Managerial Economics

Mr. Upton

Spring, 1999

Second Midterm Examination
April 15, 1999

First Part (10 point questions). Explain whether you agree or disagree with these statements.

1.      Both a monopoly firm and a competitive firm will operate where MR = MC.

Agree. For a competitive firm, MR = P

2.      A monopolist who can produce widgets for $5 each. Right now he is selling 1,000 widgets a year. He discovers a new way to produce them for $4 each. His profits will go up by more than $1,000 a year.

Disagree. MR will now be above marginal cost. If the monopolist continued to produce only 1,000 widgets a year, his profits would go up by only $1,000 a year. But the Monopolist will find that MR will now be above marginal cost and will expand output to make even more profit.

3.      If two Duopolies are in Cournot Equilibrium, they are also in a Nash Equilibrium and vice versa.

Disagree. A Bertrand Equilibrium can also be a Nash Equilibrium

4.      If the price of an input increases, a manager can substitute other factors and, if he is lucky, reduce total production costs.

Disagree. If he can do this, why didn't he make the substitution in the first place? He can offset the impact on cost, but he can never reverse the increase in cost.

Second Part (20 point questions)

Directions: Work any two (2) of the following three (3) questions. In the boxes below, check which problems you have worked:

I have worked
(Check 2)

Problem 1

 

Problem 2

 

Problem 3

 

1.       The cost of running a plant to process and freeze lima beans obviously depends on the amount of beans processed and frozen. A careful study has shown that the cost function is as follows:

Number of pounds of Lima Beans Processed and Frozen (000)

Cost ($000)

1

3

2

5

3

6

4

9

5

14

6

18

The US Department of Agriculture has conducted extensive studies of the supply and demand for frozen lima beans.. Their studies have conclusively proved that the demand function is

Q =140,000 - 20,000prr

and that the supply is

Q= 40,000+ 10,000pw

pr and pw give the retail price and wholesale price respectively. That is, these are the prices paid by consumers and by processing plants. There are no other costs of bringing lima beans to the market aside from processing costs and the cost of lima beans themselves. (I.e., you don't have to worry about shipping costs, retailing costs, etc.). While perhaps not realistic, these assumptions do simplify the problem.

What is the retail price of a pound of frozen lima beans? How many plants produce them?

The minimum average cost occurs when each plant is producing 3,000 pounds at an average cost of $2.00 each. Competition will force the price of processing down to this level. We know this means that pr = pw + 2. Now look at our two supply and demand curves. To keep supply and demand equal, we know that

140,000 - 20,000pr = 40,000+ 10,000pw

If we substitute in for the wholesale price we get

140,000 - 20,000pr = 20,000+ 10,000r

We can solve that for the retail price of lima beans as $4. Going back to our demand equation, that means the quantity demanded will be 60,000 pounds. That requires 20 plants producing 3,000 ears each.

2.       The market for a certain product is highly competitive. Right now there are numerous firms producing the product. The current technology is about 20 years old. Everyone in the industry uses it. A new technology is about to come along, which will reduce the cost of making the product to $10 each. Your firm, Wonder Technologies, Inc. has asked you to evaluate the market for this new product. Initially the job of evaluating the project fell to the management consulting firm, Dull, Dull, and Overpriced (DDP). At great expense, they had determined the cost structure for existing plants to be as follows:

Quantity

Total Cost

0

11

1

14

2

26

3

36

4

52

5

75

They had also determined that currently, 15,000 units of this product were sold annually. The price is expected to drop when the new technology comes on the market. DDP estimated that each $1 drop in price would increase annual demand by 2,000 units.

Management has asked you to answer several questions

(a)       What will be the total market for this product when the new innovation comes on the market?

Right now the minimum of the AC curve is at $12, with each plant producing 3 units. Thus the price must be $12. The new technology will drive the price down by $2, so annual sales will rise to 19,000 units.

(b)       What will be the price of the product when the new innovation comes on the market?

$10. That should be obvious.

(c)        Assuming that no firms currently producing the product leave the market, what will be the number of units produced using the new technology?

Each firm currently in the industry will reduce output so that MC = P. That means production of 2 units per plant. Since 15,000 units are now being sold, there must be 5,000 plants. Thus the old plants will continue to produce 10,000 units, so that 9,000 will be produced by the new technology.

(d)       Over time, the plants using the current technology will wear out and leave the industry. When 3,000 plants remain, what will be the annual production using the new technology? (You may assume that no, even, newer technology, comes to market).

13,000. Total production by old plants will decline to 6,000.

Note: in answering these questions, you might think it useful to know how many plants there are now, and what the current price of the product is. All that information was contained in the DDP interim report, but the only parts of that report available to you are the data given above. And, to make life more interesting, your supervisor is too cheap to authorize you to do any market research. Fortunately, you need not do any.

3.     The industry demand curve for widgets is given by

Q = 3900 - 100 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

33

2

42

3

54

4

78

5

105

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 $18.

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

Entry and exit will force the price to $18.

  1. How many will be sold?

Look at the demand curve. At a price of $18, the demand will be 2100

  1. How many plants/firms will produce widgets?

Since each firm will produce 3, there will be 700 firms.

  1. Now assume that a firm is allowed a monopoly in the production of widgets. What price will it charge?

The monopolist has a MC of 18. He must calculate MR. Revenue is

pQ =(39 -0.01 Q) Q.

Differentiating, we get MR = 39 -0.02Q. We can set that equal to MC, $18, and solve for the profit maximizing quantity of Q: 1050. The price will then be $28.50 (substitute 1050 into the demand curve and solve for P).

  1. How many plants will it operate?

350. The monopolist wants to minimize cost.