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Questions on Monopoly Behavior and Game Theory for Midterm 2 | ECON 1100, Study notes of Microeconomics

Material Type: Notes; Professor: Vesterlund; Class: INTERMEDIATE MICROECONOMICS; Subject: Economics; University: University of Pittsburgh; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

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Econ. 1100
Professor Lise Vesterlund
Review Questions for Material Covered after Second Midterm
Chapter 25.4-25.6: Monopoly Behavior
1. Suppose a monopolist offers a price p1 to one group of customers and a price p2 to another
distinguishable group of customers. If p1 < p2 what do we know about the price elasticity of
demand for group 1 as compared to group 2?
2. The demand by Danes can be described by the equation pD = 100 - yD, and the demand by
Swedes can be described by pS = 50 - yS/2. The average and marginal cost of production equals
$20. If a monopolist can distinguish the two types of customers what price will she charge each
of the two groups? What price will she charge if she can’t distinguish the two groups? What
profit will she make in each of the two cases?
3. Suppose the individual demand for rides at an amusement park can be described by the
demand function p=10-y, where y is the number of rides, and the marginal cost per ride is zero.
How much would a monopolist charge per ride? How large an entrance fee would he charge?
Chapter 27.1-27.2,27.5-27.8,27.10: Oligopoly
1. The market demand is given by p=14-2y, and there are two identical firms producing the
output. The per unit cost of producing y is $2. Suppose the two firms simultaneously choose
how much to produce. How much will each firm produce? What price will the product sell for?
How much profit will each firm make?
2. How do your answers to question 1 change when firm 1 first decides how much to produce
and firm 2 selects its preferred output level after having observed firm 1's decision?
3. Draw a picture of the two firm’s best response functions and illustrate the Cournot and
Stackelberg equilibria, as well as the outcome that would result when firm 2 is the only one
producing in the market..
4. How much is produced in total if the two firms collude and choose an output level y1 + y2
that maximizes the joint profit for the two firms? Why would it be difficult to sustain this
production level?
4. Suppose there are n identical firms who simultaneously decide how much to produce. The
market demand is p=100-Y, where Y= y1 + y2 + y3+ .... + yn . The marginal cost of production is
$1. Find the individual firm’s best response function, and determine the Cournot equilibrium.
What price is charged when n64?
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Download Questions on Monopoly Behavior and Game Theory for Midterm 2 | ECON 1100 and more Study notes Microeconomics in PDF only on Docsity!

Econ. 1100 Professor Lise Vesterlund

Review Questions for Material Covered after Second Midterm

Chapter 25.4-25.6: Monopoly Behavior

  1. Suppose a monopolist offers a price p 1 to one group of customers and a price p 2 to another distinguishable group of customers. If p 1 < p 2 what do we know about the price elasticity of demand for group 1 as compared to group 2?
  2. The demand by Danes can be described by the equation p (^) D = 100 - yD , and the demand by Swedes can be described by p (^) S = 50 - yS /2. The average and marginal cost of production equals $20. If a monopolist can distinguish the two types of customers what price will she charge each of the two groups? What price will she charge if she can’t distinguish the two groups? What profit will she make in each of the two cases?
  3. Suppose the individual demand for rides at an amusement park can be described by the demand function p=10-y, where y is the number of rides, and the marginal cost per ride is zero. How much would a monopolist charge per ride? How large an entrance fee would he charge?

Chapter 27.1-27.2,27.5-27.8,27.10: Oligopoly

  1. The market demand is given by p=14-2y , and there are two identical firms producing the output. The per unit cost of producing y is $2. Suppose the two firms simultaneously choose how much to produce. How much will each firm produce? What price will the product sell for? How much profit will each firm make?
  2. How do your answers to question 1 change when firm 1 first decides how much to produce and firm 2 selects its preferred output level after having observed firm 1's decision?
  3. Draw a picture of the two firm’s best response functions and illustrate the Cournot and Stackelberg equilibria, as well as the outcome that would result when firm 2 is the only one producing in the market..
  4. How much is produced in total if the two firms collude and choose an output level y 1 + y (^2) that maximizes the joint profit for the two firms? Why would it be difficult to sustain this production level?
  5. Suppose there are n identical firms who simultaneously decide how much to produce. The market demand is p=100-Y, where Y= y 1 + y 2 + y 3 + .... + yn. The marginal cost of production is $1. Find the individual firm’s best response function, and determine the Cournot equilibrium. What price is charged when n 64?

Chapter 28 & 29.1-29.6: Game Theory

  1. Are all Nash Equilibria also Dominant Strategy Equilibria?
  2. Are all Dominant Strategy Equilibria also Nash Equilibria?
  3. Find the pure and mixed strategy Nash Equilibria for each of the 3 games listed below. In each case you should illustrate the equilibria by drawing the best response functions for each of the two players.

Player B

Left Right

Player A Top 5,3 2,

Bottom 4,2 4,

Player B

Left Right

Player A Top 2,1 0,

Bottom 0,0 21,

Player B

Left Right

Player A Top 4,4 0,

Bottom 7,0 1,

  1. Consider the prisoner’ dilemma game. What should criminal A do if he thinks that criminal 2 will deny the charges: deny or confess to the charges?
  2. A general has two possible pure strategies, sending all his troops by land or all his troops by sea. Is it a mixed strategy to send 1/4 of his troops by land and 3/4 of his troops by sea?
  3. What is a Nash equilibrium?
  4. There are N>2 inhabitants in a small town. Each has $100. They are told that they can voluntarily contribute to a fund that will be evenly split between all residents. If $F are contributed to the fund, the local K-Mart will match the private contributions so that the total amount to be divided is $2F. That is, each resident will get back a payment of $2F/N when the fund is divided. If people in town only care about their own net incomes, in Nash equilibrium, how much will each person contribute to the fund?