Download Esame di Microeconomia avanzata (16 aprile 2004)

Advanced Microeconomics.
Examination Set (February 15th, 2012)
(Paolo Bertoletti & Giuseppe De Feo)
6 Credits: exercises I and II; 90 minutes. 9 Credits: exercise I, II and III; 120 minutes.
Exercise I
In a market characterized by the following inverse demand function:
P = 10 - Q if Q  10
0 if Q  10
where Q is the total quantity produced by all the suppliers, suppose that only one firm (firm 1) is
active on the market and that its production cost is described by the function C1 (q1 )  2q1 .
a) Compute the monopoly quantity, price, and profit.
Suppose now that a second firm (firm 2), having the same cost function as firm 1 (i.e.,
C2 (q2 )  2q2 ), enters the market and that the two firms compete in quantities.
b) Define the game being played, determine the firms' reaction functions and compute the
Nash equilibrium quantities. What are the profit earned by each firm and the market
price in equilibrium?
c) Show that the price approaches the perfectly competitive market price as the number
of firms increases and tends to infinite.
Exercise II
Malcom’s preferences over wealth can be described by the utility function U(x) = x .
a) Show that Malcom is risk averse.
Suppose that his entire wealth is provided by a property worth 1million Euro. However this
property has a 10% chance of being destroyed by a fire.
b) Compute the utility of the expected value and the expected utility of the property for
Malcom. Why do they differ?
c) Show that Malcom is willing to pay a maximum price of €190.000 for an insurance contract
fully covering the risk of fire.
Exercise III
Consider the function e(p1,p2,u)=(p1p2) u.
1) Under which conditions is it a valid consumer expenditure function, and why?
2) Obtain the corresponding indirect utility function.
3) Now obtain the direct utility function (hint: use the previous result and the Marshallian
demand functions).