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PROBLEM SET 7
1.
Keggs produces pantyhose for barmaids. Both the labor and product markets
are perfectly competitive. Keggs’ production function for pantyhose is below.
NUMBER OF
WORKERS
(L)
2
3
4
5
6
7
PAIRS OF
PANTYHOSE
PER HOUR
(Q)
25
40
54
67
79
90
TOTAL
REVENUE
(TR)
MARG. REV.
PRODUCT
(MRP)
--
Suppose that each pair of pantyhose sells for $5. Suppose further that the average
wage rate per worker is $60 a day. Keggs is currently employing four workers. Is
this the optimal number of workers for Keggs to hire? Why or why not? (HINT:
Find the TR and MRP schedules)
2.
The following table shows the marginal physical product associated with
different numbers of pizza chefs hired by “Crazy Jean’s Pizza Parlor.
NUMBER OF
PIZZA CHEFS
(L)
0
1
2
3
4
5
6
a.
b.
c.
d.
e.
MARGINAL
PHYSICAL
PRODUCT
(MPPL)
-35
30
25
20
15
10
MARG. REV.
PRODUCT
(MRP)
P = $3
--
MARG. REV.
PRODUCT
(MRP)
P = $4
--
Assuming a price per pizza of $3, find the marginal revenue product
schedule.
Draw Crazy Jean’s demand curve for pizza chefs.
If the chefs are paid $45 a day, how many will Crazy Jean hire?
How many would Crazy Jean hire if chefs’ wages rise to $60 per day?
Suppose the price of a pizza rises from $3 to $4. What happens to the
demand curve for chefs? How many chefs will Crazy Jean hire if
chefs must be paid $60 a day (as in part d)? Does Crazy Jean hire
more or fewer chefs than in part d? Does the change in the number of
chefs hired make economic sense?
2
3.
A widget producer has the following production function showing the quantity of
widgets that can be produced for various amounts of labor hired.
NUMBER OF
WORKERS
(L)
2
3
4
5
6
7
NUMBER OF
WIDGETS
(Q)
25
40
54
67
79
90
TOTAL
REVENUE
(TR)
MARG. REV.
PRODUCT
(MRP)
--
a.
Calculate the widget producer’s Total Revenue and Marginal
Revenue Schedules.
b.
Draw the widget producer’s demand schedule.
c.
If the wage rate the widget producer has to pay to each worker
hired is $20, how many workers should the producer hire?
d.
If the wage rate increases to $40, how many workers should the
producer hire?
3
4.
Suppose that a single widget producer, operating in perfectly competitive product
and labor markets has the following demand and supply curves for labor and therefore
initially hires L1 workers.
Wage rate
$20
A
SL
DL = MRP
L1
Number of workers (L)
For each separate event below, show what will happen to the number of workers
the firm will hire. Draw a separate diagram for each part.
a.
b.
c.
d.
New equipment increases the marginal productivity of labor.
A new technology reduces the marginal productivity of labor.
The wage rate that must be paid to widget workers increases to $25.
The price at which the producer can sell widgets increases.
4
SELECTED ANSWERS
1.
PAIRS OF
PANTYHOSE
PER HOUR
(Q)
25
40
54
67
79
90
NUMBER OF
WORKERS
(L)
2
3
4
5
6
7
TOTAL
REVENUE
(TR)
125
200
270
335
395
450
MARG. REV.
PRODUCT
(MRP)
-75
70
65
60
55
Hiring four workers is not optimal because MRP > wage rate: by hiring more
workers the firm can add more to its total revenue than to its total costs (NOTE: the
5th worker’s, MRP, the addition to total revenue, is $65 while the wage rate, the
addition to total costs, is only $60). Thus, the firm should hire up to 6 workers
where MRP = w.
2. a.
MARGINAL
PHYSICAL
PRODUCT
(MPPL)
-35
30
25
20
15
10
NUMBER OF
PIZZA CHEFS
(L)
0
1
2
3
4
5
6
b.
MARG. REV.
PRODUCT
(MRP)
P = $3
-105
90
75
60
45
30
MARG. REV.
PRODUCT
(MRP)
P = $4
-140
120
100
80
60
40
The demand curve for chefs is the MRP schedule:
105
90
DL = MRP
0
c.
1
2
3
4
5
5 chefs where MRP = w.
6
L
5
d.
4 chefs where MRP = w.
e.
The marginal revenue product of each additional chef hired increases.
(See chart on previous page). Thus, the demand curve shifts to the right. Crazy Jean
will hire 5 chefs, where MRP = w. Since the marginal revenue product of each
additional worker hired has increased (workers contribute more to Crazy Jean’s total
revenues), it is profitable to hire more workers than in part d.
3.
a.
NUMBER OF
WORKERS
(L)
2
3
4
5
6
7
b.
c.
NUMBER OF
WIDGETS
(Q)
25
40
54
67
79
90
6 workers where MRP = w.
4 workers where MRP = w.
TOTAL
REVENUE
(TR)
$60
110
150
180
200
210
MARG. REV.
PRODUCT
(MRP)
-$50
40
30
20
10
6
4.
a.
b.
A
A
$20
$20
c.
d.
$25
$20
$20
A
A