Macroeconomics
13th Edition
ISBN: 9781337617390
Author: Roger A. Arnold
Publisher: Cengage Learning
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Chapter A, Problem 7QP
To determine
Special characteristics of a 45-degree line.
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evaluate the impact of government interventions, such as antitrust regulations, price controls, or subsidies, on various market structures. Select a specific industry and examine how these interventions have influenced competition, consumer welfare, and economic efficiency. Provide the pros and cons of government intervention.
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.
(a) Show that this production function exhibits constant returns to scale. [2 marks]
(b) What is the per-effective-worker production function, y = f(k), (where y = Y/AL
k K/AL)? (Show your working.)
[2 marks]
(c) Find expressions for the steady-state capital-output ratio, capital stock per
effective worker, and output per effective worker, as a function of the saving rate
(s), the depreciation rate (8), the population growth rate (n), the rate of
technological progress (a), and the coefficient a. (You may assume the condition
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)
The depreciation rate (8) increases
(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
K* if just the variable mentioned in the question part changes. Your answer should
state whether K* increases, decreases, or stays the…
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