A firm faces the following production function,Y = AKL¹-a(1)Here Y is output, K is capital, L is fixed labour, and A is a measure of technology. The firmuses an optimal amount of capital determined by the condition,MPK = r + 8(2)Where MPK is the marginal productivity of capital, r is the real interest rate, and 8 is thedepreciation rate.(a) Using equations (1) and (2) find an expression for K*, the optimal amount of capital thefirm should use.(b) Referring to you result from part (a), comment on what happens to K* when each of thefollowing variables change (holding other variables constant),The measure of technology (A) fallsThe depreciation rate (8) increasesThe real interest rate (r) increases(i)(ii)(iii)[Hint: For each of parts (i)-(iii) you are being asked to comment on what happen to K* if justthe variable mentioned in the question changes. Your answers should state whether K*increases, decreases, or stays the same. This should be accompanied for each part by asentence or two of explanation.](c) Suppose that a = 0.5, L = 25, and A = 20. Further, the real interest rate, r, is 2% andcapital depreciates at a rate (8) of 18% per year. What is the optimal amount of capitalthis firm should install?(d) Now suppose that A increases to 25, while a, Land & remain unchanged. Further, theoptimal capital stock remains at the amount you found in part (c). What does this meanmust have happened to the real interest rate? Find the new real interest rate and draw aclear diagram showing MPK and user cost of capital lines before and after the changesto A and r.

A firm faces the following production function, Y = AKa L¹-a (1) Here Y is output, K is capital, L is fixed labour, and A is a measure of technology. The firm uses an optimal amount of capital determined by the condition,

A firm faces the following production function, Y = AKa L¹-a (1) Here Y is output, K is capital, L is fixed labour, and A is a measure of technology. The firm uses an optimal amount of capital determined by the condition,

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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