Week 5 Tutorial Questions
Ch.3 – Productivity, Output, and Unemployment (Labor market equilibrium)
- Review question 3 (pg.133)
- Review question 5 (pg.133)
- Numerical problem 𝜶 (not in textbook)
- Numerical problem 3 (part a to b only) (pg.132)
- Analytical problem 2 (pg.133)
- Analytical Problem 4 (pg.133)
Note: due to time constraints, it may not be possible to do all questions during your tutorial class.
Nonetheless, its HIGHLY ADVISED that you do ALL tutorials questions in your own time.
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CH.3 – PRODUCTIVITY, OUTPUT,
MARKET EQUILIBRIUM )
AND
UNEMPLOYMENT (LABOR
Review question 3 (pg.133)
Define marginal product of capital, or MPK. How can the MPK be shown graphically?
The marginal product of capital (MPK) is the output produced per unit of additional capital. The
MPK can be shown graphically using the production function.
The MPK is just the slope of the production function.
For a fixed level of labor, plot the output provided by different levels of capital; this is the
production function.
Review question 5 (pg.133)
What is the MPN curve? How is the MPN curve related to the production function? How is it related to
labor demand?
The MPN curve shows the marginal product of labor at each level of employment.
It is related to the production function because the marginal product of labor is equal to the slope
of the production function (where output is plotted against employment).
The MPN curve is related to labor demand, because firms hire workers up to the point at which
the real wage equals the marginal product of labor (i.e., 𝐰 ∗ = 𝐍 ∗ )
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Labor demand curve shows relationship between the real wage rate and the quantity of labor
demanded. It is the same as the MPN curve, since 𝒘 = 𝑴𝑷𝑵 at equilibrium.
So, the labor demand curve is identical to the MPN curve, except that the vertical axis is the real
wage instead of the marginal product of labor.
Numerical problem 𝜶 (not in textbook)
The following data give real GDP, Y, capital, K, and labor, N, for the U.S. economy in various years.
Year
1960
1970
1980
1990
2000
2010
Y
3109
4722
6450
8955
12,560
17,784
K
3883
5863
8433
11,460
15,402
18,513
N
66
79
99
119
137
139
Assume that the production function is:
𝑌 = 𝐴𝐾0.3𝑁0.7
a.
By what percentage did U.S. total factor productivity grow between 1960 and 1970? Between 1970
and 1980? Between 1980 and 1990? Between 1990 and 2000? Between 2000 and 2010?
To find the growth of total factor productivity, you must first calculate the value of A in the
production function. This is given by:
𝑨=
𝒀
𝑲𝟎.𝟑 𝑵𝟎.𝟕
Substitute in the values for Y, K, and N for each year. Values are given in column “A”
below.
Next, the growth rate in productivity can be calculated as follows:
(
𝑨𝒕 − 𝑨𝒕−𝟏
) × 𝟏𝟎𝟎
𝑨𝒕−𝟏
Values are given in column “Growth in A (%)” below and plotted in Figure below.
Year
1960
1970
1980
1990
2000
2010
Y
3109
4722
6450
8955
12,560
17,784
K
3883
5863
8433
11,460
15,402
18,513
N
66
79
99
119
137
139
A
13.874
16.42
17.172
19.118
22.234
29.491
Growth in A (%)
18.4%
4.6%
11.3%
16.3%
32.6%
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1970
1990
1980
2000
2010
Numerical problem 3 (part a to b only) (pg.132)
Acme Widget, Inc., has the following production function.
Number of workers (N)
0
1
2
3
4
5
6
a.
Number of Widgets Produced (Y)
0
8
15
21
26
30
33
Find the marginal product of labour (MPN) for each level of employment
We calculate the MPN as ∆𝒀⁄∆𝑵, which is given in column “MPN” in the table below.
N
1
2
3
4
5
6
b.
Y
8
15
21
26
30
33
MPN
8
7
6
5
4
3
Acme can get $5 for each widget it produces. How many workers will it hire if the nominal wage is
$38? If it is $27? If it is $22?
We first need to calculate the marginal revenue product of labor (MRPN) when P = 5. This is
given in column “MRPN (P = 5)” below
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N
1
2
3
4
5
6
Y
8
15
21
26
30
33
MPN
8
7
6
5
4
3
MRPN (when P = 5)
(MPN × P) = 40
35
30
25
20
15
Thus:
▻ If W = $38:
Hire one worker, since MRPN ($40) is greater than W ($38) at N = 1.
Do not hire two workers, since MRPN ($35) is less than W ($38) at N = 2.
▻ If W = $27:
Hire three workers, since MRPN ($30) is greater than W ($27) at N = 3.
Do not hire four workers, since MRPN ($25) is less than W ($27) at N = 4.
▻ If W = $22: Hire four workers, since MRPN ($25) is greater than W ($22) at N = 4.
Do not hire five workers, since MRPN ($20) is less than W ($22) at N = 5.
Analytical problem 2 (pg.133)
How would each of the following affect the current level of full-employment output? Explain.
a.
A large number of immigrants enter the country.
An increase in the number of immigrants increases the labor force, increasing employment
and increasing full-employment output.
b.
Energy supplies become depleted.
If energy supplies become depleted, this is likely to reduce productivity, because energy is
a factor of production.
So the reduction in energy supplies reduces full-employment output.
c.
New teaching techniques improve the educational performance of high school seniors.
Better education raises future productivity and output, but has no effect on current fullemployment output.
d.
A new law mandates the shutdown of some unsafe forms of capital.
This reduction in the capital stock reduces full-employment output (although it may very
well increase welfare).
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Analytical Problem 4 (pg.133)
In each of the following scenarios, state whether the labor supply curve would shift to the left, to the right,
not shift at all, or if the shift is ambiguous because there is more than one effect and they would move
the curve in opposite directions.
a.
The stock market rises sharply.
Higher wealth shifts the labor supply (NS) curve to the left.
b.
Fewer teenagers work while in school than before.
Lower participation rate shifts the labor supply (NS) curve to the left.
c.
A large fraction of the population flees the country because of a bird flu (or COVID-19) epidemic.
Smaller working-age population shifts the labor supply (NS) curve to the left.
d.
The expected future wage declines and the stock market crashes
The lower future wage shifts the labor supply (NS) curve to the right, and the stock market
crash reduces wealth, causing the labor supply (NS) curve to shift to the right.
The magnitude direction obviously matters here. That depends on which effect is larger (i.e.,
lower future wage vs stock market crash) which can be examined empirically.
e.
The current real wage rate rises.
No effect; just a movement along the curve.
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