Temple University

Department of Economics

 

Principles of Microeconomics – Honors

 

Midterm Exam

 

 

 

Name ___________________________________

 

 

Directions: You must do all parts of all questions.  You have 50 minutes to complete the exam.  Where an explanation is called for, please be brief.  The work must be your own; you may neither give nor receive help.  This is a closed book exam.  Point values of the questions are shown.  Blank answers receive no partial credit.  If your handwriting is not legible then I will grade your answers as non-responsive.

 

 

1. (20 points) Stu deBaker owns a car dealership. Pierce Arrow also owns a dealership. They compete on price.  They can price their mid-size sedan either high or low. The numbers in the table are the change in profit that each will experience as a result of the game. Find the dominant strategy solution to their pricing game. Be sure to explain your reasoning.

 

 

 

Pierce

 

 

High

Low

Stu

High

10, 10

-10, 50

Low

50, -10

0, 0

 

 

Strategy to be played by Pierce _____LOW_________________

 

 

Strategy to be played by Stu ________LOW ________________

 

 

Explanation:  For either Stu or Pierce the payoff from playing LOW is greater than the payoff from playing HIGH regardless of the strategy played by the opponent.  This is the definition of a dominant strategy.

 

 

 

 

2. Poppy Seed and Miss Ann Thrope are the only two purveyors of bagels in Temple Town.  It has come to their attention that the students expect there to be a hole in the middle of a bagel.  They are now confronted with the problem of whether to drill a hole in their product, or leave it alone.  If they drill holes in the bagels, then they must choose between a wide hole and a narrow hole. Use IDES to find the solution to their game. Be sure to explain your reasoning.

 

 

Poppy

Don’t Drill

Narrow

Wide

Miss Ann

Don’t Drill

0, 0

0, 44

0, 31

Narrow

44, 0

14, 14

-1, 16

Wide

31, 0

16, -1

1, 1

 

 

 

Strategy to be played by Poppy in the solution to the game _____WIDE_____________

 

 

Strategy to be played by Miss Ann in the solution to the game _____WIDE___________

 

 

Explanation:

 

For Poppy WIDE dominates DON’T DRILL, so cross off that column.  The same is true for Miss Ann: WIDE dominates DON’T DRILL, so cross off that row.  In the remaining 2x2 game WIDE dominates NARROW for both players, so they should both play WIDE.

3. Find the Nash equilibrium(s) in the following game between Fred and Clara.  They are trying to decide what to do on Saturday evening.  They will resolve the question by writing their vote on a piece of paper.  If they have both written opera, then that is what they do.  If they have both written football, then they go to the game.  If there is no agreement on the slips of paper then they stay home and watch TV.  The payoffs are in utils of well being.

 

 

 

Clara

 

 

Opera

Football

Fred

Opera

14, 14

2, 16

Football

16, 2

1, 1

 

 

How many Nash equilibrium(s) is(are) there? _____2_________

 

 

What strategies are played in the Nash equilibrium(s): Fred’s best response to a play of OPERA by Clara is to play FOOTBALL.  When Fred plays FOOTBALL Clara’s best response is to play OPERA.  There is a coincidence of conjectures so this is a Nash Equilibrium.

 

Fred’s best response to a play of FOOTBALL by Clara is to play OPERA.  When Fred plays OPERA Clara’s best response is to play FOOTBALL.  Again, there is a coincidence of conjectures so this is also a Nash Equilibrium.

 

4. Find the mixed strategies that will be played by Julie Yard and Anna Conda in their game for control of the neighborhood swamp. Each can choose to ‘drain and develop’ or turn it into a ‘nature preserve’.  Their payoffs from the different strategies are shown in terms of their esteem in the community.

 

 

 

Julie Yard

 

 

Drain and develop

Nature preserve

Anna Conda

Drain and develop

5, 12

0, 0

Nature preserve

0, 0

10, 4

 

With what probability will Julie play ‘drain’? ___< D, 2/3 >___________

 

With what probability will Anna play ‘drain’? ______< D, ¼ >_______

 

Explain: Anna wants to choose her mixed strategy so that Julie is indifferent between playing Drain and Preserve.  Let p represent Anna’s probability of playing Drain. Then 12p+0(1-p) = 0p+4(1-p) is Julie’s condition for indifference.  Solving for p we get p= ¼ .

 

Julie wants to pick her q so that Anna is indifferent between Drain and Preserve. 5q+0(1-q) = 0q+10(1-q) can be solved for q = 2/3 .

5. Find the elasticity of demand for movies in China using the attached newspaper article.

  1. The cost of a movie ticket has been cut to how may yuan? ____5 yuan____

  2. What was the original cost of a movie ticket (in yuan)? ___15 yuan_______

  3. Let TR1 be the revenue from ticket sales at the original price.  What is revenue at the new price, stated in terms of the original revenue? TR2 = ___3TR1_________
  4. Express TR1 in terms of the known price of a ticket and the unknown quantity sold. ___TR1=15Q1__________
  5. Express TR2  in terms of the known price of a ticket and the unknown quantity sold. ____TR2=5Q2________
  6. Using your previous answers, express the quantity sold at the new price in terms of the quantity of tickets sold at the old price. ________________

TR2=3TR1  è  5Q2=3(15Q1)  è Q2=9Q1

  1. What is the formula for the elasticity of demand?


  2. Use your previous answers to calculate the elasticity of demand for movie tickets.

Substituting we get