5 LABOR MARKETS
Purpose: To show the determinants of wages in a simple market for labor. To show the effects
of imposing an effective minimum wage in a labor market. To show how equilibrium wages
change in response to changes in output prices, and labor productivity.
Computer file: labor98.xls
Instructions and background information:
The previous exercise showed how equilibrium price was determined in the market for a
good. Economists claim that the markets for labor can also be described using a model of supply
and demand. In particular, the equilibrium wage rate, which is the price of labor services, is
determined in a labor market.
But there are important differences between the markets for goods, such as spaghetti, and
the markets for inputs, such as labor. One is that the roles of consumers and firms in input
markets are reversed from what we saw in goods markets. This is because consumers are at the
same time both the suppliers of labor and the demanders of goods, while firms have the dual role
of suppliers of goods and demanders of labor.
Open the Excel file labor98.xls. What you see are some data on the market for unskilled
labor in Flint, Michigan, including the wage rate for that labor, the price of bread (the food of the
working classes), the price firms must pay for capital inputs, an index of labor productivity,
quantity supplied, quantity demanded, and excess demand at the currently selected wage.
Quantities of labor are measured as the number of workers employed, assuming each worker
labors for 8 hours a day. The wage rate is the hourly wage. To find the daily wage just multiply
the wage rate by 8.
Firms produce automobiles that sell for $18,000 each. On the labor supply side, the
workers have the chance to be employed either in the automobile industry at the going wage, or
join the army and receive, on average, the wage of a corporal.
You should experiment by trying some different values for the selected wage, and each of
the demand and supply variables. The factors listed under DEMAND DATA and SUPPLY
DATA cause the respective curve to shift. Be sure you understand the reasoning behind the
shifts. For example, an increase in the index of labor productivity (perhaps because workers get
extra training) results in an increase in labor demand. Be sure you can explain why labor demand
changes at all in this case, and why the change in demand for labor is an increase and not a
decrease. Why does it cause the demand curve to shift, compared to moving along the curve?
5-1
In questions 7-10 you’re asked to explore the effects on labor markets of increases in the
prices of goods that consumers buy. To understand these questions you need to know the
difference between the money wage and the real wage workers are paid. The money wage is
simply the number of dollars per hour that workers get paid. The real wage is the wage in terms
of goods — the amount of goods workers earn per hour. For example, the real wage of unskilled
workers in terms of bread is the number of loaves of bread the worker earns per hour. You
compute the real wage by dividing the money wage by the price of goods. In this example the
real wage is the money wage divided by the price of bread.
Here are some things to watch for and learn as you do the problems:
1)
Labor markets can achieve equilibrium through changes in the money wage.
2)
An effective minimum wage will cause some unemployment, but may also raise the
incomes of employed workers as a group. The effect on incomes depends on the
elasticity of demand for labor.
3)
An increase in the price of the output sold by the firm will ultimately increase the
money and real wages of workers.
4)
Higher wages in other occupations such as the army have effects on the wages of
unskilled labor.
Here are some hints:
1)
The spreadsheet is not sensitive to the units of measurement, such a dollars, when
you enter answers. You can always omit dollar signs ($), for example, and still get
the right answer. But the spreadsheet is sensitive to sign (+ or -), so be careful on
that account.
2)
If you use trial and error, rather than Goal Seek, to get an answer, remember that
you usually have to be accurate to within about one-tenth of one percent of the
exact answer. Sometimes, however, being accurate within five percent (plus or
minus) will be ok.
__________________________
MATH MAVEN’S CORNER: The demand function for labor is given by D ( L) = ( A) w aT b pcc ,
where w is the money wage for unskilled labor, pc is the price of capital, and T is the technology
f
index for labor. The supply function for labor is given by S ( L) = ( M )( w − t ) n pbread
w cf , where w
is the wage rate, pbread is the price of bread, wc is the corporal’s wage, and t is a tax per hour of
labor. The values of all of the parameters are randomly assigned.
5-2
LABOR MARKETS
Questions
Set all variables to their baseline values.
1)
What is the equilibrium hourly wage for unskilled labor in this market?
2)
What is the equilibrium level of employment?
Set all variables to their baseline values, and set the wage to its equilibrium level. The price of
output (automobiles) rises to $23,000.
3)
4)
What’s the new equilibrium wage?
What’s the new level of equilibrium employment level?
Set all variables at their baseline values, including the price of automobiles. You are a consultant
to the auto industry in Flint, Michigan, and have been asked by your bosses to advise them on the
effects of a recent Pentagon proposal. The proposal is to change the military pay scale so the
average wage for a corporal in the army will rise to $12 per hour.
5)
What’s the new equilibrium wage in the unskilled labor market?
For the proposal in the last question to raise corporals’ wages to $12 per hour,
6)
What’s the new level of employment in the market for unskilled labor?
Set all variables to their baseline values. The price of bread rises to $4.00 per loaf.
7)
What’s the new equilibrium wage rate?
8)
What’s the new equilibrium level of employment?
Set all variables to their baseline values.
9)
What’s the real wage (in terms of bread) of unskilled labor in the baseline equilibrium?
When the price of bread rises to $4 per loaf, and the market for unskilled labor adjusts to
its new equilibrium,
10)
What’s the new real wage of unskilled labor?
11)
With all variables at their baseline values, and the labor market in equilibrium, what’s the
TOTAL HOURLY INCOME FROM WAGES of unskilled workers as a group?
Set all variables to their baseline values. Your task is to pick a value for an effective minimum
wage. [Choose a wage less than $20, so it shows on the graph.]
12)
What wage rate do you choose?
13)
For the minimum wage you chose in the last question, did the incomes of unskilled
workers increase or decrease compared to the market equilibrium wage
5-3
Set all variables to their baseline values, and set the wage to its equilibrium level. The
government imposes a tax of $2 per hour worked.
14)
What’s the new hourly take-home wage of workers?
5-4
2/26/2022
LABOR MARKET
4:31 PM
((Q/SSF*500)*(CORWAGE^-SSB)*(PBREAD^-SSD))^(1/SSA)+TAX
(QD/(DDA*1000)*(POUTPUT^-DDB)*(LABPROD^-DDE)*(PCAP^-DDF))^(1/DDDD)
QS=(SSF*500)*((WAGE-TAX)^SSA)*(CORWAGE^SSB)*(PBREAD^SSD))
Qd=(DDA*1000)*POUTPUT^DDB*WAGE^DDDD*LABPROD^DDE*PCAP^DDF
1000
0,012913
12102,66
12
SUP
DEM
WAGE
2000
0,04928
2776,6
12
hourly wage
3000
0,108
1174
12
DEMAND
20
SUPPLY
18
16
14
12
4000
0,188095776
637,0103092
12
5000
0,28949
396,567
12
MARKET DATA
Selected hourly wage $12,00
Quantity demanded
25.955
Quantity supplied
34.363
Excess demand
-8.408
10
8
6
4
2
L
0
0
15000
30000
45000
60000
SUPPLY DATA
Corporal’s hourly wage $5,00
Price of bread
$3,00
Per hour tax on labor
$0,00
75000
DEMAND DATA
Output price
$18.000
Labor productivity
0,500
Price of capital
$100
6000
0,411752
269,2407
12
7000
0,554619
194,0663
12
8000
0,717879
146,1434
12
9000
0,901347
113,7981
12
10000
1,104861
90,98065
12
11000
1,32828
74,3077
12
12000
1,571475
61,76942
12
13000
1,83433
52,11241
12
14000
2,116738
44,52286
12
15000
2,418601
38,45415
12
16000
2,739828
33,52835
12
17000
3,080335
29,47754
12
18000
3,440043
26,10764
12
19000
3,818878
23,27531
12
20000
4,21677
20,87286
12
21000
4,633652
18,81816
12
22000
5,069462
17,04773
12
23000
5,52414
15,51186
12
24000
5,99763
14,17119
12
25000
6,489877
12,99426
12
26000
7,00083
11,95567
12
27000
7,530439
11,03473
12
28000
8,078657
10,21447
12
29000
8,645436
9,48085
12
30000
9,230735
8,822183
12
31000
9,834509
8,228683
12
32000
10,45672
7,692101
12
33000
11,09732
7,205446
12
34000
11,75629
6,762762
12
35000
12,43357
6,358954
12
36000
13,12913
5,989637
12
37000
13,84295
5,651027
12
38000
14,57498
5,33984
12
39000
15,32519
5,05322
12
40000
16,09356
4,788668
12
41000
16,88004
4,543996
12
42000
17,68461
4,317279
12
43000
18,50724
4,106816
12
44000
19,34791
3,911105
12
45000
20,20657
3,72881
12
46000
21,08321
3,558743
12
47000
21,9778
3,399845
12
48000
22,89032
3,251166
12
49000
23,82073
3,111857
12
50000
24,76901
2,981154
12
51000
25,73514
2,858369
12
52000
26,71909
2,74288
12
53000
27,72084
2,634126
12
54000
28,74038
2,531598
12
55000
29,77766
2,434833
12
56000
30,83268
2,343413
12
57000
31,90541
2,256953
12
58000
32,99583
2,175104
12
59000
34,10392
2,097548
12
60000
35,22966
2,023993
12
2/26/2022
ANSWER SHEET
LABOR MARKET ANSWERS
Question
Answer
1
$8,95
CORRECT
2
3
$10,20
CORRECT
4
5
6
7
8
9
10
11
12
13
14
Name: Deartis Holt
Student Num.:
1239461
4:31 PM
ANSWER BIN
change in demand
change in quantity demanded
complements
decrease
elastic
excess demand
excess supply
income
increase
inelastic
inferior
normal
own-price
price of labor
price of sauce
price of tacos
price of wine
substitutes
Page 3
20 COMPETITIVE MARKETS IN
THE SHORT-RUN
Purpose: To illustrate price determination in the short-run in a competitive market, and to relate
price determination to the choices made by competitive firms.
Computer file: srmkt198.xls
Instructions and background information:
You are a government economist studying the wine industry with an eye to commenting
on some proposed policies that may affect the industry.
On the spreadsheet for this problem set the graph at the left shows the short-run average
and marginal cost curves for a typical wine producing firm. The graph at the right shows the
market supply and demand curves for wine when there are 500 firms in the industry, and
consumer incomes are $55,000 per family. Market price is $40 per case. At this price the market
is probably not in equilibrium, nor is the typical firm maximizing total profit.
The variables you can choose here are market price, the firm’s output, income, a tax rate,
and the number of firms. Excel automatically computes all the other values in the tables.
The wine industry is assumed to be perfectly competitive. The price of wine is determined
in the market by supply and demand. In equilibrium excess demand for wine must be zero. Firms
in the industry take the market price as a constant, and try to maximize profits by choosing an
output level. In equilibrium for the firm, marginal revenue must equal marginal cost. Firms in the
industry must adjust their outputs in response to changes in the market equilibrium price.
Your report about the wine industry must contain information about the industry’s likely
responses to changes in underlying economic conditions, as well as changes in government
policies. To this end, you will conduct a series of hypothetical experiments using the model in this
problem set.
You will first explore a change in income that affects the market demand for wine. Then
you will explore the effects of government imposing a per unit tax on wine, including effects on
price, quantity, profits, and social welfare measured by consumer and producer surplus.
Here are some things to watch for and learn as you do the problems:
20-1
1)
Competitive markets adjust to equilibrium through changes in price. If a good is
produced in perfect competition, it is supply and demand in the market that determine the price.
2)
A competitive firm takes market price as given, and tries to maximize profit by
choosing output so that marginal cost equals marginal revenue. Because price is constant for the
typical competitive firm, marginal revenue and price (average revenue) are equal.
3)
An increase in market demand raises equilibrium price, induces firms to sell more,
and increases economic profit.
4)
An increase in a per unit (excise) tax raises the market supply curve and firms’
marginal and average cost curves by the amount of the tax per unit. The decrease in market
supply raises price, but by less than the tax, and reduces quantity. Firms reduce output because
marginal cost rises by more than price. Profits fall.
5)
The excise tax causes a loss in total welfare as measured by consumer and
producer surplus.
Here are some hints to help you get the answers more quickly:
1)
Use Goal Seek to find the market equilibrium price. After you find the price, use
Goal Seek again to find the firm’s output that will make MR-MC equal to zero.
2)
You’ll need a calculator to figure out total profits. The quickest way to do that is
to find the profit per unit (P-AC) and multiply by output.
3)
To find the loss in welfare from the tax, sketch the supply and demand curves
before and after the tax on a piece of scrap paper. Previously computed market quantities will
give you the important information you’ll need to find the deadweight loss.
___________________________
MATH MAVEN’S CORNER: For this problem the market demand curve is given by
Q ( D ) = aI − b( P ) , where I is income, P is price, and a and b are randomly picked constants. The
market supply curve is given by Q ( S ) = N ( P − t − d ) / c , where N is the number of firms in the
industry, t is the tax per unit of output placed on all firms, and d and c are constants. The cost
curves of the typical firm are AC = d + (c / 2)( q ) + ( FC / q) + t , and MC = d + c ( q) + t . FC is
fixed cost.
20-2
COMPETITIVE MARKETS IN THE SHORT-RUN
Questions
Set income, the tax, and the number of firms to their baseline values.
1) What’s the market equilibrium price of wine?
2) What’s the market equilibrium quantity of wine?
Set income, the tax, and the number of firms to their baseline values.
3) With the market in equilibrium, what output should the firm produce to maximize
profit?
4) How much is maximum total profit?
With the tax still at zero, reduce income to $45,000.
5) Is wine normal or inferior?
Continuing on from question 5,
6) What’s the new market equilibrium price?
7) What’s the new market equilibrium quantity?
With income still at $45,000, and the market in equilibrium,
8) What output should the typical firm produce?
9) What are the maximum profits of the typical firm?
10A) Return all variables to their baseline values, and make sure the number of firms is
500. Make sure the market is in equilibrium, and that the typical firm is maximizing
profit. Go on to question 10B).
The government imposes a tax of $10 per case on all wine produced and sold.
10B) What’s the new equilibrium market price of wine?
Continuing on from the last question,
11) What’s the new equilibrium market quantity of wine?
12) For the $10 tax on wine, how much did the price of wine rise?
13) At the new equilibrium price of wine, what is the profit maximizing output of the
typical firm?
14) What are the firm’s maximum profits after the tax?
15) For the $10 tax on wine, how much total tax is paid by the typical firm?
16) What are the total tax collections of the government?
17) For the $10 tax on wine, with the market and firm in the new equilibrium, what is the
deadweight loss to society in consumer and producer surplus due to the tax?
20-3
2/26/2022
SR COMP
4:31 PM
AC(FIRM)
MC(FIRM)
1
2
# 135,98171
# 11,673316
3
94,660848
12,364921
5
62,01912
13,74813
6
54,03159
14,43973
7
48,42501
15,13134
8
44,30653
15,82294
9
41,1801
16,51455
10
38,74813
17,20615
11
36,8212
17,89776
12
35,27307
18,58936
13
34,01631
19,28096
14
32,98848
19,97257
15
32,14381
20,66417
16
31,44794
21,35578
17
30,87463
22,04738
18
30,40344
22,73899
19
30,01824
23,43059
20
29,70615
24,12219
21
29,45672
24,8138
22
29,26139
25,5054
23
29,11312
26,19701
24
29,00603
26,88861
25
28,93516
27,58022
26
28,89635
28,27182
27
28,88603
28,96342
28
28,90114
29,65503
29
28,93906
30,34663
30
28,99751
31,03824
31
29,07449
31,72984
32
29,16828
32,42145
33
29,27734
33,11305
34
29,40032
33,80465
35
29,53604
34,49626
36
29,68343
35,18786
37
29,84154
35,87947
38
30,00954
36,57107
39
30,18665
37,26268
40
30,37219
37,95428
41
30,56556
38,64589
42
30,76618
39,33749
43
30,97355
40,02909
44
31,18722
40,7207
45
31,40676
41,4123
46
31,63179
42,10391
47
31,86196
42,79551
48
32,09694
43,48712
49
32,33645
44,17872
50
32,58022
44,87032
51
32,82798
45,56193
52
33,07951
46,25353
53
33,3346
46,94514
54
33,59305
47,63674
55
33,85468
48,32835
56
34,11931
49,01995
57
34,3868
49,71155
58
34,65698
50,40316
59
34,92972
51,09476
60
35,2049
51,78637
61
35,4824
52,47797
62
35,7621
53,16958
63
36,0439
53,86118
64
36,3277
54,55278
65
36,6134
55,24439
66
36,90093
55,93599
67
37,1902
56,6276
68
37,48113
57,3192
69
37,77365
58,01081
70
38,06769
58,70241
71
38,36319
59,39402
72
38,66009
60,08562
73
38,95832
60,77722
74
39,25785
61,46883
S(MKT)
D(MKT)
PRICE
0
1000
# 11,673316
# 56,569686
#
40
2000
13,056525
55,850982
40
4000
15,82294
54,41358
40
5000
17,20615
53,69487
40
6000
18,58936
52,97617
40
7000
19,97257
52,25747
40
8000
21,35578
51,53876
40
9000
22,73899
50,82006
40
10000
24,12219
50,10136
40
11000
25,5054
49,38265
40
12000
26,88861
48,66395
40
13000
28,27182
47,94525
40
14000
29,65503
47,22654
40
15000
31,03824
46,50784
40
16000
32,42145
45,78914
40
17000
33,80465
45,07043
40
18000
35,18786
44,35173
40
19000
36,57107
43,63303
40
20000
37,95428
42,91432
40
21000
39,33749
42,19562
40
22000
40,7207
41,47692
40
23000
42,10391
40,75821
40
24000
43,48712
40,03951
40
25000
44,87032
39,32081
40
26000
46,25353
38,6021
40
27000
47,63674
37,8834
40
28000
49,01995
37,1647
40
29000
50,40316
36,44599
40
30000
51,78637
35,72729
40
31000
53,16958
35,00859
40
32000
54,55278
34,28988
40
33000
55,93599
33,57118
40
34000
57,3192
32,85248
40
35000
58,70241
32,13378
40
36000
60,08562
31,41507
40
37000
61,46883
30,69637
40
38000
62,85204
29,97767
40
39000
64,23525
29,25896
40
40000
65,61845
28,54026
40
41000
67,00166
27,82156
40
42000
68,38487
27,10285
40
43000
69,76808
26,38415
40
44000
71,15129
25,66545
40
45000
72,5345
24,94674
40
46000
73,91771
24,22804
40
47000
75,30091
23,50934
40
48000
76,68412
22,79063
40
49000
78,06733
22,07193
40
50000
79,45054
21,35323
40
51000
80,83375
20,63452
40
52000
82,21696
19,91582
40
53000
83,60017
19,19712
40
54000
84,98338
18,47841
40
55000
86,36658
17,75971
40
56000
87,74979
17,04101
40
57000
89,133
16,3223
40
58000
90,51621
15,6036
40
59000
91,89942
14,8849
40
60000
93,28263
14,16619
40
61000
94,66584
13,44749
40
62000
96,04904
12,72879
40
63000
97,43225
12,01008
40
64000
98,81546
11,29138
40
65000
100,1987
10,57268
40
66000
101,5819
9,853975
40
67000
102,9651
9,135271
40
68000
104,3483
8,416568
40
69000
105,7315
7,697865
40
70000
107,1147
6,979162
40
71000
108,4979
6,260458
40
72000
109,8811
5,541755
40
73000
111,2643
4,823052
40
$/q
$/Q
60
60
50
50
40
40
30
30
20
20
MC
10
AC
0
q
0
20
40
60
FIRM DATA
Output
39,66
AC
$30,31
MC
$37,72
MR-MC
$2,28
MC-AC
$7,41
80
SUPPLY
10
DEMAND
0
0
20000 40000 60000 80000 100000
100
MARKET DATA
Price
$40,00
Q(D)
24.055
Q(S)
21.479
Q(D)-Q(S)
2.576
No. of firms
500
Q
POLICY VARIABLES
Income
$55.000
Tax per unit
$0,00
2/26/2022
SR COMP
75
39,5586
62,16043
76
39,86055
62,85204
77
40,16363
63,54364
78
40,4678
64,23525
79
40,77304
64,92685
80
41,07928
65,61845
81
41,3865
66,31006
82
41,69467
67,00166
83
42,00374
67,69327
84
42,31368
68,38487
85
42,62447
69,07648
86
42,93607
69,76808
87
43,24846
70,45968
88
43,56161
71,15129
89
43,87549
71,84289
90
44,19008
72,5345
91
44,50536
73,2261
92
44,8213
73,91771
93
45,13788
74,60931
94
45,45509
75,30091
95
45,77289
75,99252
96
46,09128
76,68412
97
46,41024
77,37573
98
46,72974
78,06733
99
47,04977
78,75894
100
47,37032
79,45054
39,66
74000
112,6475
4,104349
40
75000
114,0308
3,385645
40
76000
115,414
2,666942
40
77000
116,7972
1,948239
40
78000
118,1804
1,229536
40
79000
119,5636
0,510832
40
80000
120,9468
-0,20787
40
81000
122,33
-0,92657
40
82000
123,7132
-1,64528
40
83000
125,0964
-2,36398
40
84000
126,4796
-3,08268
40
85000
127,8628
-3,80139
40
86000
129,2461
-4,52009
40
87000
130,6293
-5,23879
40
88000
132,0125
-5,9575
40
89000
133,3957
-6,6762
40
90000
134,7789
-7,3949
40
91000
136,1621
-8,11361
40
92000
137,5453
-8,83231
40
93000
138,9285
-9,55101
40
94000
140,3117
-10,2697
40
95000
141,6949
-10,9884
40
96000
143,0781
-11,7071
40
97000
144,4613
-12,4258
40
98000
145,8446
-13,1445
40
99000
147,2278
-13,8632
40
100000
148,611
-14,5819
40
0
39,66
$40,00
4:31 PM
2/26/2022
ANSWER SHEET
COMPETITIVE MARKETS IN THE SHORT-RUN
Question
Answer
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Name:
Student Num.:
4:31 PM
ANSWER BIN
a
ac
b
c
change in demand
change in quantity demanded
complements
decrease
elastic
equal
excess demand
excess supply
greater
income
increase
inelastic
inferior
less
mc
no
normal
own-price
price of labor
price of sauce
price of tacos
price of wine
substitutes
yes
Page 4
Purchase answer to see full
attachment
