managerial economics – 1st homework assignment

1ST HOMEWORK ASSIGNMENT
MANAGERIAL ECONOMICS
MANAGERIAL ECONOMICS – 1ST HOMEWORK ASSIGNMENT
Please solve the following exercises and keep your answers in English language. Send your
solution in PDF format to [email protected]. Handwritten as well as late submissions will
not be accepted. Make sure to include your surname as well as your matriculation number
in the filename. The points you can achieve for each specific exercise are indicated in
brackets. You can reach a maximum of 6 points. Solve the exercises individually – cheating
such as joint work will not be tolerated.
Deadline for submission: Monday, November 17, 2014 (midnight)
1. PERFECT COMPETITION [1 POINT]
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 𝑄! = 200 light bulbs are sold
at a price of 𝑃! = 900 in the entire industry. At a price of 𝑃! = 400 consumers purchase 600
units of the good (𝑄! = 600). The whole industry is composed of 𝑁 = 10 firms. The total
cost function of each company reads 𝑇𝐶 𝑄 = 50𝑄 + 100.
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 costs at this level of output.
d) Is the market in equilibrium? Why or why not?
2. MONOPOLY [1 POINT]
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 =
1 𝑀𝑖𝑜 at a price of 𝑃 = $100. The marginal costs are 𝑀𝐶 = $40 and the average costs at this
level of output are 𝐴𝐶 1,000,000 = $90. You know that price elasticity of demand 𝜂! =
−2.
a) Would you recommend the company to change its pricing behavior?
b) What’s 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?
d) What are the characteristics of monopolies and why is the output inefficient? Under
which circumstances are they likely to occur?
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WS 2014/15
1ST HOMEWORK ASSIGNMENT
MANAGERIAL ECONOMICS
3. MONOPOLY II [1 POINT]
Suppose that the government is the only provider of water. The market demand function reads
𝐷: 𝑄 𝑃 = 50 − 2𝑃. The government’s total cost for producing water are described as
follows: 𝑇𝐶 𝑄 = 100 + 10𝑄.
a) What price will the government charge if it wants to ensure an efficient allocation of
water?
b) What price will the government charge if it wants to maximize profits?
c) Calculate the economic profit in both scenarios.
d) Calculate the dead weight loss (loss in welfare) resulting from the inefficient
allocation in example b)
e) How will the consumer as well as the producer surplus change and why?
4. PRICE DISCRIMINATION [1 POINT]
The XOCOLAT FACTORY operates in two different and wholly independent markets. It sells a
special kind of peanut butter cups in both, the US and in Europe. The demand curve for the
market in the US is described as 𝑃!" = 320 − 8𝑄!" and the demand function for the
European market is 𝑃!" = 160 − 2𝑄!" . The marginal cost function reads 𝑀𝐶 = 5 + 2𝑄
where 𝑄 = 𝑄!" + 𝑄!" . There are fixed costs of 𝐹𝐶 = $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?
5. REGRESSION ANALYSIS [1 POINT]
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.
(𝑅! = 0.82)
𝑄! = 500 − 6.8𝑃! + 4.2𝑃! + 1.2𝐴! − 0.0012𝐴!! + 0.21𝐼 + 𝜖
(3.2)
(7.5)
(12.4)
(9.2)
(6.8)
(1.1)
𝑄! is the quantity of vegetables demanded, 𝑃! is the price the Greenhouse company charges
(in dollars), 𝑃! is the price of its main competitor (in dollars), 𝐴! are advertising expenditures
(in dollars) and 𝐼 is disposable income per capita (in 100 dollars).
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WS 2014/15
1ST HOMEWORK ASSIGNMENT
MANAGERIAL ECONOMICS
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
effect 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 increase its output by spending
$1,000 on advertising?
e) Interpret the 𝑅! and the t-values, what do they suggest in this specific case? What is
the error term 𝜖?
6. ELASTICITIES [1 POINT]
Now assume that the price of the GREENHOUSE COMPANY is 𝑃! = $80, the price of its main
competitor is 𝑃! = $100 and that GREENHOUSE spends 𝐴! = $300 on advertising. The
income is 𝐼 = $120,000.1 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 𝜂!" .
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, 𝜂!" . Are the goods complementary or substitutive goods?
c) Calculate the income elasticity of demand 𝜂! . Are vegetables inferior goods?
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Note that 𝜖 is 0 by definition.
WS 2014/15