Economics 370
Professor H.J. Schuetze
Practice Problem Set 3
(ANSWERS)
1. a)
Income
•
0
•
Leisure Time
Substitution Effect: As the wage falls the opportunity cost of leisure goes down (leisure becomes
relatively cheaper). Thus, the worker will substitute away from consumption and towards
leisure. The individual will work less.
Income Effect: As the after-tax wage falls, the real wealth of the individual also falls. As income
falls the individual will purchase less leisure if leisure is a normal good. The individual will work
more.
Overall Effect: Putting together the income and substitution effects it is clear that the overall
effect is unknown. The income and substitution effects oppose one another.
Note: you should also draw a diagram that illustrates the income and substitution effects.
b) According to the dynamic model of labour supply, the effects on hours worked of the
permanent change in the tax (hence the wage) are likely to be less than those of the short-term or
transitory change. This is because of difference in the likely magnitude of the income effects of
the two tax increases. Both transitory and permanent increases in the tax will result in a
substitution effect. In other words, the relatively lower after-tax wages will induce workers to
substitute consumption with more leisure because it has become cheaper. The difference,
however, is in the relative size of the income effects. The permanent increase in the tax will
result in a larger reduction in lifetime income than a transitory increase. In both cases the
reduction in income will result in a reduction of leisure consumed provided leisure is a normal
good. Thus, the permanent increase in the tax has a larger “work inducing” income effect that
counteracts the “work reducing” substitution effect.
c) The results in the case of the static labour supply model in a) are exactly the same as the
results for a permanent increase in the tax in b). Both of these have the usual income and
substitution effects. Assuming an increase in taxes in a static model is exactly the same as
assuming the tax increases forever (there is only one period). This also means that the results in a
will differ from the results in b) for a transitory increase in the tax.
2. a) MRPN = P*MPN
= 10(50 + .25N - .025N2)
= 500 + 2.5N – 0.25N2
A maximum is reached at 5 workers.
∂MRPN
= 2 .5 N − 0 .5 N = 0
∂N
Max occurs at N = 2.5/0.5 = 5
Marginal revenue product falls to zero at 50 workers.
500 + 2.5N – 0.25N2=0, or
N2 - 10N - 2000 = 0
(N-50)(N+40) = 0
So, at N=50
b) Given w = $250
The firm will hire up to the point where w = MRPN
250 = 500 + 2.5N – 0.25N2
0 = 250 + 2.5N – 0.25N2
N2 – 10N -1000 = 0
It turns out that this question does not have a simple solution. Instead you need to use the
formula for solving a quadratic.
N=
2
− b ± b 2 − 4ac 10 ± 10 − 4(1)(1000)
=
2a
2
Solving, you get N = 37.
c) In this case, the monopsonist’s marginal cost curve is the industry supply curve. Thus, the firm
will equate supply with MRPN.
4.75N = 500 + 2.5N – 0.25N2
Rearranging, you get:
N2 + 9N -2000 = 0
Once again, you will need to solve using the formula for a quadratic.
You get N is approximately equal to 40.
3. a) The diagram below illustrates how in a monopsony, the firm faces the upward sloping
market supply curve. Since hiring more workers implies paying a higher wage, the marginal cost
of labor is above the supply curve and also upward sloping. The firm follows the profit
maximizing rule of setting marginal revenue product of labor (MRP) equal to the marginal cost
of labor (MC), and chooses to hire L* units of labor. The equilibrium wage is read off of the
supply curve (w*). Wages are below MRP.
MC
w
S
MRP
wpc
w*
MRP
L*
Lpc
L
In a perfectly competitive market, the MRP curve is the demand curve, so that where supply and
demand intersect there is more labor hired (Lpc) at a higher wage (wpc).
b) They test for whether the wage is below marginal revenue product. They find evidence of
monopsony behavior, because w/MRP in the disputed years is less than w/MRP in years not
suspected of monopsony behavior. (You should be able to expand on this)
c) Now, wpc=$50k, and a minimum wage is imposed at $75k. The minimum wage becomes
the new supply curve, as long as it is above the market supply curve. A flat supply curve implies
the marginal cost of labor is the supply curve. Thus, if MRP>$75k then profit maximizing
implies hiring more labor (L') as shown below. If MRP< $75k, then fewer professors will be
hired, since the minimum wage will cross MRP at less than L*.
MC
w
S
MRP
wpc
w*
MRP
L*
Lpc
L
4. State whether you agree or disagree with each of the following statements. If you agree with
the statement, explain why you agree, and if you disagree, explain why you disagree (include the
correct statement in your answer). I encourage you to illustrate your answers using diagrams
where appropriate.
a) In a dynamic life-cycle model of labour supply, the labour supply response to a permanent
unanticipated wage decrease is likely to be bigger than the response to a transitory unanticipated
wage decrease of similar magnitude.
Disagree:
Wage
B
D
C
A
Age
The labour supply response is smaller to a permanent unanticipated wage decrease than
to a transitory one. In the above graph, movement from A to B shows a permanent unanticipated
wage increase. Here you can see that this person’s entire wage schedule has been shifted
upwards. A movement from C to D shows a transitory unanticipated wage increase. This only
shifts the wage schedule up for a short period of time. Although the effect on lifetime wages is
greater for a permanent increase, the effect on labour supply is smaller. The reason for this is
because of the income and substitution effects. In both cases the increase in wages leads to
people substituting towards labour. The income effect however, is spread over the whole
lifetime in the life cycle model. Since the increase in income due to a permanent wage change is
much larger, the income effect (which induces a person take more leisure at all wages) is much
larger in the case of a permanent wage change.
b) The short-run labour demand curve is the firm's MRPN curve below ARPN.
Agree:
wage
w1
w0
ARPN
MRPN
N1
N0
Why is the MRPN curve the demand curve?:
With perfect competition MC=AC=wage
So, the firm hires up to the point where MRPN = wage
N
If the wage = w0 the firm will hire N0 workers.
Why just below ARPN?
The firm will shut down in the short-run if total cost of labor (VC) exceeds the total revenue
product of labor (TR)
i.e. if VC > TRPN or if VC/N > TRPN/N ⇒ w > ARPN
So at wages higher than w1 the firm would choose to shut down.
c) Non-Discriminating Monopsonists are at a disadvantage relative to competitive buyers of
labour because when the monopsonist wants to expand its work force, it has to raise wages,
while the competitive buyer can get all the labour it wants at the going wage.
This statement should be qualified. It is true that if the monoposonist wants to hire another
worker, it has to move up its upward-sloping labour supply curve a little bit, which means that
the wage paid to the entire work force increases. In comparison, the employer in a competitive
labour market can recruit another employee by paying her the same wage as all of the other
workers are receiving. The incorrect part of the statement is that the monopsonist operates at a
disadvantage due to the differing nature of labour supply. All other factors held constant, the
total wage bill (and not just the marginal cost of hiring one worker) is lower in a monopsonistic
setting. The monopsonist will pay a lower equilibrium wage and employ a lower number of
people than is the case in the competitive labour market (This is illustrated in your notes).