The representative household supplies a constant unit of labor idealistically and has standard preference+86.teexp(-pt) In c(t)dt, p>0 c(t)= (ca(t)-YA)"A CM (t)" (cs(t) +7s)",in which cA (t) > 7A, CM (t) > 0, cs(t) > 0, and the parameters satisfy YA > 0, 7s > 0, 7A > 0, 7M > 0, ns > 0,and Σje{A.M.S) = 1. The prices corresponding to (CA(t), CM (t), cs(t)) are (pA(t), 1, ps(t)). Each of the threesectors je {A, M, S} has a common production function on capital K, (t) and effective labor X(t)L, (t)Y, (t)=B, K, (t)" (X(t)L, (t))¹-a, in which X(t): = exp(g-t), 00.Assume no capital depreciation and only sector j = M produces investment goods. All sectors share the samefactor market for capital and labor. Answer all questions about the economy in competitive equilibrium.(a) What is the lower bound of initial capital that makes sure c₁(t) > YA, CM (t) > 0, cs(t) > 0?(b) Prove that the capital-labor ratio is identical across all sectors?(c) Solve for PA (t) and ps(t) in terms of the parameters?(d) What is the relationship between CA (t), CM (t), and cs(t)?(e) Prove that cs(t) grows faster than CM (t) and CM (t) faster than cA(t).LM (1)CM (1)CM (L)LM (1)(f) Find the condition of parameters under which(g) Prove that the growth rate of the three sectors will converge under (f). A<=9and= 0 in the equilibrium.

Given the parameters and the production function, we can derive the lower bound of initial capital…

(a) What is the lower bound of initial capital that makes sure CA (t) > YA, CM (t) > 0, cs(t) > 0? (b) Prove that the capital-labor ratio is identical across all sectors? (c) Solve for PA (t) and ps(t) in terms of the parameters? (d) What is the relationship between CA(t), CM (t), and cs(t)? (e) Prove that cs(t) grows faster than CM (t) and CM (t) faster than cA(t). (f) Find the condition of parameters under which CM (1) CM (L) (=g and LM = 0 in the equilibrium. (t) (g) Prove that the growth rate of the three sectors will converge under (f). A

(a) What is the lower bound of initial capital that makes sure CA (t) > YA, CM (t) > 0, cs(t) > 0? (b) Prove that the capital-labor ratio is identical across all sectors? (c) Solve for PA (t) and ps(t) in terms of the parameters? (d) What is the relationship between CA(t), CM (t), and cs(t)? (e) Prove that cs(t) grows faster than CM (t) and CM (t) faster than cA(t). (f) Find the condition of parameters under which CM (1) CM (L) (=g and LM = 0 in the equilibrium. (t) (g) Prove that the growth rate of the three sectors will converge under (f). A

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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