Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 3, Problem 3.10P
(a)
To determine
To discuss:If
(b)
To determine
To explain:Along with diagram, why MRS > 1 when
(c)
To determine
To discuss: If the function is homothetic.
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Consider an economy that exhibits both population growth (L grows at rate n) and
technological progress (A grows at rate a) described by the production function,
Y = F(K, AL) = Ka (AL)¹-α
Here K is capital and Y is output.
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[2 marks]
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that capital per effective worker evolves according to Ak = sf (k) - (a+n+8)k.)
[5 marks]
(d) Show that at the Golden Rule steady state the saving rate for this economy is
equal to the parameter a.
[6 marks]
A firm faces the following production function,
Y = AKα 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,
MPK = r +8
(2)
Where MPK is the marginal productivity of capital, r is the real interest rate, and ♪ is
the depreciation rate.
(a) Using equations (1) and (2) find an expression for K*, the optimal amount of
capital the firm should use.
[3 marks]
(b) Referring to your result from part (a), comment on what happens to K* when
each of the following variables change (holding other variables constant),
(i)
The measure of technology (A) falls
(ii)
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(iii)
The real interest rate (r) increases
[2 marks]
[2 marks]
[2 marks]
[Hint: For each of parts (i)-(iii) you are being asked to comment on what happens to
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state whether K* increases, decreases, or stays the…
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