Managerial Economics

Mr. Upton

Spring, 2000

Second Midterm Examination
April 11, 2000

 

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First Part (10 point questions

  1. Monopolistic competition occurs when several firms compete to see who will monopolize the industry. Explain whether you disagree or disagree with this statement. Disagree.  Monopolistic competition occurs when there is free entry into a business, but several firms have some degree of monopoly power..
  2. For a competitive firm, the short run supply curve is the entire upward sloping portion of the marginal cost curve.  Disagree.  It is only the part above AVC.
  3. . If independent truckers are allowed to raise their shipping rates to offset higher fuel prices, they will not be adversely affected by any surge in gas prices.  Explain whether you disagree or disagree with this statement. Disagree.  There will be a reduction in the demand for trucking services and this will mean that truckers with the higher cost functions will be adversely affected.  They will no longer be able to cover their fixed costs..
  4. Two firms, Applebee’s and Birdsong’s produce a product, for which the market demand function is

 

Quantity Produced

Price

3

17

4

15

5

13

6

11

7

10

8

9

 

Everyone in the industry knows the demand function. Each firm can produce either three or four units, at zero cost.  You are the CEO of Applebees.  In a few minutes you are going to announce your production decision.  The decision will be irrevocable.  Birdsong has yet to announce and will be watching what you do.  Set up the payoff matrix.  Then tell me how many you will produce.  Tell me why.

 

 

Applebee’s choices

 

 

Produce 3

Produce 4

 

Birdsong’s choices

Produce 3

pA =33

pB = 33

pA = 40

pB = 30

 

Produce 4

pA = 30

pB = 40

pA = 36

pB = 36

 

Announce you will produce 4.  This is a dominant strategy.  Let Birdsong take care of himself.

Second Part (30 point questions)

Directions:  Work any two (2) of the following three (3) questions.  In the boxes below, check which problems you have worked:  If you do not check the boxes, I will assume you want to work problems 1 and 2.

I have worked(Check 2)

Problem 1

 

Problem 2

 

Problem 3

 

1.       The industry demand curve for widgets is given by

Q = 4200 - 50 P

There is one and only one way of producing widgets. The cost varies with the number produced at each plant. Specifically, the cost of production for a given plant is:

 

Quantity

Total Cost

1

50

2

80

3

90

4

140

5

220

 

Assume initially that, by law, a firm is limited to operating one and only one plant.

  1. What level of output minimizes average cost? Explain your answer.

A quick calculation shows the output to be 3 per plant. LRAC is $30.

  1. Assuming that the industry is competitive, what will be the price of widgets?

Entry and exit will force the price to $30.

  1. How many will be sold?

Look at the demand curve. At a price of $30, the demand will be 2700

  1. How many plants/firms will produce widgets?

Since each firm will produce 3, there will be 900 firms.

  1. Widget plants are monitored by the Bureau of Widget Inspection, United States Department of Commerce.  (No doubt you have read stories about this Bureau).  In a move to recover the cost of monitoring these plants, the government imposes a fee of $100 per plant.  What will happen to the price of widgets, the number of plants, the quantity demanded?

Each entry in our cost function will rise by $100, and the new minimum average cost will occur at 4, with a minimum average cost of $60.  The effect will be to raise the price to 60.  The quantity demanded will fall to 1200, and the number of plants will fall to 1200/4.

 

2.       There is a particular product produced in a duopolistic industry. The industry demand curve is

Q = 80- P

 

where Q is the total quantity demanded each day and P is the price charged. To make life easy, we will assume that the product can be produced at zero marginal cost.. Given the peculiar nature of the industry, each firm must produce its output each night and then bring it to market the next day. The actual price is then set each day to clear the market.

  1. Suppose initially that the two firms can collude and set price and production to maximize combined profits. What would be the total quantity produced? At what price would it sell? And, assuming that the firms split output 50-50, what would be the profits of each firm?

In this case, the firms will act as a monopoly. They will find where MR = 0. There are a number of ways you can do this, but the bottom line is that MR = 0 at Q = 40. The price will be 40, and each firm will produce half of output. Thus each firm will sell 20 and get total revenues of (20)(40) = 800. Since there are no costs, this means each firm will earn profits of 800 as well.

  1. Now assume that the firms cannot collude or otherwise engage in cartel-like behavior.  If we assume that, when all is said and done, the two forms act as if they are in a Cournot duopoly, describe how much each firm will produce.. Show why this is a Nash equilibrium. (And yes, you will need to define what you mean by Nash equilibrium).

The duopoly solution is of course 2/3 of the monopoly competitive solution or (2/3)(80) = 53 1/3.  Thus, each firm will produce 26 2/3 units.  To be a Nash equilibrium, each firm must be acting rationally, and believe its actions do not impact the behavior of others. And given the other’s output, each firm is acting rationally.

3.  The demand function for a particular product is shown below.  The product is produced by a monopolist.   Using this graph, show the profit maximizing quantity and price.  Also show graphically, the firm’s profits. Hint:  you are going to want to draw one more line.   Tell me what you can about where this line hits either or both of the axes.  Be sure to label the graph appropriately and explain your symbols.  This is important:  this is not a class in drafting and I want to make sure you mean what you draw.

 

Answer:

I have reproduced the exam.  Sorry, I used color so it looks great on a monitor but doesn’t print out so well in black and white.

Some key features that should be noted:  First the MR curve hits the quantity axis at Qo/2.  The firm produces Q1, where MR = MC.  This is close to the point where MR =AC, but that answer is not at all acceptable for a variety of reasons.  The price P1 is the price at which Q1 is demanded.  The shaded area, the difference between  AC and price, shows profits.

The extra curve is of course the MR curve and I have shown what we know about where it hits both axes.