Managerial
Economics
Mr.
Upton
Spring,
2000
Second Midterm
Examination
April 11, 2000
S1 |
S2 |
S3 |
S4 |
L1 |
L2 |
L3 |
ĺ |
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.
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.
A
quick calculation shows the output to be 3 per plant. LRAC is $30.
Entry
and exit will force the price to $30.
Look
at the demand curve. At a price of $30, the demand will be 2700
Since
each firm will produce 3, there will be 900 firms.
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.
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.
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.