Download economic growth, production function, and the labor

ECONOMICS 161
FALL 2003
E. McDEVITT
STUDY QUESTIONS-SET #3
ECONOMIC GROWTH, PRODUCTION FUNCTION, AND THE LABOR MARKET
1. What is a production function? What is meant by human capital? What are the key factors that determine
the level of output an economy can produce?
2. Use the following tables to answer the questions below:
Table 1
L Y MP VMP
0
0
---1 10
2 14.1
3 17.3
4 20
a. Fill in the rest of Table 1. Assume that P=$2. Draw a graph of the production function and marginal product
curve based on the numbers in Table 1.
b. If the nominal wage rate (W) is $10 per unit of labor, then a profit-maximizing firm will hire how many
workers? If the nominal wage rate (W) is $6 per unit of labor, then a profit-maximizing firm will hire how
many workers?
c. Suppose there is an increase in physical capital (K), holding A, H, and N constant. This change leads to a
new set numbers given in Table 2.
L
0
1
2
3
4
Table 2
Y
MP VMP
0
--14.1
20
24.5
28.3
Fill in the rest of Table 2 and a draw a graph of the production function and marginal product curve.
What general conclusion can you draw about how a change in K affects the production function and the MP
curve? Using Table 2, if the nominal wage rate (W) is $10 per unit of labor, then a profit-maximizing firm
will hire how many workers?
d. What other variables cause the production function and MP curve to shift? What are the reasons for this?
3. a.The MP of labor curve and the demand curve for labor are the same. True or false, explain.
b. An increase in labor causes the production function to shift up. T or F, explain.
c. A drop in the real wage rate causes the demand for labor curve to shift out. T or F, explain.
d. Improved technology destroys jobs for the economy as a whole. T or F, explain.
4. What variables cause a shift in the labor supply curve?
5. Use graphs of the production function and labor market to show how each of the following events affect the
level of US employment, real wages, and employment:
a. A war in the Middle East results in a large cut-off of oil.
b. New legislation that allows transferable pollution permits and thereby significantly reduces the burden of
environmental legislation.
c. A severe drought in the West.
d. A wave of new technological developments occurs.
e. A general rise in the level of educational attainment occurs.
6. Over the past couple of centuries there has been a large in increase in the population of the U.S., yet real
wages have risen dramatically over this same period of time. How would you explain this? Use the labor
market and production function graphs to explain your answer along with a brief written explanation.
7. What is meant by property rights? How does the protection of property rights affect economic growth?
Give your answer in terms of the variables A, K, H and N.
8. What role does saving and investment play in determining economic growth?
ANSWERS
1.Production Function: a table, graph or equation that shows the maximum amount of output that can be
produced from a given set of inputs and a given state of technology. More formally, the production function
is expressed as Y = Af(L, K, H, N), where Y = real output (real GDP), A= a measure of technology known
as total factor productivity, L= labor, K= physical capital (machines, buildings, tools, etc.), H= human
capital, and N = natural resources.
Human capital refers to the knowledge and skills that workers acquire through education (formal and
informal), training and experience.
The key factors are listed above—L, K, H, N, and A. As the level of employment (L) rises, an economy can
produce more output—that is, Y rises. Same with K, H, N and A.
2. a.
Table 1
L Y
0
0
1 10
2 14.1
3 17.3
4 20
MP VMP
---10
$20
4.1 $8.2
3.2 $6.4
2.7 $5.4
Y Production Function
MP
Marginal Product of Labor Curve
PF
20
17.3
14.1
10
10
4.1
3.2
2.7
MP curve
1 2
3
4
L
1
2
3
4
L
2b. A firm will another worker as long as VMP > W (or MP > W/P ). At a nominal wage of $10 the firm
would hire the first worker (since $20>$10), but not higher any more workers beyond this. Therefore, L=1.
If the nominal wage rate was $6, then the firm higher 2 workers (notice that VMP of the 2nd worker, $8.2,
exceeds $6).
2c.
L
0
1
2
3
4
Table 2
Y
MP VMP
0
--14.1 14.1 $28.2
20
5.9 $11.8
24.5 4.5 $9
28.3 3.8 $7.6
Y
Production Function
28.3
24.5
MP
Marginal Product of Labor Curve
PF(Table 2)
14.1
PF (Table 1)
20
17.3
14.1
10
5.9
4.1
3.2
2.7
10
MP curve (Table 2)
MP curve
(Table 1)
1
2
3
4
L
1
2
3
4
L
The general conclusion we can draw is that a change in K causes the production function and MP curve to
shift.
At a nominal wage rate of $10, the firm would hire 2 workers.
2d. In addition to K, the variables A, H, and N would also the shift these curves. An increase in anyone of
these variables makes labor more productive—that is, the economy can produce more any given amount of
labor. Thus, as K rises, workers have more machines, buildings, and tools to work with and this will allow
workers to produce more output. An increase in human capital means that workers have, on average, a greater
level knowledge and skills and are therefore the economy can produce more output with any given amount of
labor. Likewise, better technology makes workers more productive. Finally, a greater abundance of natural
resources means that the economy can produce more output at any given amount of labor.
3. True. A firm will continue to workers up the point at which MP = W/P. This means we can read off of the
MP curve the quantity of labor demanded at any given real wage rate. But this precisely what a demand curve
tells us—so they must be the same curve.
3b. False. An increase in L is represented as a movement ALONG a given production function curve. See
above graphs.
3c. False. A drop in the real wage rate is a movement ALONG a given labor demand curve—it does NOT
shift this curve.
3d. False. See answer to question 5d.
4. Population. There are other shift variables that may discuss in future lectures.
5. a. This would cause a drop in the variable N. This is, in turn, causes the PF and MP (i.e., Lad) curves to shift
down. The result is a drop in Y, L, and W/P. See Figure 5a.
5b. This would cause an increase in the variable A. This is, in turn, causes the PF and MP curves to shift up.
The result is a rise in Y, L, and W/P. See Figure 5b.
5c. This would result in a drop in A. See 5c.
5d. This would result in an increase in A. See Figure 5d.
5e. This would result in an increase in H. See Figure 5e.
5b,5d,5e
Y
Y
5a & 5c.
.
2
PF2
PF1
Y
Y
1
PF2
2
L
L
W/P
W/P
Ls
Ls
(W/P)
(W/P)
1
(W/P)
2
2
(W/P)1
Ld2=MP2
d
L 1=MP1
Ld2=MP2
L
2
L
1
L
Ld1=MP1
L
1
L
2
L
6. Although rising population shifts the labor supply curve to the right over time, the labor demand curve has
shifted to right at an even faster rate. This would explain the large rise in real wages despite the dramatic
increase in population. This large shift in labor demand can be explained by the following factors: an increase
in technology (increase in A), capital stock (increase in K), increase in human capital (H),and the rise in N.
Y
PF (2003)
Y2003
PF (c. 1800)
Y1800
W/P
L
Ls (2003)
(W/P)2003
Ls(c.1800)
(W/P)1800
Ld (2003)
Ld (c.1800)
L1800
L2003
Labor (L)
7. Property rights refer to the ability of people to use, sell, rent, and change the resources they own.
The protection of property rights allows owners to capture the gains from the development of resources and
inventions/innovations. Thus the adoption of institutions that reward productive behavior by protecting
property rights will encourage investment in research and development (for example, patents grant property
rights to the inventor/innovator of the idea or process) and this increases the variable A. It will encourage
investment in human capital (via education) and the discovery and development of natural resources. If
property rights are protected then savers will capture the gains of their saving effort. In turn, a higher level of
saving means a higher level of investment in physical capital (K), in human capital (H), in the development of
natural resources (N) and in R&D (A).
In summary, the link is roughly as follows: Institutions  A, K, H,N  labor productivity  real wage
rate
8. See answer to question (7).