. The production function is given by Y = AK + BK³3/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb- Douglas production function. • (i) Does this production function exhibit constant returns to scale? Explain why. • (ii) Does it exhibit diminishing returns to physical capital? Explain why. (iii) Express output per person, y =, as a function of capital per person, k =. • (iv) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (v) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. • (vi) Suppose first that sA 8 + n. Draw the savings and depreciation curves, making sure to label the steady state level of capital(if it exists). Under these…
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