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1. (50 points total – 5 points for each of 8 parts plus 10 for diagram)
The production technology of a firm is given in the table below.
Table 1: Production Technology of a Firm
Number of workers
0
1
2
3
4
5
6
7
Units of output
0
48
84
108
128
143
155
165
MPN
N/A
48
84-48=36
108-84=24
128-108 = 20
143-128=15
155-143=12
165-155=10
a. Define the marginal product of labor,, explain how it relates to the production
function (with N on horizontal axis and Y on vertical axis) and find the marginal
product of labor (MPN) for each level of employment (fill in the third column of
table).
Marginal Product is the additional output each unit of labor provides, therefore if N is on the
horizontal axis and Y on the vertical axis, it is a function with decreasing returns to scale. To find
the table values simply calculate the increase in output each unit of labor provides.
b. Assume that the price of a unit of output is $10. Calculate the number of workers
that will be hired if the nominal wage rate = $190. Calculate the number of
workers the firm will hire if the nominal wage is $140. Calculate the number of
workers that the firm will hire if the nominal wage is $110.
To do this, you need to multiply output produced per person, on MPN, by $10, then
subtract the wage, and if the person is producing less than their wage, they will not be
hired. For the wage of 190, 4 workers will be hired. This is because 20*10=200 – 190 =
10, therefore that worker produces a positive cumulative output for the company. If the
5th worker was hired he would produce 15*10=150-190=-40, so the firm would lose
money hiring him. Similarly, the firm will hire 5 workers when the wage is 140, and 6
workers when the wage is 110.
Draw a production function and real labor demand curve vertically with the PF on top,
labeling point A as the wage / price combo of $190 / $10, point B as the $140 / $10
combo, and point C as the $110 / $10 wage / price combo. A correct and completely
labeled diagram is worth 10 points
c. What could cause wages to fall like this (name and support 2 reasons)?
Reasons that the wage could fall like this include many things. First, on the
demand side, competition for the jobs could increase, causing the workers to take
a smaller wage in an effort to get one of the jobs as more people are now
competing for them. Wages could also decrease like this on the supply side, for
example, if fixed costs rise, the company now has a smaller amount of money
with which they can pay wages, and wages fall.
d. Why exactly does the firm’s behavior change when the nominal wage fall like it
did, all else constant? In particular, explain exactly why the firm changes their
labor input when nominal wages fall from $190 to $140,all else constant (point A
to B). Make sure you refer to the profit maximizing condition when answering
this question.
When the nominal wage falls, the firm employs more labor because the wage, or
the price of labor has fallen. Because the wage has fallen, the firm can now
employ more workers, all else held the same, and still make the same level of
profit. In fact, the firm must change the level of labor to maximize profits. The
profit maximizing level of labor requires that the firm hire more workers when
wages are lower, because profits will increase with each additional worker who
can produce more than he is paid. Therefore, to maximize profits, the firm can
hire more, albeit less productive, workers at a lower wage.
e. Let’s return back to the initial conditions in the beginning of part b, with prices at
$10 and nominal wages at $190 (point A). Now we let prices change and fall
from $10 to $9. What could cause such a change (name at least 2 reasons)?
The price dropping from $10 to $9 could be caused by a variety of things,
including things on both the supply and demand side. For example, on the supply
side, if more people are producing this product, it will cause the price to drop as
there are now more people to buy the product from. Similarly, if demand for the
product drops, for example if a new, better version of the product is introduced,
then the price will drop like this.
f. Locate this ‘new’ point (W= $190, P=$9) as point D on your two diagrams.
Similar to part d) why exactly does the firm’s behavior change when price fall
from $10 to $9, all else constant? Make sure you refer to the profit maximizing
condition when answering this question, just as you did in part d. above.
The firm’s behavior changes in this instance because now, all else held the same,
labor is more expensive. This is because a person used to be able to produce his
MPN * 10, now he only produces his MPN * 9. Therefore, it makes it more
expensive to hire workers at every level, as what they produce is worth less than
before, and in order to maximize profit, the firm will hire less workers, and now
only to the point where MPN * 9 = wage.
g. Let’s return to point A, the initial conditions where the nominal wage rate = $190
and the price of a unit of output = $10. Assume that a new technology increases
the number of units of output that each worker can produce by 50%. Calculate
the number of workers that the firm will hire and the number of units of output
that will be produced (fill in the table below).
To find 50% increase, multiply the previous MPN of a worker by 1.5, and add
them all together to find total increase in output.
Table 2: Effects of New Technology
Number of workers
0
1
2
3
4
5
6
7
Units of output
0
72
72+54=126
162
192
214.5
232.5
247.5
MPN
0
48*1.5=72
36*1.5 = 54
36
30
22.5
18
15
Now locate this point as point E on both diagrams.
h. Comment on the macroeconomic implications of this technology shock (as in assume
many firms in the economy experience similar technology shocks) on: prices (inflation),
employment, the unemployment rate, economic growth, real wages (assume workers can
bargain for higher nominal wages), the stock market via the profit implications, and the
budgetary implications for the Government (make sure you refer to each economic
variable).
Prices will increase, as now all people make a higher wage as their MPN increases. This
will allow companies to increase their prices as people can afford the higher price, all else
held the same.
As far as employment is concerned, overall employment will rise as the MPN of workers
now increases, more workers will be hired, given any wage level. This will also cause the
unemployment rate to drop.
Real wages will increase, because, in equilibrium MPN = wage. Because MPN is now
higher for every worker, the wage will also be higher.
Because profits have risen due to the increase in output, the stock market will now
become stronger and more active as there are more profits to invest into the stock market.
Because there are higher wages and profits, the government will now have a larger base
to tax, given the same tax rate, and the government’s budget constraint will move
outward.
2. (50 points total – 5 for each of 8 parts and 10 for diagram)
For the new Real World State College season MTV is looking for Penn State students.
Students are asked to produce “drama” as a part of their contract. The marginal
productivity of labor curve is given by MPN = 135-2N.
The supply of Penn State students is given by Ns = 30 + 2 w; where w is the real wage
per hour.
a) Compute equilibrium values for the real wage and employment.
MPN = wage at equilibrium, so 135 – 2N = w
N = 30 + 2w, plug it in
135 – 2(30+2w) = w
135 – 60 – 4w =w
5w = 75
w = 15
Using the equilibrium wage, equilibrium employment can be found by plugging the
equilibrium wage into the supply function
30 + 2(15) = Ns
Ns = 60
Illustrate this equilibrium on a labor market diagram in real wage space. Please be sure
you label the diagram completely and label this initial equilibrium point as point A. A
correct and completely labeled diagram is worth 10 points
b) Now the Penn State student union successfully forces MTV to pay each student a
minimum “happy valley living real wage” equal to 25.00 per hour. That is, 25.00 per
hour is the effective real minimum wage. What is the level of employment now?
The level of Desired employment now is
Ns = 2(25) + 30 = 80. This is not the same as employment demanded now though, as
there is now a surplus of labor and the economy is in a disequilibrium.
c) Compare the number of people willing to work vs. the number of people MTV is
willing to hire under this living wage program. What do we call the difference in these
values when the quantity of labor supplied exceeds the quantity of labor demanded? Add
these two points to your diagram and label these points as point(s) B. Make sure you
identify the unemployed in your diagram.
At this point, the wage is higher than the equilibrium wage, so more people want the job
than there are jobs.
There is a surplus when the quantity supplied is larger than the quantity demanded.
d) The intuition part 1: Why exactly did we move along the labor demand curve? In
particular, why does the profit maximizing level of labor input change with the living
wage program (make sure you write out the profit maximizing condition and explain why
it has changed i.e., why does MTV rationally change their quantity demanded of labor the
way they did)?
We move along the demand curve rather than moving the curve out because it is simply a
shift in the price of Labor, or the wage. The profit maximizing condition is where MPN =
w. Because the w increased, the profit maximizing point also changes, as now a higher
MPN must be had to equal the increase in the wage.
e) The intuition part 2. We also experience a movement along the labor supply curve.
Explain the intuition here as in why are more people are willing to work using and
explaining the substitution and income effects associated with labor supply. Which effect
dominates and what has happened to the price of leisure given the living wage program?
The substitution effect claims that as the wage goes up, it becomes more costly to sit
at home and use leisure, because the opportunity cost of not working increases. The
income effect states that because your wage has increased, you are now richer, given
any level of work. In this case the substitution effect and income effects go in
opposite directions, and the substitution effect wins out, as more people now want to
work.
f) Suppose now that a new course offered by the Drama Department increases the
productivity of each student (via an increase in human capital!) so that the NEW
marginal product of labor equals MPN = 185 – 2N. Find the equilibrium ‘market’
clearing wage and level of employment. Please show all work below.
185 – 2(30+2w)=w
125 = 5w
w = 25
N = 30+25*2 = 80
Please depict this new development on your original diagram labeling this new
equilibrium point as point C. Be sure to label diagram completely.
g) Compare the welfare of the workers under the two scenarios: 1) the living wage
program vs. 2) no living wage program but the productivity shock as in part f. In other
words, are workers better off in part b) or are they better off in part f)? Be sure to explain.
Workers are better off under the no living wage program, as there is no deadweight loss
and instead all resources are being allocated efficiently, meaning the workers are better
off in part f.
h) .Compare the welfare of the firm, the producer. Is the firm better off in terms of
profits in part b) or in part f)? Be sure to explain (feel free to refer to the plastering
example and/or the new economy).
The firm is also better off in part f, because there is no deadweight loss. When an
economy is at a disequilibrium, it is bad for all actors involved as resources are not being
used efficiently and there could be an increase in economic surplus by reaching an
equilibrium. Therefore producers are better off in part f.
3. (40 points total – 5 for each of five parts and 15 points for diagram)
An economy’s aggregate production function is given by Y = A·K·N – N2. The marginal
product of labor for this production function is MPN = A·K – 2N.
a) Assume that A = 2 and K = 16. Suppose that the labor supply function for this
economy is given by NS = 4 + w. Find the equilibrium real wage rate, the full
employment level of employment, and the full-employment level of output for this
economy.
Real Wage Rate – where MPN = w, so AK – 2N = w, or where AK – 2(4+w)= w
2*16 – 8 -2w = w
24 = 3w
w=8
when w = 8, employment in the economy is Ns = 4 + 8 = 12
At this point Y = AKN – N2 = 16 * 2 * 12 – 122 = 240
Draw a production function and labor demand curve vertically as we did in class (many
times) and label this initial equilibrium point as point A. A correct and completely
labeled diagram is worth 15 points
b) Suppose that a new innovation leads to an increase in total factor productivity so that
A increases to 2.75. Everything else remains as in part a). Find the equilibrium real wage
rate, the full employment level of employment, and the full-employment level of output
for this economy and label on your diagrams as point B.
solve all equations the same way, expect A = 2.75
AK – 8 = 3w
2.75 * 16 – 8 = 3w
w = 12
Ns = 12 + 4 = 16
Y = 2.75 * 16 * 16 – 162 = 448
c) Let’s go back to our initial conditions (point A). Instead of a new innovation impacting
the economy, assume that severe weather destroys a portion of the capital stock, so that K
= 13. Everything else is as it was in part a). (In particular, A = 2.) Find the new levels of
the equilibrium real wage rate, the full employment level of employment, and the fullemployment level of output for this economy and label (on both diagrams) as point C.
Same thing again, except K = 13
2 * 13 – 8 = 3w
w= 6
N = w +4 = 10
Y = 10 *13 *2 – 10 2 = 160
d) Instead of a new innovation or bad weather impacting the economy (we are back to
point A), suppose that there is a change in the supply of labor so that NS = 7 + w (All else
remains as in part a)). (In particular, A = 2 and K = 16.) Find the new levels of the
equilibrium real wage rate, the full employment level of employment, and the fullemployment level of output for this economy and label on your diagrams as point D.
MPN = AK – 2 (7+w) = w
16 * 2 – 14 =3w
3w = 18
w=8
N = 7+6 = 13
Y = 16 *2 *13 – 132 = 247
e) Give two well supported answers as to why Ns might have changed as it did in part d)
above.
Ns means that at any given wage, there is a larger amount of labor in society. This may
have changed like it did above because of an increase in people who are qualified for that
job, for example there may be an recent increase in graduates from a university that are
now all qualified for that job only a few people could have earlier. Also, the opportunity
cost of leisure could’ve increased, so at every level of the wage there are more people
supplying their labor, as it is more expensive now to not supply than it was before.