Consider a price-taking firm that has total fixed cost of $50 and faces a
market determined price of $2 per unit for its output. The wage rate is $10 per
unit of labor, the only variable input. Using the following table, answer the
questions below.
|
1 units of labor
|
2 Output
|
3 Marginal product
|
4 Marginal revenue product
|
5 Marginal Cost
|
6 Profit
|
|
1
|
5
|
|
|
|
|
|
2
|
15
|
|
|
|
|
|
3
|
30
|
|
|
|
|
|
4
|
50
|
|
|
|
|
|
5
|
65
|
|
|
|
|
|
6
|
77
|
|
|
|
|
|
7
|
86
|
|
|
|
|
|
8
|
94
|
|
|
|
|
|
9
|
98
|
|
|
|
|
|
10
|
96
|
|
|
|
|
Fill in the blanks in column 3 of the table by computing the marginal
product of labor for each level of labor usage. b. Fill in the blanks in column
4 of the table by computing the marginal revenue product for each level of
labor usage. c. How much labor should the manager hire in order to maximize
profit? Why? d. Fill in the blanks in column 5 of the table by computing
marginal cost. e. How many units of output should the manger produce in order
to maximize profit? Why? f. Fill in the blanks in column 6 with the profit
earned at each level of labor usage. g. Do your answers to parts c and e
maximize profit? Does it matter whether the manager chooses labor usage or
chooses output in order to maximize profit? Why? h. How much labor should the
manager hire when the wage rate is $20? How much profit is earned? Is marginal
product greater or less than average product at this level of labor usage? Why
does it matter? Q2: Suppose you own a home remodeling company. You are
currently earning short-run profits. The home remodeling industry is an
increasing-cost industry. In the long run, what do you expect will happen to a.
Your firm’s costs of production? Explain. b. The price you can charge for your
remodeling services? Why? c. Profits in home remodeling? Why? Q3: Higher
unemployment caused by the recession and higher gasoline prices have
contributed to a substantial reduction during 2008 in the number of vehicles on
roads, bridges, and in tunnels. According to The Wall Street Journal (April 28,
2009), the reduction in demand for toll bridge and tunnel crossing created a
serious revenue problem for many cities. In New York, the number of vehicles
traveling across bridges and through tunnels fell from 23.6 million in January
2008 to 21.9 million in January 2009. “That drop presents a challenge, because
road tolls subsidize MTA subways, which are more likely to be used as people
get out of their cars.” In an apparent attempt to rise toll revenue, the MTA
increased tolls by 10 percent on the nine crossings it controls. a. Is MTA a
monopolist in New York City? Do you think MTA possesses a high degree of market
power? Why or why not? b. If the marginal cost of letting another vehicle cross
a bridge or travel through a tunnel is nearly zero, how should the MTA set
tolls order to maximize profit? In order to maximize toll revenue? How are
these two objectives related? c. With the decrease in demand for bridge and
tunnel crossings, what is the optimal way to adjust tolls: raise tolls, lower
tolls, or leave tolls unchanged? Explain carefully? Q4: The Ali Baba Co. is the
only supplier of a particular type of Oriental carpet. The estimated demant for
its carpets is Q = 112,000 – 500P + 5M Where Q = number of carpets, P = price
of carpets (dollars per unit), and M = consumers’ income per capita. The
estimated average variable cost function for Ali Baba’s carpets is AVC = 200 –
0.012Q + 0.000002Q2 Consumer’s income per capita is expected to be $20,000 and
total fixed cost is $100,0000. a. How many carpets should the firm produce in order
to maximize profit? b. What is the profit maximizing price of carpets? c. What
is the maximum amount of profit that the firm can earn selling carpets? d.
Answer parts a through c if consumers’ income per capita is expected to be
$30,000 instead. Q5: A firm with two factories, one in Michigan and one in
Texas, has decided that it should produce total of 500 units to maximize
profit. The firm is currently producing 200 units in the Michigan factory and
300 units in the Texas factory. At this allocation between plants, the last
unit of output produced in Michigan added $5 to total cost, while the last unit
of output produced in Texas added $3 to total cost. a. Is the firm maximizing
profit? If so, why? If not, what should it do? b. If the firm produces 201 units
in Michigan and 299 in Texas, what will be the increase (decrease) in the
firm’s total cost? Q6: In 1999 Mercedes-Benz USA adopted a new pricing policy,
which it called NFP (negotiation-free process), that sought to eliminate price
negotiations between customers and new-car dealers. An article in The New York
Times (August 29, 1999) reported that a New Jersey dealer who had his franchise
revoked is suing Mercedes, claiming that he was fired for refusing to go along
with Mercedes’ no-haggling pricing policy. The New Jersey dealer said he
thought the NFP policy was illegal. Why might Mercedes’ NFP policy be illegal?
Can you offer another reason why the New Jersey dealer might not have wished to
follow a no-haggling policy? Q7: When Apple introduced its first portable media
player, the iPod, its constant marginal cost of producing the top-ofthe-line
model was $200 (iSuppli), its fixed cost was approximately $376 million, and we
estimate that its inverse demand function was p = 600 – 25Q, where Q is units measured
in millions. What was Apple’s average cost function? What were its
profit-maximizing price and quantity, profit, and Lerner Index? What was the
elasticity if demand at the profit-maximizing solution in a figure. (Hint: See
Q&A 9.2.) Q8: (10%) a. A Jean manufacturer would find it profitable to
charge higher prices in Europe than in the United States if it could prevent
resale between the two countries. What techniques can it use to discourage
resale? (Hint: See the Mini-Case, “Disneyland Pricing.”) b. As described in the
Mini-Case, “Google Uses Bidding for Ads to Price Discriminate,” Google uses
auctions to charge advertisers according to how much they are willing to pay to
reach a target audience. What type of price discrimination is this? Q - B onus :
Alpha and Beta, two oligopoly rivals in a duopoly market, choose prices of
their products on the first day of the month. The following payoff table shows
their monthly payoffs resulting from the pricing decisions they can make.
|
Alpha's price
|
|||||
|
High
|
Low
|
||||
|
Beta's
price
|
High
|
A
$200, $300
|
B
$50, $350
|
||
|
Low
|
C
$300, $150
|
D
$75, $200
|
|||
ANSWER
|
1.Unit
of labour
|
2.
Output
|
3.
Marginal product
|
4.
marginal revenue product
|
5.
Marginal Cost
|
6.
Porfit
|
7.
Overall Profit
|
|
1
|
5
|
5
|
10
|
10
|
0
|
-50
|
|
2
|
15
|
10
|
20
|
10
|
10
|
-40
|
|
3
|
30
|
15
|
30
|
10
|
20
|
-20
|
|
4
|
50
|
20
|
40
|
10
|
30
|
10
|
|
5
|
65
|
15
|
30
|
10
|
20
|
30
|
|
6
|
77
|
12
|
24
|
10
|
14
|
44
|
|
7
|
86
|
9
|
18
|
10
|
8
|
52
|
|
8
|
94
|
8
|
16
|
10
|
6
|
58
|
|
9
|
98
|
4
|
8
|
10
|
-2
|
56
|
|
10
|
96
|
-2
|
-4
|
10
|
-14
|
42
|
a. Fill in blanks in column 3 of the
table by computing marginal product of labour for each level of labour usage
: Done
as above
b. Fill in blanks in column 4 of the
table by computing marginal revenue product for each level of labour
usage : Done
as above
c. How much labour the manager hire
to maximise profit ?
The manager
should hire labour till margical revenue of product is higher than the marginal
cost ( implying the marginal product is contributing). The manager should hire
8 units of labour.
d. Fill in blanks in column 5 of the
table by computing marginal cost:
Done as above
e. How much unit the manager produce
in order to maximise profit? and Why ?
The manager
should produce output till marginal revenue is higher than the marginal cost.
So the manager should produce 84 units of out from 8 units of labour.
f. Fill column 6 with profit earned
with each level of labour usage.
Done as above (
column 5 marginal/incremental profit). Please also see another column 6
inserted and overall profit ( net of fixed cost) calculated for each level of
labour usage and output
Do your answer to par c and e
maximise profit ?
Yes, For
validations please also see column 6 which shows overall profit of $58 at 84
units of output from 8 units of labour.
Does it matter whether the
manager choose labour usage or chooses output in order to maximise profit ?
why?
No, it
should not matter so long the relationship between unit of labour and unit of
output remains same.
h. How much labour the manager
should hire when the wage rate is 20$? How much profit is earned? Is marginal
product is greater or less than the average product at this level labour usage?
Why does it matter?
Please find
below table with column 5 filled in based on labour rate at $20 per unit.
Porfit will be maximum ( loss will be minimum) at 77 level of output from 6
units of labour.
At this level
labour usage marginal product is 12 whereas the avaerage product is ( 77
divided by 6 equal to) 12.83; hence average product is higher. When marginal
product per additional unit of labour starts decreasing average product will
also start coming down.
|
1. Unit of labour
|
2. Output
|
3. Marginal Product
|
4. Marginal Revenue product
|
5. Marginal Cost
|
6. profit
|
7. Overall profit
|
|
1
|
5
|
5
|
10
|
20
|
-10
|
-60
|
|
2
|
15
|
10
|
20
|
20
|
0
|
-60
|
|
3
|
30
|
15
|
30
|
20
|
10
|
-50
|
|
4
|
50
|
20
|
40
|
20
|
20
|
-30
|
|
5
|
65
|
15
|
30
|
20
|
10
|
-20
|
|
6
|
77
|
12
|
24
|
20
|
4
|
-16
|
|
7
|
86
|
9
|
18
|
20
|
-2
|
-18
|
|
8
|
94
|
8
|
16
|
20
|
-4
|
-22
|
|
9
|
98
|
4
|
8
|
20
|
-12
|
-34
|
|
10
|
96
|
-2
|
-4
|
20
|
-24
|
-58
|
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