Final Exam Microeconomics
Geschwandtner, Pratt, Ramsauer, Rupff and Yurtoglu
28.01.2005
Exercise 1
a) Because of a fixed stock of apartments the supply function S1 for apartments in
Vienna is Q=600 (thousand apartments). The demand function D of all tenants is
Q=1100 – p (also thousand apartments).

Compute the equilibrium price and quantity for the apartment market and
illustrate this equilibrium in a diagram.

Show the area of producer surplus in the diagram. Compute the producer
surplus.

What is the price elasticity of demand in the equilibrium?
b) In addition to the fixed supply S1 the landlords are willing to construct and supply
more apartments, if the achievable rent is higher than 350 Euro.
The supply function S2 for these additional apartments is Q=p – 350 (inverse supply
function: p=350 + Q). Hint: The quantity supplied never takes on negative values.

Illustrate the function S2 in a diagram.

What supply function Stotal results from the fixed supply S1 and the additional
supply S2? Please quote Stotal as a formula.

Illustrate the function Stotal in a diagram. Draw also the demand function D
(Q=1100 – p) and determine graphically the new equilibrium.

Also compute the new equilibrium.

Show in the diagram what surpluses the producers earn.

The computation of the producer surplus shows, that this surplus is about 14%
lower than in section a).

Explain why it may be reasonable for a landlord to construct and rent a new
apartment although the producer surplus, which all landlords together acquire,
decreases.
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Exercise 2
Julia likes to go to the restaurant, R, and to buy clothes, C. Julia’s utility function is
U=RC. It costs Julia 10 € to buy clothes or to spend an evening at her favorite
restaurant. Her monthly income is equal to 100 €.
a) Solve mathematically for her optimal bundle.
What is his utility at this
bundle?
b) Julia’s favorite restaurant offers her a membership, which costs 50 € per
month to join, but lowers the price per dinner to 2.5 €. Again, solve
mathematically for her optimal bundle. What is his utility at this bundle? Will
Julia decide to become a member?
c) Show how to determine the two bundles in a diagram using indifference
curves and budget lines. What do you observe?
Exercise 3
The cost functions of two firms are given by C1=100+y1² and C2=16+8 y2+y2².
a) Suppose that the two firms are plants of the same company (which is not a
monopoly). If the company wants to produce 23 units of output, how much
should it produce in each plant?
b) How high are the total costs? How high would these costs be if the firm would
produce the whole 23 units only in the first or only in the second plant?
c) Suppose that the two firms act independently. What is the short supply curve of
the two firms?
d) If the price is 6, what is the number of firms active in the market in the short
run? Explain why.
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Exercise 4
The government wants to drive up the price of soybeans from the equilibrium price p1
to a price p  p1 . For this purpose, it buys up and destroys the excess supply at
price p . Let the quantity demanded at price p be Q and let the quantity supplied at
price p be Q2.
(a) What are the effects of this program on consumer surplus, producer surplus,
tax revenues and total welfare?
(b) Is there an obvious reason why this policy must lead to a welfare loss?
Hint for (a): Indicate p1, p , Q and Q2 in a demand & supply diagram and label all
relevant areas with letters.
Exercise 5
Consider a duopoly with the following (inverse) demand schedule: p = 20 -y, where y
is the total output (y1 + y2). Firm 1 and 2 both have constant marginal costs of MC1 =
MC2 = 2. There are no fixed costs and y1 and y2 are the output levels of firm 1 and 2.
a) Determine the equilibrium price, the quantities and the profits in a Cournot
equilibrium?
b) Determine the equilibrium price and the profits in a Bertrand equilibrium?
c) The firms decide to form a cartel and act like a single firm. Determine the
equilibrium price, the quantities and the profits, assuming that both produce
one-half of the cartel quantity and share profits equally.
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