UNIVERSITY OF SOUTH FLORIDA
Department of Economics
Spring 2023
ECO 3203 002
1.
2.
Michael Loewy
Answers, Problem Set #2
If the consumer chooses to work, then they must work q hours which implies that they have h − q
units of leisure and wq − T units of consumption (since dividends equal zero). If the consumer
choose not to work, then they have h units of leisure and, due to the unemployment benefit,
consume b. It is possible for either of these allocations to yield higher utility than does the other.
a.
Suppose, as asked, that the real wage increases. For those consumers who previously chose
not to work, now they might choose to begin working. For those consumer who previously
chose to work, by assumption they can only work q units of time and so cannot increase
their hours of work when w increases. Combining these two results, it follows that because
in practice some consumer work and others do not, then an increase in the real wage will
lead to an increase in the quantity of labor supplied (all coming from those who switch
from not working to working).
b.
Suppose, as asked, that the unemployment benefit increases. For those consumers who
previously chose not to work, then they will continue to choose not to work. For those
consumers who previously chose to work, now they might chose to not work. Combining
these two results, it follows that because in practice some consumers work and others do
not, then an increase in the unemployment benefit will lead to a decrease in the quantity of
labor supplied (all coming from those who switch from working to not working).
a.
Computations
b.
13
12
11
10
9
8
7
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020
ln APL
ln z
It is apparent that the two productivity measures behave quite similarly, although there is
somewhat more variability in log z than in ln APL.
2
3.
c.
The average rate of growth of average labor productivity is 1.68% while the average rate
of growth of total factor productivity is 1.20%.
d.
Since total factor productivity includes both physical capital and labor in the denominator
while average labor productivity includes only labor in the denominator, we would expect
that the former grows more slowly than does the latter. In particular, the former effectively
removes the growth effect of capital on output and so will be smaller than is the latter.
a.
If the consumer’s preferences change such that their marginal rate of substitution of leisure
for consumption rises everywhere, then their indifference curves become steeper
everywhere. Effectively, the consumer now care more about leisure relative to
consumption than they did previously.
b.
If such a change in preferences were to occur, then graphically we have the following:
As we see from the graph, the consumer would choose to increase leisure and decrease
consumption. With the consumer choosing more leisure, employment and thus output must
decrease. Last, since the MRS is now greater than before, it follows that the real wage must
increase. [Effectively, there is a decrease in labor supply with no change in labor demand
so employment decreases and the real wage increases.]
c.
The change in preferences implies that consumption and employment are procyclical
(which they are) and that real wage is countercyclical (which it is not). This would lead us
to question whether business cycles are due to changes in preferences, here “contagious
laziness.” Moreover, changes in preferences are not observable so there is no way to verify
empirically that the decline in employment, consumption, and output were due to such a
change. For this reason, economists try to avoid using changes in preferences to explain
real world observations.
3
4.
a.
According to the graph, the coincident correlation coefficient between G and Y is weakly
positive, taking on a value of approximately 0.1.
b.
The largest correlation coefficient occurs when G lags Y by four quarters (one year). This
suggests that it might be the case that an increase in Y causes an increase in G since the
latter occurs later in time than does the former. [Be that as is may, one must not confuse
correlation for causation.]