ECON 103, 2008-2
ANSWERS TO HOME WORK ASSIGNMENTS
Due the Week of July 14
Chapter 11
WRITE: [2]
Complete the following labour demand table for a firm that is hiring labour competitively and selling its product in
a competitive market.
Units of
Labour
Total Product
0
0
MPP
Product
Price
TR
$2
$0
17
1
17
$34
$2
$34
14
2
31
3
43
4
53
$28
$2
$62
$2
$86
12
$24
10
$20
$2
$106
7
5
60
6
65
MRP
$14
$2
$120
$2
$130
5
$10
a. How many workers will the firm hire if the going wage rate is $27.95? $19.95? Explain why the firm
will not hire a larger or smaller number of workers at each of these wage rates.
b. Show in schedule form and graphically the labour demand curve of this firm.
c.
Now redetermine the firm’s demand curve for labour, assuming that it is selling in an imperfectly
competitive market and that, although it can sell 17 units at $2.20 per unit, it must lower product
price by 5 cents in order to sell the marginal product of each successive labour unit. Compare this
demand curve with that derived in question 2b. Which curve is more elastic? Explain.
ANS: See table for marginal product data, total revenue data, and marginal revenue product data.
(a) Two workers at $27.95 because the MRP of the first worker is $34 and the MRP of the second
worker is $28, both exceeding the $27.985 wage. Four workers at $19.95 because workers 1 through 4
have MRPs exceeding the $19.95 wage. The fifth worker’s MRP is only $14 so he or she will not be
hired.
(b)
The demand schedule consists of the first and last columns of the table:
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Question
2-b
Question
11-2b
Quantity of labour demanded
(plotted at the halfway points
along the horizontal axis)
(c) Reconstruct the table.
Units of
Labour
Total
Product
0
0
MPP
Product
Price
TR
$0.00
17
1
17
$37.40
$2.20
$37.40
14
2
31
3
43
4
53
5
60
6
65
MRP
$29.25
$2.15
$66.65
12
$23.65
$2.10
$90.30
10
$18.35
$2.05
$108.65
7
$11.35
$2.00
$120.00
5
$6.75
$1.95
$126.75
The new labour demand is less elastic. Here, MRP falls because of diminishing returns and because product
price declines as output increases. A decrease in the wage rate will produce less of an increase in the quantity
of labour demanded, because the output from the added labour will reduce product price and thus MRP.
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WRITE [3] Suppose that marginal product tripled while product price fell by one-half in Table 11-1. What would
be the new MRP values in Table 11-1? What would be the net impact on the location of the factor demand
curve in Figure 11-1?
ANS: New MRP values (top to bottom): $21, 18, 15, 12, 9, 6, 3.
The factor demand curve would shift up, with the MRP fifty percent greater for each quantity of factor
demanded.
Units of
Resource
TP
0
0
MPP
Product
Price
TR
$1
0
21
1
21
$21
$1
21
$1
39
$1
54
$1
66
$1
75
$1
81
$1
84
18
2
39
3
54
4
66
5
75
6
81
7
84
MRP
$18
15
$15
12
$12
9
$9
6
$6
3
$3
WRITE [5]
What are the determinants of the elasticity of factor demand? What effect will each of the following have on the
elasticity or the location of the demand for factor C, which is being used to produce commodity X? Where there
is any uncertainty as to the outcome, specify the causes of that uncertainty.
a. An increase in the demand for product X.
b. An increase in the price of substitute factor D.
c.
An increase in the number of factors substitutable for C in producing X.
d. A technological improvement in the capital equipment with which factor C is combined.
e. A decline in the price of complementary factor E.
f. A decline in the elasticity of demand for product X due to a decline in the competitiveness of the
product market.
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ANS:
Four factors determine elasticity:
1. the rate at which the factor’s MP declines;
2. the ease of substituting other factors;
3. elasticity of product demand;
4. the ratio of the factor cost to the total cost of production.
(a)
Increase in demand C.
(b)
The price increase for D will increase the demand for C through the substitution effect, but decrease the
demand for all factors—including C—through the output effect. The net effect is uncertain; it depends on which
effect outweighs the other.
(c)
Increases the elasticity of demand for C.
(d)
Increases the demand for C.
(e)
Increases the demand for C through the output effect. There is no substitution effect.
(f)
Reduces the elasticity of demand for C.
WRITE [6]
Suppose the productivity of labour and capital are as shown below. The output of these factors sells in a purely
competitive market for $1 per unit. Both capital and labour are hired under purely competitive conditions at $3
and $1 respectively.
Units of
capital
MP of
capital
Units of
labour
MP of
labour
1
24
1
11
2
21
2
9
3
18
3
8
4
15
4
7
5
9
5
6
6
6
6
4
7
3
7
1
8
1
8
0.5
a. What is the least-cost combination of labour and capital to employ in producing 80 units of output?
Explain.
b. What is the profit maximizing combination of labour and capital the firm should use? Explain. What
is the resulting level of output? What is the economic profit? Is this the least costly way of producing
the profit-maximizing output?
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ANS:
(a) 22capital;
capital; 44labour.
labor. MPL /PL
7 / 1; MPC /PC 21/ 3 7 / 1.
(b) 7 7capital
capitaland
and77labour.
labor. MRP L / L 1
1/ 1
MRPC /PC
1 3 / 3 . Output is 142 (= 96 from
capital + 46 from labour). Economic profit is $114 (= $142 - $28) assuming there are no fixed costs.
Yes, least-cost production is part of maximizing profits; the profit-maximizing rule includes the leastcost rule.
WRITE [7]
In each of the following four cases, MRPL and MRPC refer to the marginal revenue products of labour and
capital, respectively, and PL and PC refer to their prices. Indicate in each case whether the conditions are
consistent with maximum profits for the firm. If not, state which factor(s) should be used in larger amounts and
which factor(s) should be used in smaller amounts.
a.
MRPL
$8; PL
b.
MRPL
$10; PL
c.
MRPL
$6; PL
d.
MRP L
$ 22; PL
$4; MRPC
$8; PC
$12; MRPC
$6; MRPC
$4 .
$14; PC
$12; PC
$26; MRPC
$16; PC
$9.
$12.
$19.
ANS:
(a) Use more of both.
(b) Use less labour and more capital.
(c) Maximum profits obtained.
(d) Use less of both.
CONSIDER: [1]
What is the significance of factor pricing? Explain in detail how the factors determining factor demand differ from
those underlying product demand. Explain the meaning and significance of the notion that the demand for a
factor is a derived demand. Why do factor demand curves slope downward?
ANS: All factors that enter into production are owned by someone, including the most important factor of all for
most people, self-owned labour. The most basic significance of factor pricing is that it largely determines
people’s incomes. Factor pricing allocates scarce factors among alternative uses. Firms take account of the
prices of factors in deciding how best to attain least-cost production.
Finally, factor pricing has a great deal to do with income inequality and the debate as to what
government should or should not do to lessen this inequality. It is here that the factors that determine factor
demand are most different from those that determine demand for products. Demand for products is a question
of income and tastes. But factor demand is more passive in the sense that it is derived from the demand for the
products the factor can produce. If a factor can’t be used in production of a desired product, there will not be any
demand for it. Additionally, factors are often less mobile than products, so their geographic location relative to
demand for the output they produce may be an important factor determining demand for factors in particular
geographic areas.
Factors of production are not hired or bought because their employer or buyer desires them for
themselves. The demand for factors is entirely derived from what the firm believes the factors can produce. If
there were no demand for output, there would be no demand for input.
The demand for a factor depends, then, on how productive it is in producing output and on the price of
the output. The demand for a factor is downsloping because of the diminishing marginal product of the factor
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(because of the law of diminishing returns) and, in imperfectly competitive markets, also because the greater the
output, the lower its price.
WRITE: During the 1980s Fraser Valley raspberry growers found it increasingly difficult to find people to pick
their crops. Students were no longer willing to do the work and recent immigrants were finding better paid jobs.
Many farmers purchased mechanical harvesting machines that cost upwards of $125,000. What impact did this
have on the demand for human berry pickers? What does that imply about the relative strengths of the
substitution and output effects? Currently some farmers are hiring Mexican pickers under the Seasonal
Agricultural Workers Program (SAWP). What will happen to the demand for mechanical harvesters if this
programme expands?
ANS: Since farmers could not hire workers to manually pick raspberries it is likely that the machines substituted
for labour. In this case the substitution effect likely dominated the output effect. Also, machine operators have a
higher level of skill than hand pickers, and clearly their MRP was higher. Ceteris paribus that would mean they
would earn higher wages. If the SAWP programme expands, it is likely that labour will be substituted for capital.
This will depend in part on the wages paid to that labour.
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