Download (1) Perfect Competition (2) Monopoly I (3) Monopoly II

Managerial Economics, SS15
First Problem Set
(1) Perfect Competition
GREYROCK INC. produces light bulbs and is a member of a perfectly competitive market. The
exact demand curve is not known. However, you observed that Q1 = 200 light bulbs are sold at a
price of P1 = 900 in the entire industry. At a price of P2 = 400 consumers purchase 600 units of
the good (Q2 = 600). The whole industry is composed of N = 10 firms. The total cost function
of each company reads:
T C(Q) = 50Q + 100.
(1)
a) Construct the market demand curve.
b) Calculate the profit maximizing output as well as the corresponding price and economic
profit.
c) Calculate the average cost at this level of output.
d) Is the market in equilibrium? Why or why not?
(2) Monopoly I
You are hired to consult the ADOL CORPORATION, the single supplier of a special medical care
product that promises to mitigate headache. The company sells a quantity of Q = 1M io $ at a
price of P = 100$. The marginal costs are M C = 40$ and the average costs at this level of output
are AC(1, 000, 000) = 90$. You know that price elasticity of demand is ⌘D = 2.
a) Would you recommend the company to change its pricing behavior?
b) What is the marginal revenue of the firm if it maximizes profits?
c) The managers of ADOL believe that investing 100, 000$ in advertising will increase total
sales by 300, 000$. Is this the optimal amount to spend on advertising? If not, should the
company spend less or more?
(3) Monopoly II
Suppose that the government is the only provider of water. The market demand function reads:
Q(P ) = 50
2P
(2)
The government’s total costs for producing water are described as follows:
T C(Q) = 100 + 10Q.
a)
b)
c)
d)
(3)
What price will the government charge if it wants to ensure an efficient allocation of water?
What price will the government charge if it wants to maximize profits?
Calculate the economic profit in both scenarios.
Calculate the dead weight loss (loss in welfare) resulting from the inefficient allocation in
example b).
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Managerial Economics, SS15
First Problem Set
(4) Monopsony
ALASCORP is a large company, which is located in a very remote area, where it is the only
provider of jobs. The labor supply curve reads:
PS = 100 + 1.5QS
(4)
PD = 600
(5)
The demand is given by:
2QD
where Q is the number of employees and P is the wage. Answer the following questions:
a) How many workers will ALASCORP employ? What would the optimal wage be?
b) Calculate the equilibrium price and quantity under perfect competition.
c) Calculate the dead-weight-loss resulting from the inefficient allocation in example a).
(5) Multiproduct Firm
Consider the WILSON Company, which manufactures two goods, A and B, that are jointly produced in equal quantities (for every unit of product A produced, the firm also produces a unit of
product B). The total cost function of the firm is:
T C = 50 + 0.5Q + Q2
(6)
where Q = QA + QB . The demand curves for the firm’s two products are given by:
PA = 100
0.5QA
(7)
QB
(8)
and
PB = 75
where PA and QA are the price and output of product A and PB and QB are the price and
output of product B.
a) How much should the WILSON Company produce and sell?
b) What price should the WILSON Company charge for each product?
c) Prove if the underlying assumption, that the WILSON Company sells all it produces of
both products is valid.
(6) Regression Analysis
Using regression analysis, the GREENHOUSE COMPANY obtained the following estimate of
the demand function for vegetables. The t-values are given in the parentheses below coefficients.
[R2 = 0.82]
“ = 500
Q
G
(3.2)
6.8 PG + 4.2 PR + 1.2 AG
(7.5)
(12.4)
(9.2)
0.0012 A2G + 0.21 I + "
(2.1)
(1.1)
Where QG is the quantity of vegetables demanded, PG is the price the Greenhouse company
charges (in dollars), PR is the price of its main competitor (in dollars), AG are advertising
expenditures (in dollars) and I is disposable income per capita (in 100 dollars).
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Managerial Economics, SS15
First Problem Set
a) The company wants to increase its output by 100 units. Think of a realistic scenario how it
might be able to achieve this goal? Provide a reasonable suggestion regarding potential
investments the company ought to commit.
b) The company decides to reduce its price by 5$. What is, ceteris paribus, the estimated
e↵ect of such a price reduction?
c) If the competitor decides to raise its prices by 10$, how would the GREENHOUSE
COMPANY’s output change?
d) Is it reasonable for the GREENHOUSE COMPANY to spend 1, 000$ on advertising?
Calculate the maximum level of advertising expenditures after which every additional
dollar spent on advertising will actually lead to a decrease in the company’s output.
e) Interpret the R2 and the t-values, what do they suggest in this specific case? What is the
error term "?
(7) Elasticities
Now assume that the price of the GREENHOUSE COMPANY is PG = 80 $, the price of its
main competitor is PR = 100$ and that GREENHOUSE spends AG = 300 on advertising. The
income is I = 120, 000. Note that I is measured in 100$. You are asked to interpret the results
of your calculations properly.
a) Calculate the own-price elasticity of demand ⌘P .
b) Can you determine whether the products are complementary or substitutive goods without
calculating the exact result? Why or why not? Calculate the cross price elasticity of
demand, ⌘P R. Are the goods complementary or substitutive goods?
c) Calculate the income elasticity of demand ⌘I . Are vegetables inferior goods?
(8) Price Discrimination I
The XOCOLAT FACTORY operates in two di↵erent and wholly independent markets. It sells
some special kind of peanut butter cups in both the United States and Europe. The demand
curve for the market in the US is described as
PU S = 320
8QU S
(9)
and the demand function for the European market is
PEU = 160
2QEU
(10)
The marginal cost function reads
M C = 5 + 2Q
(11)
where Q = (QU S + QEU ). There are fixed costs of F C = 1, 000$.
a) How many units of output should the XOCOLAT FACTORY sell in the European market?
b) What is the XOCOLAT FACTORY’s optimal level of output in the United States?
c) Calculate the optimal prices in each market.
d) What would be the profit of the XOCOLAT FACTORY if it decided to engage in price
discrimination?
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Managerial Economics, SS15
First Problem Set
(9) Price Discrimination II
In Westeros, there are two di↵erent royal families competing for the throne, the Lannisters and
the Starks. Both families want to attend the tournaments that are held regularly in Weteros.
However, they carry out a feud, which makes it impossible for both families to join the events
together. The Lannisters have access to credit; therefore they would be willing to pay an upfront
fee in order to join the events. The Lannisters have a weak demand for attending the
tournaments, which is described as follows:
PL = 55
2QL
(12)
The Starks live from paycheck to paycheck and would be willing to pay for each tournament visit
individually. They cannot a↵ord to pay an upfront fee. Their demand is given by:
PS = 75
2QS
(13)
The marginal cost of hosting the tournament is M C = 5. The fixed costs of hosting the
tournament are F C = 150$. You can design the events to attract either the Lannisters or the
Starks, but not both. Each family has an equal number of members.
Which family should the host of the tournament decide to invite if she wants to maximize profits?
(10) Two-Part-Tari↵
The demand for a strong demander for a round of golf is:
PS = 6
QS
where Qs is the number of rounds demanded by a strong demander when the price of a round of
golf is Ps .
PW = 4 Q W
where Qw is the number of rounds demanded by a weak demander when the price of a round of
golf is Pw . The cost of providing an additional round of golf to either type of golfer is a constant
2, additionally the club faces fixed costs of 1. For simplicity, assume that there is only one golfer
of each type.
The club has decided that the best pricing policy is a two-part tari↵. However, it’s your job to
tell the club the optimal entry fee and the optimal use fee to maximize the club’s profit. The
club cannot price discriminate on either the use or the entry fee. What are the club’s optimal use
fee and optimal entry fee?
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Managerial Economics, SS15
First Problem Set
(11) Peak-Load Pricing
You are asked to give an airline some advice on its pricing behavior. The passengers’ inverse
demand functions facing the Airline during summer and winter are given by:
PS = 410
0.5QS
(14)
QW
(15)
and
PW = 260
where QS (QW ) and PS (PW ) are the quantity of tickets sold and the price charged during
summer (winter). The toal cost funciton of the company reads:
1
T C(Q) = 1000 + 10Q + Q3
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(16)
Answer the following questions:
a) What prices should the company charge during the peak and through season?
b) Calculate the total profit of the airline.
c) Do the marginal costs of the airline di↵er in the two seasons? Why or why not?
(12) Bundling
The Livingroom Corporation produces Computers and TV-screens. It can identify four di↵erent
types of customers with the following reservation prices:
Customer
Computers
TVs
A
e40
e100
B
e50
e70
C
e70
e50
D
e100
e40
a) Consider three alternative pricing strategies; pure bundling, mixed bundling and charging
individual prices for each product. Determine the optimal price for each strategy and
calculate the resulting profits. The company faces marginal costs of zero. For reasons of
simplicity, suppose that there is only one customer of each type. What is the profit
maximizing strategy?
b) Suppose that the production of Computers as well as TV screens entails a marginal cost of
45$. Does the profit maximizing strategy change?
c) Do you think that the optimal bundling and pricing strategies for complements und
substitutes di↵er from those for independently valued products? Explain your answer by
taking the willingness to pay into account.
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Managerial Economics, SS15
First Problem Set
(13) Transfer Pricing
The WHITE Company is composed of a marketing division and a production division. The
marginal cost of producing a unit of the firm’s product is 20$ per unit, and the marginal cost of
the marketing division is 5$ per unit. The demand curve for the product is:
Q = 125
0.5P
(17)
The WHITE Company engages in interfirm-trading. The Production company is the upstream
division. There is no external market for the good made by the production division.
a) What is the firm’s optimal output?
b) What price should the White Company charge?
c) How much should the production division charge for the optimal amount of output?
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