Download HW #2

ECON 3560/5040
Homework #2 (Answers)
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Part A (7 points) Fill-in Questions
(1) [2 points] If a firm hires an additional unit of capital while keeping other inputs constant, its
production increases by the Marginal Product of Capital (MPK)
(2) [2 points] The Real Wage is what a worker is paid measured in units of output rather than
in dollars
(3) [3 points] The circular flow model shows that households use income for Consumption,
Tax , and (Private) Saving
Part B (13 points)
(1) [4 points] Neoclassical Theory of Income Distribution
Use the neoclassical theory of distribution to predict the impact on the real wage (w) and
real rental price of capital (r) of each of the following events
(a) [2 points] A wave of immigration increases the labor force
According to the theory, the real wage equals the MPL. Because of diminishing returns
to labor, an increase in the labor force causes the MPL to fall. Hence the real wage (w)
falls and real rental rate (r) rises
(b) [2 points] An earthquake destroys some of the capital stock
Since MPK equals the real rental price of capital, the earthquake causes the MPK to rise
and , hence, the real rental rate (r) rises and the real wage (w) falls
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Table 1: Output, Labor, and MPL
L
Y
MPL
0
1
2
3
4
0
5
9
−
5
2
1
12
(2) [5 points] Production Function
(a) [3 points] Graph the production function holding K constant
See lecture note
(b) [2 points] Graph the M P L curve with M P L on the vertical axis and L on the horizontal
axis. Is M P L diminishing?
See lecture note
(3) [4 points] State whether you think each of the following questions is true (T), false (F), or
uncertain (U) and briefly explain your answer. No credit will be given for an answer without
any explanation
(a) [2 points] If bread is produced by using a constant returns to scale (CRS) production
function, then if the number of workers doubled, twice as much bread will be produced
False. A production function has CRS if an increase of an equal percentage in all factors
of production causes an increase in output of the same percentage. Therefore, if bread
is produced by using a constant returns to scale (CRS) production function, then if the
amounts of equipment (capital) and workers (labor) are both doubled, twice as much
bread will be produced
(b) [2 points] A competitive, profit-maximizing firm hires capital until the marginal product
of labor (M P L) equals money wage (W )
False. A competitive, profit-maximizing firm hires capital until the marginal product of
labor (M P L) equals real wage (w = W/P ) or price of output multiplied by the marginal
product of labor equals the money wage (P × M P L = W )
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Part C (10 points) Working with Macroeconomic Data
For data to use in these exercises, go to the Federal Reserve Bank of St. Louis FRED database
at research.stlouisfed.org/fred
(1) [5 points] On the same figure, graph national saving (Series ID: GPDI) and investment (Series
ID: GSAVE) as fractions of GDP (Series ID: GDP), using quarterly U.S. data since 1947.
How is it possible for investment to exceed national saving, as it does in some period?
See attached figure 1
(2) [5 points] Graph the annual (December to December) CPI inflation rate and the annual
(fourth quarter to fourth quarter) GDP deflator inflation rate since 1960 on the same figure.
What are the conceptual differences between these two measures of inflation? Use CPI for all
urban consumers: all item (Series ID: CPIAUCNS) and GDP deflator (Series ID: GDPDEF)
to calculate the inflation rates
See attached figure 2
3
24
22
20
18
16
14
12
10
50
55
60
65
70
75
80
I/Y
85
90
95
00
05
S/Y
Figure 1: Investment and national saving as fractions of GDP, using quarterly U.S. data (1947:Q12008:Q3)
4
14
12
10
8
6
4
2
0
-2
60
65
70
75
CPI
80
85
90
95
00
05
GDP_DEFLATOR
Figure 2: Annual CPI inflation rate and the annual GDP deflator inflation rate (1960-2008)
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