Economics (MindTap Course List)
13th Edition
ISBN: 9781337617383
Author: Roger A. Arnold
Publisher: Cengage Learning
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Chapter 19.1, Problem 3ST
To determine
Identify the change in total revenue in different circumstances.
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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.
(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…
In the week-4 materials, when deriving labour supply, we assumed that the
substitution effect dominated the income effect. What impact would there be on
labour supply if this was not the case? Briefly investigate how such a change could
theoretically affect the imposition of a minimum wage above the market clearing
wage. (Your answer is likely to benefit from diagrammatic support.)
Chapter 19 Solutions
Economics (MindTap Course List)
Ch. 19.1 - On Tuesday, the price and quantity demanded are 7...Ch. 19.1 - What does a price elasticity of demand of 0.39...Ch. 19.1 - Prob. 3STCh. 19.1 - Prob. 4STCh. 19.2 - Prob. 1STCh. 19.2 - Prob. 2STCh. 19.4 - Prob. 1STCh. 19.4 - Prob. 2STCh. 19.4 - Prob. 3STCh. 19.4 - Prob. 4ST
Ch. 19 - Prob. 1QPCh. 19 - For each of the following, identify where demand...Ch. 19 - Prove that price elasticity of demand is not the...Ch. 19 - Prob. 4QPCh. 19 - Prob. 5QPCh. 19 - Suppose a straight-line downward-sloping demand...Ch. 19 - Prob. 7QPCh. 19 - Prob. 8QPCh. 19 - Prob. 9QPCh. 19 - Prob. 10QPCh. 19 - Prob. 11QPCh. 19 - Prob. 12QPCh. 19 - Prob. 13QPCh. 19 - Prob. 14QPCh. 19 - A college raises its annual tuition from 23,000 to...Ch. 19 - As the price of good X rises from 10 to 12, the...Ch. 19 - The quantity demanded of good X rises from 130 to...Ch. 19 - The quantity supplied of a good rises from 120 to...Ch. 19 - Prob. 5WNG
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