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ECON 102 Homework 5

Homework 5      

   Read these instructions carefully!

  • Carefully answer each of the questions below. 
  • You can write or type your answers for the questions EXCEPT ANY GRAPHS MUST BE COMPLETED BY HAND (NOT USING THE DRAWING TOOLS IN WORD OR ANY OTHER PROGRAM). 

  • 1.  Suppose that a monopolistically competitive firm must build a production facility in order to produce a product.  The fixed cost of this facility is FC = $24.  Also, the firm has constant marginal cost, MC = $3.  Demand for the product that the firm produces is given by P = 27-3Q. 

a) Fill in the table below.  If any of your values have decimals, you may round to only one numeral after the decimal (nearest 10th of a dollar). 

Quantity of OutputPriceTotal CostAverage Total CostTotal RevenueProfits
115331512
215633024
315934536
4151236048
5151537560
6151839072
71521310584
81524312096
915273135108

b) (10 points) How much output will this firm produce if it maximizes profit?

c) (5 points) What price should this firm charge if it wants to maximize profit?

2.  Carefully explain what will happen as we move from the short run to a long run equilibrium in a monopolistically competitive industry if firms are making a positive profit in the short run.  Your explanation should clearly state what will happen to the demand curve facing an individual firm and the reason why this happens.

SAMPLE ANSWER :

Monopolistic competition refers to the market organization where there are a fairly large number of firms which sell somewhat differentiated products.

 In the figure 1 the downward sloping demand curve (AR curve) is quite elastic. The MR curve lies below-the average curve except at point N. The SMC curve which includes advertising and sales promotional costs is drawn in the usual fashion. The SMC curve cuts the MR curve from below at point Z. The firm produces and sells an output OK, as at this level of output MR = MC. The firm sells output OK at OE/KM per unit price. The total revenue of the firm is equal to the area OEMK, whereas the total cost of producing output OK is OFLK. The total profits of the firm are equal to the shaded rectangle FEML. The firm earns abnormal profits in the short run.


3.  Suppose that two players are playing the following game.  Player A can choose either Top or Bottom, and Player B can choose either Left or Right.  The payoffs are given in the following table, where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B:

                     Player B
  Player A LeftRight
Top 2        5          1             4
 Bottom 0         1 3             8

A) Does player A have a dominant strategy, and if so what is it?

SAMPLE ANSWER:

Player A has  a  dominant strategy : top when
player B chooses left  or right.

B) Does player B have a dominant strategy and if so what is it?

C) For each of the following say True if the strategy combination is a Nash equilibrium, and False if it is not a Nash equilibrium:

i) Player A plays Top and Player B plays Left

ii) Player A plays Bottom and Player B plays Left

 iii) Player A plays Top and Player B plays Right

iv) Player A plays Bottom and Player B plays Right

D) If each player plays her maximin strategy what will be the outcome of the game?  (Give your answer in terms of the strategies each player chooses—for example, “Player A plays Bottom and Player B plays Right”)

SAMPLE ANSWER:

With a maximin strategy, a player determines the worst outcome for eachoption, then chooses the option that maximizes the payoff among the worst outcomes. If player A chooses top, the worst payoff would occur if player B chooses right: player A’s payoff would be 4. If player A
chooses bottom, the worst payoff would occur if player B chooses left:
player A’s payoff would be 0. With a maximin strategy, therefore
player A chooses bottom.

E) Now suppose the same game is played with the exception that Player A moves first and Player B moves second.  Draw the game tree associated with this situation.  Using the backward induction method discussed in the online class notes, what will be the outcome of the game?

4. Suppose there are 12 firms in an industry.  The percentage of total sales is given in the following table:

FirmPercentage of total sales
116
214
312
412
510
68
76
86
95
104
114
123

A) Calculate the HHI for this industry.

FirmPercentage of total sales%Share(%Share)²
11616256
21414196
31212144
41212144
51010100
68864
76636
86636
95525
104416
114416
12339
HHI  1042

B)If firms 6 and 7 decide to merge, would this merger be challenged by the FTC?  Why or why not?

FirmPercentage of total salesMerge%Share(%Share)²
116 16256
214 14196
312 12144
412 12144
510 10100
68 00
76 00
86 636
95 525
104 416
114 416
123 39
HHI   1138

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