Download Managerial Economics MGCR 293 Practice

Managerial Economics MGCR 293
Practice Questions for the Final Examination
2009 - 2010
Part 3
Please note that these sample questions are chosen from mass tutorial notes in previous years. Solutions
are checked by my Teaching Assistant. Please e-mail me if any errors, calculations or otherwise, are
detected.
Regards,
Dr. Salmasi
1) The Lamour Manufacturing Company’s short-run average cost function in 2001 is: AC
= 5+6Q, Where Ac is the firm’s average cost (in dollars per unit of the product), and Q is
its output rate.
a. Obtain an equation for the firm’s short-run total cost function.
b. Does the firm have any fixed costs? Explain.
c. If the price of the Lamour Manufacturing Company’s product (per pound) is $2, is
the firm making profits or losses? Explain.
a. Because the total cost equals the average cost times the output, the firm’s total
cost function is: C=AC× Q= 5Q + 6Q2
b. No, since total cost equals to zero when Q=0
c. If price is $2 then total revenue (R) equals 2Q. Thus, the firm’s profit equals:
π= R-C=2Q-(5Q+6Q2)=-3Q-6Q2
If Q is greater than zero, π must be negative, and therefore means the firm is
incurring losses. If the firm is producing nothing, it is incurring neither profits nor
losses. Thus, the firm is better off producing nothing.
2) Jacob’s total variable cost function has been calculated to be TVC = 100Q + 30Q² - Q³,
where Q is the number of units of output.
a. When marginal cost is a minimum, what is the output level?
Marginal cost = dTVC/dQ
= 100 + 60Q -3Q² , dMC/dQ= 60 - 6Q = 0, 6Q = 60, Q = 10
Therefore, the output level is 10 units.
b. When average variable cost is a minimum, what is the output level?
Average variable cost = TVC/Q = 100 + 30Q - Q²
It is a minimum when dAVC/dQ = 30 - 2Q = 0, Q = 15, Therefore, the output
level is 15 units.
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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c. What is the average variable cost and marginal cost at output level found in part
b?
a. Marginal cost = 100 + (60×15) - (3×225)
= 100 +900 - 675 = $325
b. Average Variable Cost = 100 + (30×15) – (225)
= 100 + 450 - 225
= $325
d. If Jacobs’s produces 3000 shirts and 2000 pants a year, the total cost is $100,000. If
it produced only 3000 shirts, the cost would be $80,000. If it produced only the
pants, it would $30,000. What is the degree of economies of scope?
S = C(Q1) + C(Q2) – C(Q1 + Q2)
C(Q1 + Q2)
= 80,000 + 30,000 – (100,000)
100,000
= 0.1
3) Vogue Inc, an international fashion Magazine is developing a special edition for
pregnant women interested in buying maternity clothing. The cost of developing the
special edition is $100 000. Vogue receives $150 000 from clothing sponsors in return for
advertising in the catalogue. The cost (excluding developing costs) of printing and
advertising each magazine is $2.50.
The demand schedule for the magazines is as follows:
Price per Magazine (in can$)
6.00
6.50
7.00
7.50
8.00
8.50
Magazines Sold (in thousands)
30
28
24
21
18
15
a) What price should Vogue Inc. charge for a magazine?
b) What is the maximum amount that Vogue should pay (excluding what it receives from
sponsors) in order to develop the special edition?
c) Given the money it receives from its sponsors, how much profit does Vogue effectively
make by selling the special edition?
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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(a) :
Magazines Sold
( in Thousand)
30
28
24
21
18
15
Price
(Can. $)
6.0
6.5
7.0
7.5
8.0
8.5
Total Revenues
(000 Can$)
180
182
175
165
152
127.5
Total Cost (000)
(Excluding Dvl’t cost)
75
70
62.5
55
47.5
37.5
Total Profits
(000 Can$)
105
112
112.5
110
104.5
90
Vogue Inc. will therefore maximize profit if it sets a price of $7.00.
b) The maximum Vogue could pay, excluding what it receives from sponsors is $112 500
since this is the maximum it could make given the demand schedule of the magazine.
c) Given the money it receives from sponsors, vogue makes a profit of 112 500 +
(150 000 – 100000) = 112 500 + 50 000 = $162 500.
4) Titan Inc. produces steel sheets, and its president believes the company to be the price
leader of the industry (due to its advance technology, Titan believes that it offers high
quality steel at very competitive prices).
The Demand curve for the whole steel market is Qd =100 + 2P and the Supply
curve for the small firms in the market is Qs = 5 + 4P. Where Q is the number of sheets to
produce daily, and P is the price charged per sheet.
1)
2)
3)
Answers:
1)
If Titan’s TC is 80 +0.75Q², at what level should Titan operate to
maximize its profits?
What price should Titan charge?
What is the total output of the industry?
TCt= 80+0.75Q2
so MCt = 1.5Q
Residual Demand (for Titan the price leader)
Qt = Qd - Qs = 100 + 2P – 5 – 4P = 95 – 2P
P = 95/2 – 1/2Qt
TRt = 47.5Q – 0.5Qt²
MRt= 47.5 –Qt
Setting MR=MC, we obtain 47.5 – Qt = 1.5Qt
47.5 = 2.5Qt therefore Qt=19 units
In order to maximize its profit Titan should produce 19 sheets of steel daily.
2) Titan should charge P= 47.5 – 0.5(19) = 38$
3) The output of the whole industry is Qd = 100+2(38)=176.
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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5) Royal Waters Inc. has been providing water services in the Principality of Monaco for
nearly a century. The demand for water is determined to be P= 40 – 5Q, where Q is the
number of clients served (in millions) and P is the price charged (in millions of Euro).
Royal Waters total costs are determined by TC= 10 – 0.75Q. If Royal Waters total assets
equal 550,000,000 what is the company’s rate of return, if it produces at profit maximizing
level of output?
To maximize output Royal must produce at MR = MC, i.e. 40 – 10Q = - 0.75
40.75 = 10Q
Q = 4.075
Consequently, P = 40 – 5(4.075) = 19.63€
Accounting profit therefore is
Π = 19.63*4.08 – [10 – 0.75(4.08)] = 80.07 – 6.94 = 73.13€ (i.e. 73,130,000€)
Royal Water’s rate of return is therefore 73.13/550 = 0.133 or 13.3%
6) Last year, the cola industry was perfectly competitive. At an output of 15 000 bottles
per month, the average cost was $3 at the lowest point on the long-run average cost curve.
The market demand for cola is: QD = 75 000 - 8 000P, Where QD is the quantity of cola (in
bottles) demanded on a monthly basis and P is the price of one bottle (in dollars).
Accordingly, the market supply curve for the cola is: QS = 60 000 + 4 000 P, Where QS is
the quantity of cola (in bottles) produced or supplied per month.
a. What is the equilibrium price of a bottle of cola? What is the equilibrium
quantity?
b. If a tax of $2 is imposed on each cola bottle, what happens to the equilibrium
quantity?
a. QD = QS
75 000 – 8 000P = 60 000 + 4 000P
15 000 = 12 000P
$1.25 = P
Q = 75 000 – 8 000 (1.25), Q = 65 000
The equilibrium price is $1.25 per bottle and the equilibrium quantity is 65 000
bottles.
b. P = $3.25
Q = 75 000 – 8 000 (3.25), Q = 49 000
If a $2 tax is imposed on the cola, the equilibrium quantity drops from 65 000 to
only 49 000.
7) The Mapo Company and the Fringa Company are the only two firms that produce a
particular part used in the construction of the new Tevo system. The demand for tevo’s is
increasing due to an increase in popularity. This leads to an increase in the demand of
the particular part. The demand curve for the product is:
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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P = 1540 – 3.5Q
Where P is the price (in dollars) of the product and Q is the total amount demanded.
The total cost function for the Mapo Company is:
TCM = 1230QM
Where TCM is the total cost (in dollars) and QM is its output.
The total cost function for the Fringa Company is:
TCF = 1190QF
Where TCF is the total cost (in dollars) and QF is its output.
a) Should these two firms collude? Why or why not?
b) What are the advantages of colluding? Are there any risks?
c) If these two firms collude, and if they want to maximize their profits, how much will
the Mapo Company produce?
d) Using the above conditions, how much will the Fringa Company produce?
e) Will Mapo want to collude?
Answers:
a) Yes, the two firms should collude because the number of firms providing the Tevo
parts is small. Therefore, there is interdependence between the two firms.
b) Advantages of collusion for these firms would be increased profits, decreased
uncertainty, and a better opportunity to prevent entry. The companies should be
aware that collusive agreements are often hard to maintain. Cheating is a very
tempting to firms because it is a quick way to increase profits. Collusive agreements
in the United States are illegal as well.
c) Mapo’s Marginal cost: $1230
Fringa’s Marginal Cost: $1190
Fringa will produce all the output because their marginal costs are always less than
Mapo’s.
MR = MC
1540 – 7Q = 1190
7Q = 350
Q = 50
Therefore, Fringa will produce all 50 units and Mapo would produce 0.
d) See above calculation = 50.
e) No Mapo will not. Mapo produces nothing. The only way Mapo may consider
colluding is if Fringa makes a very attractive profit share offer.
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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8) Bates Corporation is composed of a marketing division and a product division The
marketing division packages and sells the fabric produced by the product division. The
demand for the finished product sold by the marketing division is
PM = 100 – 1.5QM
where PM is the price of the finished product, and QM is the quantity sold. Excluding the
production cost of the basic fabric item, the marketing division’s total cost function is
TCM = 50 + 7.5QM
where TCM is the marketing division’s total cost. The production division’s total cost
function is
TCP = 2.5 - 1.5QP + 0.2QP2
Where TCP is total production cost, and QP is the total quantity produced of the basic
fabric item.
(a) If QM = QP (i.e. the production division only sells its fabric to the marketing
division), what is the optimal output for both divisions and what is the optimal
price for the finished product?
(b) If there is a perfectly competitive market for the basic fabric item, the price being
$10 per unit, what will be the optimal output for each division, and what is the
optimal price for the finished product?
(a) First, we must find the marginal cost for the marketing division:MCM = dTCM = 7.5
dQM
Now, we must find the marginal cost for the product division:
MCP = dTCP = -1.5 + 0.4QP
dQP
QM = QP, therefore, MCP = -1.5 + 0.4QM
The total marginal cost of the product is,
MC = MCM + MCP
MC = 7.5 – 1.5 + 0.4QM
MC = 6 + 0.4QM
PMQM = 100QM – 1.5QM2 or MRM = 100 - 3QM
At optimal output for both the marketing division and product division is,
MC = MRM
6 + 0.4QM = 100 - 3QM
QM = 27.65
We can now find the optimal price, PM = 100 – 1.5QM
PM = 100 – 1.5(27.65)
PM = $58.53
(b) The marginal revenue for the basic fabric item is constant, as is its price. MRP = 10,
PP = 10
We must find the total marginal cost for the marketing division:
MCT = dTCM + PP = 7.5 + 10 = $17.5
dQM
Now, we must find the marginal cost for the product division:
MCP = dTCP = -1.5 + 0.4QP
dQP
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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At optimal output,
MCP = MRP
-1.5 + 0.4QP = 10, QP = 28.75
Recall, MCT = 17.5
TRM = PMQM, or TRM = (100 – 1.5QM)QM, TRM = 100QM – 1.5QM2
MRM = dTRM = 100 – 3QM
dQM
At optimal output,
MRM = MCT, 100 – 3QM = 17.5,
QM = 27.5
The optimal price of the finished item is
PM = 100 – 1.5QM
PM = 100 – 1.5(27.5)
PM = 58.75
9) Company Z is selling product A for $4/unit. The average variable cost is $2, and the
total fixed costs are $300,000.
a) How much should the company produce in order to break even?
b) Company Z decides to add a new product to its production line. They decide to
produce the same quantity of product B. This would usually cost 500,000.
However, the Total cost of producing both products together is 1,000,000. Calculate
the degree of economies of scope.
a) Set
TC = TR
TFC
+ TVC
= Q * P
300000 + (2* Q) = Q * 4
300000 = 2Q
Q = 150,000
TC(A) = 300000 + 2* 150000 = $600,000
Or Selling Price(SP)= $4 Variable Cost(VC) = $2, Fixed Costs = $300000,
Contribution Margin(CM) = SP-VC = $2
BEP in units = Fixed Costs/CM = 300000/2 = 150,000 units
or 150,000 x $4=$600.000
b) Economies of scope= TC(A) + TC(B) – TC(A + B)
TC(A + B)
= 600,000+ 500,000 – 1,000,000
1,000,000
= 0.10 (Positive answer indicating economies of scope)
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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10) The demand function for a monopoly is: Q= 4000 - 4P
Its total cost function is: TC= Q² + 300Q+ 100
a) What is the maximum profit this company can make? what is the quantity that
maximizes profit?
b) Determine the price for its product at this point.
a) To maximize profit: MR= MC
P= 1000-(1/4) Q
TR= Q* P= 1000Q- (1/4)Q²
MR= 1000- (½)Q
MC= 2Q+ 300
Set MR= MC
1000- (1/2)Q= 2Q +300
(2.5) Q = 700
Quantity = 280
Profit = TR- TC
= 4000(280)- (1/4)(280)² - (280)²- (300)(280) – 100
= $ 937900
b)
Q= 4000- 4P
280= 4000- 4P
4P= 3720
Price= $930
11) The Smith Corporation and the Jones Company are the only two producers of a
certain type of escalator part. The demand for this particular part has the following
equation: P = 1000-5Q
Each of the companies has a different total cost function.
TCSmith = 600 + 100Q +50Q2
TCJones = 100 + 200Q + 100Q2
The companies want to collude.
a. How many escalator parts should the Smith Company produce?
b. How many parts should Jones produce?
c. What price should the companies charge?
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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a) To maximize profit, find QSmith and QJones where marginal revenue is equal to
marginal cost for each of the firms:
Since P = 1000-5Q,
Total profit for the industry = 1000Q – 5Q2
Therefore, MR = 1000 – 10Q
MR = MCSmith
1000-10Q = 100 + 100Q
900 = 110Q
Q = 8.18
Therefore, Smith should produce about 8 parts.
b) MR = MCJones
1000-10Q = 200 + 200Q
800 = 210Q
Q = 3.81
Therefore, Jones should produce about 4 parts.
c) To find optimum price, find total number of parts produced,
which is 8 + 4 = 12(approx.).
Now insert Q = 12 into demand equation:
P = 1000-5Q
= 1000-5(12)
= 1000-60
= 940
Therefore, the firms should charge $940 per part.
12) A lens manufacturer is jointly producing both camera and telescope lenses in fixed
proportions. The demand curve for telescope lenses is given by Pt=50-Qt. The demand for
camera lenses is given by Pc=125-2Qc. The companies overall total cost for Q units of
output is given by TC=3Q^2-5Q+400. Assuming that everything produced is sold.
a) Calculate the companies total output
b) Calculate the price for camera lenses
c) Calculate the price for telescope lenses
d) Is the assumption that everything produced is sold a reasonable assumption?
a) TR=PcQc+PtQt
TR= (125Qc-2Qc^2) + (50Qt-Qt^2)
Since production is in fixed proportions Qc=Qt=Q
TR= (125Q-2Q^2) + (50Q-Q^2)
TR=-3Q^2+175Q
MR=-6Q+175
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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TC=3Q^2-5Q+400
MC=6Q-5
To maximize profit MR=MC
-6Q+175=6Q-5
12Q=180
Q=15
b) Pc=125-2Qc
Pc=125-2(15)
Pc=95
c) Pt=50-Qt
Pt=50-15
Pt=35
d) As long as marginal revenues of both the camera lenses and telescope lenses are
positive at output Q the assumptions is reasonable. If either of the marginal revenues are
negative the assumption is invalid because this would mean that some of production must
be withheld from the market since it results in loses.
Pc=125-2Qc
TRc=125Qc-2Qc^2
MRc=125-4Qc=125-4(15) =65
Pt=50-Qt
TRt=50Qt-Qt^2
MRt=50-2Qt=50-2(15) =20
Since both marginal revenues are positive the assumption made was reasonable.
13) Chapter XI is a new store in the basement of the Bronfman building. It currently has
a new line of shirts. There is a production and a marketing division involved in the
launching of these shirts. The marginal cost of producing a shirt is $10/shirt. The
marginal cost of marketing a shirt is $8/shirt. The demand equation for the Chapter XI
new shirts is: P = 300 – 0.03Q
Where;
P = price (in dollars)
Q = quantity (in units)
There is no external market for the good made by the production division.
a) What is the optimal output of shirts for Chapter XI?
b) What price should it charge to management faculty members?
c) Production wants to transfer the shirts to marketing at $12/shirt but marketing
wants to buy at $9/shirt. Is anyone right? Why? Then what should be the transfer
price from production to marketing?
a) The optimal output is where the firm produces units where MR = MC.
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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MCp = 10, MCm =8, P= 300 – 0.03Q.
TR = Q* P
= Q*(300 – 0.03Q)
= 300Q – 0.03Q^2.
MR = dTR
dq = 300 – 0.06Q
MCt = MCp + MCm
= 10 + 8 = 18
Therefore, optimal output;
MR = MC
300 – 0.06Q = 18
300 – 18 = 0.06Q
282 = 0.06Q
Q = 282/0.06
Q = 4700
The optimal output of shirts to produce is 4700 units.
b) Using the demand equation and substituting 4700 for Q we will get the price.
P = 300 – 0.03Q
(Q= 4700)
P = 300 – 0.03(4700)
P = 300 – 141
P = 159
Chapter XI should charge a price of $157.
c) i) None of the divisions are right.
ii) If the production division sells for $12, marketing will be paying more than
they need to for the shirts and if production sells for $9, they will be receiving less
than their cost of production and will not be able to cover their cost.
iii) The transfer price of production to marketing should be $10, which is equal to
production’s marginal cost.
14) The Lotus Company’s average variable cost is AVC = 65- 7Q + Q2
where Q is the number of units of output produced.
a) What is the output level where marginal cost is a minimum?
Since Q*AVC = TVC
TVC = 65Q- 7Q2 + Q3
Since Marginal Cost equals dTVC/dQ, it equals MC = 65- 14Q + 3Q2
It is a minimum when dMC/dQ = -14 + 6Q = 0 Æ Q = 14/6 or 7/3
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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b) What is the output level where average variable cost is a minimum?
It is a minimum when dAVC/dQ = -7 +2Q = 0 Æ Q = 7/2
c) What is the value of average variable cost and marginal cost at the output
specified in the answer part B?
If Q = 7/2, average variable cost equals 65- 7(7/2) + (7/2)2 = 52.75. Marginal cost
equals 65- 14(7/2) + 3(7/2)2 = 52.75. Thus, MC = AVC at this output level.
15) The Rocco Corporation is the only maker of Indians’ totem poles. The demand curve
for its product is QD = 13,100- 7P
and its total cost function is TC = 3,500 + 350Q + 17Q2
where P is the price (in dollars), TC is total cost (in dollars), and Q is quarterly
output.
a) Derive an expression for the firm’s marginal revenue curve.
Since P = (13,100- Q)/7 = 1871- 0.143Q (approx.). TR = 1871Q – 0.143Q2
MR = 1871- 0.286Q
b) To maximize profit, how many totem poles should Rocco produce and sell per
quarter?
MC = 350 + 34Q. If MC = MR then
350 + 34Q = 1871- 0.286Q
34.143Q = 1521
Q = 44.36
Thus, Rocco would make 44.5(approx.) totem poles per quarter. If Q = 44.5, P =
1871- 0.143(44.5) = 1864.64. Therefore, the price should be $1864.64.
c) If the number in part B is produced and sold, what will be the firm’s quarterly
profit?
[1871Q- 0.143Q2]- [3,500 + 350Q + 17Q2]
= [1871(44.5) - 0.143(44.5)2]- [3,500 + 350(44.5) + 17(44.5)2]
= [83,259.5 – 283.18] - [3,500 + 15575 + 33664.25]
= [82,976.32] - [52,739.25] = 30,237.07
Rocco’s quarterly profit equals $30,237.07
16) Suppose Steel Corp is the largest steel producer with a majority of the market share.
The demand curve for steel is Q = 400 - 20P. The supply curve for the small firms in the
industry (all firms except Steel Corp) is given as Qsm = 30 - 2.5P
Steel Corp’s marginal cost is given as MC= 1.5Qsc
At what price should Steel Corp sell its product?
Qsc = Q - Qsm = 400 - 20P – 30 + 2.5P
= 370 - 17.5P
Therefore P = 370/17.5 - Qsc /(17.5)
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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P= 21.14 - 0.057 Qsc
TR = 21.14Qst - 0.057Q2st
δTR =21.14 – 0.114Qst
δQsc
MR = MC Therefore 21.14 – 0.114Qst = 1.5Qsc
Qsc = 13
Since P =21.14 – 0.057Qsc we can replace Qsc with 13 and we find
P = 21.14 – 0.057(13) = $20.40
17) A doughnut company produces doughnuts and doughnut holes in a joint process
therefore they are produced in a fixed ratio.
Their total cost function is given as TC = 10 + Q + Q2
The demand curves for doughnuts and doughnut holes are given as
PD = 20 - QD
PH = 10 - 1.5QH
How many doughnuts and doughnut holes should the company produce?
At what Price should the company sell their products?
TR = PDQD + PHQH but since the products are produced in a fixed ration QD=QH=Q
= PDQ + PHQ
= (20-Q)Q + (10-1.5Q)Q
= 20Q -Q2 + 10Q -1.5Q2
= 30Q - 2.5Q2
Profit = π = 30Q - 2.5Q2 - 10 -Q -Q2
= -10 + 29Q - 3.5Q2
δ π = 29 - 7Q = 0 therefore Q = 4.14
δQ
PD = 20 – QD = 15.86
PH = 10 – 1.5QH = 3.79
Now check marginal revenues. Substitute the value of Q calculated above we get
MRD = δTRD = δPDQD = 20 - 2QD = 11.72
δQ
δQD
MRH = δTRH = δPHQH = 10 - 3QH = -2.42
δQH
δQ
Thus the Co. should only sell QH = 3.33. Which is the point where MRH = 0.
MRH = 10 - 3QH = 0 so QH = 3.33
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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18) The Automatic Rifles industry is composed of two main producers: the Westminster
and the Harrington corporations. It has been estimated that the demand for automatic
rifles is described by the function P = 5000 – 4Q, where P is the unitary price of an
automatic rifle in dollars and Q, the total numbers of automatic riffles sold in thousand
units.
Further, financial analysts have established through a series of studies that the total cost
functions for Westminster Corp. and Harrington Corp. are the following:
TCW(Q) = 9000 + 500QW
and
TCH(Q) = 12 000 + 450QH.
a) Assuming that both firms want to maximize profits, what will be the equilibrium
unitary price of an automatic rifle?
b) At the above equilibrium price, what will the output of each corporation be?
Westminster and Harrington Corporations enjoy their status as oligopolists, since the
automatic rifle industry in America is very lucrative.
c) What actions could they take in order to diminish the probability of new entrants in
the industry?
Answers:
a) We have that Price = 5000 – 4Q, but since Q = QH + QW, we can write Price = 5000 –
4 (QH + QW). Let PH and PW be the total profit functions of Harrington Corp. and
Westminster Corp., respectively. Then we can express PH = TRH – TCH = QH (5000 –
4(QH + QW)) – (12 000 + 450QH) = -4QH2 + 4550QH - 4QHQW – 12 000, and
similarly, we have PW = TRW – TCW = QW (5000 – 4(QH + QW)) – (9000 + 500QW) =
-4QW2 + 4500QW – 4QHQW – 9000. Each firm has control over its own level of
production, so we will set d(PH)/dQH = d(PW)/dQW = 0. So, we must have d(PH)/dQH
= -8QH + 4550 - 4QW = 0 and d(PW)/dQW = -8QW + 4500 – 4QH = 0, which is a
system of linear equations with solution QW = 370.83 and QH = 383.33.
At these levels of output, we can compute equilibrium market price. Indeed, we
obtain that price = 5000 – 4(370.83 + 383.33) = 1983.33. So, equilibrium price for
automatic riffles will be 1983.33$.
b) As found in a), Westminster Corp. will have an output of 370 833 rifles, while
Harrington Corp.’s output will be equal to 383 333 rifles.
c) They can lobby the government to limit the number of riffle manufacturers, they can
lower profit margins in order to render the industry less attractive to newcomers, they
can protect their designs with proper patents, they can engage in aggressive marketing
campaigns, …
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
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19) The total variable cost function of Bell’s company is:
TVC = 100Q - 20Q2 + Q3 (where Q is the number of units of output produced)
a. What is the output level where marginal cost is a minimum?
b. What is the output level where average variable cost is a minimum?
Answers:
a.
MC = dTVC/dQ = 100 - 40Q + 3Q2
Marginal cost is a minimum when dMC/dQ = - 40 + 6Q = 0
Ö Q = 20/3
Therefore, the output level where marginal cost is a minimum is at 20/3 units.
b.
AVC = TVC/Q = (100Q - 20Q2 + Q3)/Q = 100 - 20Q + Q2
Average variable cost is a minimum when dAVC/dQ = - 20 + 2Q = 0
Ö Q = 10
Therefore, the output level where average variable cost is a minimum is at 10 units.
20) Future shop wants to determine if it is profitable to sell a new model DVD player.
Future shop would like to earn a profit of $35000 per month from selling the DVD
player. The price of each DVD player is $670, and the average variable cost is $230.
a) What is the required sales volume if Future shop’s monthly fixed costs are $7800
per month?
b) If the firm were to sell each DVD player at a price of $600 rather than $670, what
would be the required sales volume in order to achieve the targeted profit?
c) If total fixed costs were $25000, and the price is $670; how many units should
Future shop sell in order to achieve target profit, $35000?
Answers:
a) 670Q - (230Q+7800) =35000
670Q - 230Q-7800 =35000
440Q = 42800
Q=97.3 units
Ö Future shop will need to sale 97.3 units of the model.
b) 600Q-(230Q+7800)=35000
600Q-230Q-7800=35000
370Q=42800
Q=115.7 units
Ö 115.7 units of the model would need to be sold in order to achieve the
targeted profit
c) Q= (25000+35000)/(670-230)
Q=60000/440
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
15
Q=136.4 units
136.4 units need to be sold in order to achieve the target.
21) The Sweet Tooth Company makes two types of candies-ChocoWhirls and Toffee Tops.
The cost of producing 5000 units of ChocoWhirls alone is $700, while the cost of
producing 3500 units of Toffee Tops is $600. The cost of producing both ChocoWhirls
and Toffee Tops jointly is $1150. Is there an economy of scope within the Sweet Tooth
Company? If so, what is the savings? Explain your answer.
Answers:
S=(C(Q1)+(C(Q 2)-C(Q1+Q2))/( C(Q1+Q2))
S=(700+600-1150)/1150
=0.1304 or 13.04%
There is an economy of scope within the Sweet Tooth Company. By producing both
ChocoWhirls and Toffee Tops jointly rather than producing the two individually, the
company will save 13.04% in costs.
22) Nokia is a Finnish cell phone producer. The price of a cell phone is $250. The firm’s
total cost function is
TC= 2500+55Q+2.5Q2
Where TC is total cost (in dollars) and Q is hourly output.
a) If the firm is perfectly competitive, what output maximizes profit?
b) What is the firm’s profit at this output level?
c) What is the firm’s average cost at this output level?
Answers:
a) to optimize profit => MC= MR (Price - in a perfectly competitive Market)
MC = 55+5Q = P
55+5Q = 250
5Q=195
Q=39
b) profit = TR (PQ) - TC
= (250*39)-[2500+(55*39)+(2.5*392)]
= $1302.50
c) AC= TC/Q
= 8447.50/39
= $216.60
23) Hannah Inc. is a producer in a perfectly competitive industry. The total cost function
of the industry is: TC = 450 + 4Q + Q²
a) If the selling price of product is $12, what is the optimal output rate for Hannah
Inc?
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
16
b) What is the average cost at the optimal output rate?
c) What are the characteristics of a perfectly competitive industry?
d)
Answers:
a) Marginal cost = dTC = 4 + 2Q
dQ
P = MC
$12 = 4 + 2Q
Q= 4
b) Average cost = Total cost = 450 + 4 + Q
Q
AC (4) = 450 + 4+ 4 = 120.5
4
c) - Identical products
- Easy entry and exits
- No firm has control over price. Price is established according to the market
equilibrium
- Many, producers in the industry
24) The industry demand for flavored gum is given by:
Qd = 130 – 6P
And the supply curve for the smaller firms in the industry is given by:
Qs = 70 - 2P
where Q is the quantity of boxes of gum demanded/supplied and P is the price per box (10
packets of gum in each box).
Squiggley, a flavored gum producer’s, marginal cost is given by: MCq = 2Qq
a) Find the demand for the dominant firm in the industry.
b) At what price will Squiggley maximize its profits?
Answers:
a) Demand for dominant firm equals
Industry demand – supply by small firms
Hence it is given by,Qq = Qd - Qs
130 – 6P – (70 - 2P)
= 60 – 4P
So,
Qq = 60 – 4P
Putting it in terms of P, we get
P = 15 – ¼ Qq
[1]
b) Profit is maximized when MCq = MRq
Keeping in mind that Total Revenue = PQ, from [1] we get
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
17
TR = (15 – ¼ Qq) * Qq
= 15Q – ¼ Qq2
And since, MR = dTR/dQ, so MR = 15 – ½ Qq
Hence, equating MR with the given MC for Squiggley, we get
2Qq = 15 – ½ Qq
Qq = 6
Substituting back into [1] we get
P = 13.5
In other words, if Squiggley sets its price to $13.5 per box of gum, it will
maximize its profits.
25) The Soleil Company and the Lune Company produce and sell a kind of machine.
The demand curve for their machine is P=1200-5Q, where P (in dollars) is the price of
the machine and Q (in thousands of units) is the total amount demanded. The total cost
function of the Soleil Company is TC=3000+200Q, where TC is the total cost (in dollars)
and Q is its output. The total cost function of the Lune Company is TC=5000+200q, where
TC is the total cost (in dollars), and q is the output (in thousands of units.)
a) If these 2 firms collude and they want to maximize their combined profits, how much
will each firm produce?
b) What if the total cost function of Lune Company is TC=3000+100q, how much will
each firm produce?
Answers:
a) Because these two firms have the same amount of marginal cost, they will produce
equal amount of the output. The MC of these two firms is 200. As well, if we want to
maximize the profit, marginal revenue should be equal to marginal cost.
Total revenue= PQ= 1200Q-5Q²
So, MR=1200-10Q
MR=MC Æ 1200-10Q= 200; therefore, Q=100(thousands of units)
As a result, each firm will produce 100/2=50(thousands of units)
b) Now MC of the Lune Company is smaller than MC of the Soleil Company.
So, the Lune Company will produce all the amount of the products.
MC of the Lune Company is 100 and to maximize the profit, marginal revenue should
be equal to marginal cost.
That is 1200-10Q=100, Q=110(thousands of units)
As a result, the Lune Company will produce a total number of 110(thousands of
units) and the Soleil Company will produce nothing.
26) Fido is the only Canadian company in Montreal that provides the GSM network for
cellular phones. They supply Cell phones with a SIM card that allows users to use the
same phone number in different cellular phones by just switching the SIM card from one
phone to the other. Fido’s demand curve for this service is:
QD= 9000-0.3P
and its total cost function for this service is:
TC= 3,300+720Q+30Q2
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
18
Where P is price of owning a SIM card (in dollars), TC is total cost (in dollars), and Q is
the number of SIM cards that Fido provides for its customers.
a) Derive an expression for Fido’s Marginal Revenue curve.
b) To maximize profit, how many SIM cards must Fido sell per month?
c) If this number of SIM cards is available and sold, what will be the firm’s monthly
profit?
Answers:
a) To find the Marginal revenue, you must first find Total revenue then take its
derivative.
QD= 9000-0.3P Æ P= (9000-Q)/0.3
TR=P*Q= (9000Q-Q2)/0.3 Æ TR= 30,000Q- (Q2/0.3)
So MR= dTR/dQ= 30,000-6.667Q
b) Maximum profit occurs when MR=MC
TC= 3,300+720Q+30Q2
So MC=dTC/dQ=720+60Q And MR from part (a) is 30,000-6.667Q
Therefore MR=MC Æ 30,000-6.667Q=720+60Q Æ 66.667Q=30,000-720
Æ Q= 439.19(Approximated to 440) Since we cannot provide 0.19 parts of a SIM card,
then we round it and we find that the number of SIM cards that Fido should provide is
440 SIM Cards.
c) For 440 SIM cards sold, the firm’s monthly profit will be Profit=TR-TC
TR=P*Q= [(9000-Q)/0.3]*Q= 12,554,666.667
TC= 3,300+720(440) +30(440) 2=6,128,100
Æ Profit=12,554,666.667-6,128,100=$6,426,566.667 or approximately $6,426,600
27) Via rail engages in price discrimination pricing technique. Students who travel from
Montreal to Ottawa receive a discount for the fare. Suppose that the demand curve for
non-students is PN = 140 – 0.01QN, where PN is price for non-students in dollars and QN is
number of tickets sold. The demand curve for students is PS = 83 – 0.007QS, where PS is
price for students in dollars and QS is number of tickets sold. The total cost for the service
is TC = 61000 + 3Q, where TC is total cost in dollars, and Q is total number of tickets sold.
(a) How many tickets should be sold and what is the price for each of a non-students
ticket and student’s ticket to maximize the firm’s profit?
(b) What is the total profit of the firm?
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
19
(c) How much additional profit will the firm make because if it engages in price
discrimination?
(a) PN = 140 – 0.01QN ; PS = 83 – 0.007QS ; TC = 61000 + 3Q
П1 = (PNQN) + (PSQS) – (TC)
П1 = (140 – 0.01QN)(QN)+ (83 – 0.007QS)(QS) – (61000 + 3Q)
To maximize the profit with respect to QN and QS;
dП1/dQN = 140 – 0.02QN - 3 = 0
QN = 6850 , PN = $ 71.50
dП1/dQS = 83 - 0.014QS – 3 = 0
QS = 5714.3 , PS = $ 43.00
(b) П1 = (140 – 0.01QN)(QN)+ (83 – 0.007QS)(QS) – (61000 + 3Q)
= (140 – 0.01(6850))(6850)+ (83 – 0.007(5714.3))(5714.3) – (61000 +
3(6850+5714.3))
= $ 636 797
(c) Q = QN + QS = (140 - P) / (0.01) + (83 - P) / (0.007)
Q = 25857 – 242.86P
=> P = (25857 - Q) / (242.86)
П2 = PQ – TC
= (25857 - Q) Q / (242.86) - (61000 + 3Q)
dП2/dQ = 106.47 – 0.008235Q – 3 = 0
Q = 12564.66 , P = $54.73 , П2 = $ 588969
Therefore the additional profit is П1 – П2 = $ 47828
28) Deep Tunes Inc. is the first mainstream online MP3 streaming service that provides
broadcast to Canada and the USA. The demand functions for these groups are:
QCAN = 100 – (2/3) PCAN
QUSA = 75 – (3/4) PUSA
where Q is the online user subscriptions in thousands per year and P is the subscription
price per year. The cost for providing Q units of service is given by
C = 750 + 25Q
where Q = QCAN + QUSA
Find the profit-maximizing prices and quantities for the US and Canadian markets of
Deep Tunes.
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
20
Answers:
In this case, it is safe to assume that Deep Tunes Inc. is acting as a monopolist. Thus, to
maximize profits, it should pick quantities in each market that have equal marginal
revenues and which are also equal to marginal cost. Marginal cost is given by the slope of
the total cost curve.
Hence, MC = 25.
Writing the above expressions with respect to P:
PCAN = 150 – 3/2 QCAN
PUSA = 100 – 4/3 QUSA
Hence the total revenue is given by
TRCAN = QCANPCAN
= 150QCAN – 3/2 QCAN2
TRUSA = QUSAPUSA
= 100QUSA – 4/3 QUSA2
And marginal revenue of each market is given by the first derivatives of the respective
Total Revenues:
MRCAN = 150 – 3QCAN
MRUSA = 100 – 8/3 QUSA
Setting marginal revenue equal to marginal cost
MRCAN = 25
150 – 3QCAN = 25
QCAN = 41.6
MRUSA = 25
100 – 8/3 QUSA = 25
QUSA = 28.1
Plugging these optimum quantities back into the equation for demand in each market, we
get the price for each market
PCAN = 150 – 3/2 (41.6)
= $87.6
PUSA = 100 – 4/3 (28.1)
= $62.5
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
21
29) Air Canada estimates that they will sell 60 million plane tickets this year. Their gross
operating assets are 625 million dollars and the marginal cost of flying an additional
customer is 20$. Total fixed costs will be 315 million dollars. Air Canada’s objective is to
achieve a 25 rate of return.
a) Given that their cost per unit is 22$ for labor, 16$ for material, 4$ for marketing, at
what price should they sell their tickets? (Assume that all tickets are priced the same)
b) How will Air Canada be certain that they are maximizing profit?
c) From your answer from part (b), what condition must be met if the answer in part (a)
will maximize profit?
Answers:
a) P= L + K + M + F/Q + xA/Q
P= 22 + 4 + 16 + 5.25 + 2.60 = 49.85
b) Their markup must be equal to MC (-1/η +1) to be maximizing profit.
c) Price elasticity must be equal to –1.401
P = MC (-1/η + 1)
49.85 = 20 (-1/η+1)
2.4925 = (1/η+1)
2.4925 (η +1) = -1
2.4925η = -3.4925
η = -1.401
30) Two companies, MTL Candies and TDOT Candies are strong competitors in the candy
industry. They are leaders in the industry and they will have to choose a strategy that
will determine if they can stay as leaders in terms of profit. MTL Candies can choose
between strategy 1 or 2, and TDOT Candies can choose between strategy A or B. The
payoff, in term of profit for each company, is given below for each combination of
strategies.
TDOT Candies
Strategy A
Strategy B
TDOT’s profit: $9 million
TDOT’s profit: $8 million
Strategy 1
MTL’s profit:
$7 million
TDOT’s profit:$7 million
MTL’s profit:
$5 million
TDOT’s profit:$6 million
Strategy 2
MTL’s profit
$8 million
MTL’s profit
$4 million
MTL
Candies
a) What Strategy will TDOT Candies adopt? Why?
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
22
-
TDOT Candies will choose to adopt Strategy A because it is the dominant
strategy for TDOT.
b) What Strategy will TDOT Candies adopt? Why?
-
MTL Candies will choose strategy 2. Why? It is because MTL is sure that TDOT
Candie will choose strategy A. As mention in answer a), TDOT’s best choice is
to adopt strategy A. Therefore, MTL’s profit will be of $8 million with strategy 2,
which is better than $7 million otherwise.
31) Below are the respective demand curves for software distributed in Europe and the
United States by a particular firm. Software purchased in one country cannot be sold in
the other.
Pu = 55 – Qu
P e = 40 – 2.5Q e
Where Qu is the number of software copies distributed in the United States (in millions)
and Qe are the number of copies distributed in Europe (in millions)
Total Cost = 25 + 15(Qu + Q e)
a) What output will maximize profits within each geographic region?
b) What will the optimal prices for the software be within these regions?
c) What will the firm’s total profit be?
d) Justify the use of price discrimination in the software industry (using calculations)
Answers:
a)
Step 1. Derive the firm’s total revenue function
TRu = PuQu
TRe = PeQe
TRu = (55 – Qu)Qu
= 55Qu - Qu2
TRe = (40 – 2.5Qe)Qe
= 40Qe - 2.5Qe2
Step 2. Derive the firms’ Profit Function
π = TRu + TRe - TC
π = 55Qu - Qu2 + 40Qe - 2.5Qe2 – (25 + 15Qu + 15Qe)
π = 40Qu - Qu2 + 25Qe- 2.5Qe2 - 25
To maximize π take the partial derivative of the profit function with
respective to Qe and Qu and equate to zero.
∂π = 40 - 2Qu = 0;
Qu = 20
∂Qu
∂π = 25- 5Qe = 0;
Qe = 5
∂Qe
∴ Outpul levels of Qu and Qe that will maximize profit is 20 million
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
23
units in the United States and 5 million copies in Europe respectively.
b) Having determined the optimal levels of output for either geographic region to
determine the optimal prices, replace the optimal levels of output in the demand function
of each region.
Pu = 55 – Qu and Qu = 20
Pu = 55 – 20
Pu= $35
P e = 40 – 2.5Q e and Qe = 5
Pe = 40 – 12.5
Pe= $27.50
c) To determine the firm’s total profit substitute the optimal output
levels of Qu and Qe into the firm’s profit equation
π = 40Qu - Qu2 + 25Qe- 2.5Qe2 - 25
π = 40(20) - (20 2) + 25(5)- 2.5(52) - 25
π = 800 - 400 + 125- 62.5 - 25
π = $437.50 (in millions)
d) To justify the use of price discriminations in its various market segments (as created
through geographic markets), we need to determine the firm’s profit in the absence of
the price discrimination alternative. In this case:
Q = Q u + Qe
Q u = 55 – P
Q e = 16 –2/5 P
So:
Q = 55 – P + 16 –2/5 P
Q = 71 – 7/5P
∴P = 355/7 – 5/7Q
TR = 355/7Q – 5/7Q2
Since Q = Q u + Qe
TC = 25 + 15Q
And
π = 355/7Q - 5/7Q2 - 25- 15Q
π = 250/7Q - 5/7Q2 – 25
For max profits as before the derivative of π with respect to Q is taken and set to 0.
∂π = 250/7 - 10/7Q = 0;
Q = 25
∂Q
Substituting Q=25 back into the π function:
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
24
π = 250/7(25) - 5/7 (252) – 25
π = 892.86 –446.43 –25
π = $421.43(in millions)
Since the profit attainable in the absence of price discrimination is lower ($421.43 million
when compared to $437.50 million) than when it is in effect, it clearly shows the
advantages of engaging in price discrimination in the software industry.
32) In the following two cases predict GAT will enter the market or not. In each case is
the threat to resist credible? Why or why not?
a)
Strategies
for
AMT
Resist Entry
Do not resist entry
Strategies for GAT
Enter
AMT Profit:$ 5 Million
GAT Profit:$ 6 Million
Do not Enter
AMT Profit:$10 Million
GAT Profit:$5 Million
AMT Profit:$ 7 Million
GAT Profit:$ 7 Million
AMT Profit:$15 Million
GAT Profit:$5 Million
Strategies for GAT
Enter
AMT Profit:$ 8 Million
GAT Profit:$ 4 Million
Do not Enter
AMT Profit:$15 Million
GAT Profit:$5 Million
AMT Profit:$ 7 Million
GAT Profit:$ 7 Million
AMT Profit:$15 Million
GAT Profit:$5 Million
b)
Strategies
for
AMT
Resist Entry
Do not resist entry
Answers:
a)
In this case AMT will choose not to resist the entry of GAT (It’s AMT’s dominant
strategy), and GAT’s will enter. Therefore the threat to resist GAT’s entry is not credible
since it would not be to AMT’s benefit to do so.
b)
In this case AMT will choose to resist the entry of GAT. If GAT chooses to enter, they
will suffer. In this case the threat by AMT to resist entry is credible and will likely deter
GAT from entry.
33) Suppose that Provigo and Métro are the only two producers of an expensive form of
triple chocolate fudge. Although the grocers have formed a cartel with respect to this
extremely trendy product, both parties are individually considering the effect that
cheating would have on company profits and the long-term relationship with the other
firm by analyzing the following payoff matrix:
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
25
Provigo
Abide by agreement
Cheat
Métro
Abide by agreement
Cheat
$7 million
$9 million
$7 million
$2 million
$5 million
$2 million
$9 million
$5 million
Given the above information, justify:
(a)
(b)
why one or both grocer(s) would decide to cheat and
why one or both grocer(s) would decide to abide by the agreement.
In both cases, identify the respective profits for both firms.
Answers:
If agreements between the two grocers are rare and last only on a shortterm basis, it is likely that both firms will cheat because neither can trust
the other well enough. In this case, both sacrifice potentially higher profits
and, in their place, earn $5 million. This is a textbook example of a
prisoner’s dilemma.
If, however, the grocers regularly form agreements, of which many are
often on a long-term basis, it is possible that both firms have developed
enough trust with each other that they are willing to abide by the
agreement and, thus, both maximize profits at $7 million.
The most important concept in this problem is one of trust. If trust is
absent, both firms end-up sacrificing a potential $2 million of profit
because of fear that the “other guy” will not abide by the agreement.
Practice questions for the final exam, Part Three (Dr. Salmasi’s sections)
26