Download PROBLEMS

PROBLEMS
1.
In Figure 7.1,
a.
What is the highest price the monopolist could charge and still sell fish?
b.
What is total revenue at that highest price?
c.
What happens to total revenue as price is reduced from its maximum?
d.
Is marginal revenue positive or negative as price declines?
e.
At what price is total revenue maximized?
a.
b.
c.
d.
e.
2.
Use Figure 7.2 to answer the following questions:
a.
b.
c.
What rate of output maximizes total profit?
What is MR at that rate of output? What is price?
If output is increased beyond that point, what is the relationship of MC to
MR? How will this affect total profits?
a.
b.
Profit is maximized where MR=MC which occurs at the output level of 4.
The MR is equal to $7 at 4 units of output. Price, the maximum price
consumers are willing and able to pay, at 4 units of output is $10.
If output is increased beyond 4 units of output, MC>MR. This will cause
total profits to fall because the additional costs incurred exceed the
additional revenue received for each unit of output produced.
c.
3.
The highest price firms can charge and still sell fish is $13 as shown on
the demand curve.
At a price of $13, the firm could sell 1 basket of fish for a total revenue of
$13.
As shown in the table in Figure 7.1, as price is reduced from its maximum
level, the total revenue increases.
Marginal revenue is still positive as price declines but is decreasing in
value.
Total revenue is maximized at a price of $7 for a total revenue of $49. If
price is dropped to $6, total revenue will begin to decline as MR becomes
negative.
Suppose the following data represent the market demand for catfish.
Price (per unit)
$20 19 18 17 16 15 14 13 12 11
Quantity demanded 10 11 12 13 14 15 16 17 18 19
(Units per day)
Total Revenue
Marginal Revenue
a.
b.
c.
d.
Compute total and marginal revenue to complete the table above.
At what rate of output is total revenue maximized?
At what rate of output is MR less than price?
At what rate of output does MR become negative?
e.
Graph the demand and MR curves.
a.
Price (per unit)
Quantity
demanded
(Units per day)
Total Revenue
Marginal
Revenue
b.
c.
d.
e.
$20 19
10 11
18
12
17
13
16
14
15
15
14
16
13
17
12
18
11
19
200 209 216 221 224 225 224 221 216 209
---- 9
7
5
3
1
-1
-3
-5
-7
Total revenue, P x Q, is maximized at 15 units of output.
Marginal revenue is less than price at all levels of output.
Marginal revenue becomes negative at 16 units of output.
Market for Catfish
$25
$20
Price per unit
$15
Demand
$10
$5
$0
($5)
0
5
10
($10)
15
20
Marginal
Revenue
Quantity (Units per Day)
4.
Assume that the following marginal costs exist in catfish production:
Quantity produced 10 11 12 13 14 15 16 17 18 19
(Units per day)
Marginal cost
$3 5 7 9 12 15 18 21 25 29
(per unit)
a.
b.
Graph the MC curve.
Use the data on market demand from problem 3 to graph the demand and
MR curves on the same graph.
c.
d.
e.
At what rate of output is MR=MC?
What price will a monopolist charge for that much output?
If the market were perfectly competitive, what price would prevail? How
much output would be produced?
a and b:
$ per unit
Market for Catfish
$35
$30
$25
$20
$15
$10
$5
$0
($5) 0
($10)
MC
D
MR
5
10
15
20
Quantity (Units per day)
This chart of numbers helps answer the rest of the question
P
Q
TR
MR
MC
20
19
18
17
16
15
14
13
12
11
10
11
12
13
14
15
16
17
18
19
200
209
216
221
224
225
224
221
216
209
9
7
5
3
1
-1
-3
-5
-7
3
5
7
9
12
15
18
21
29
33
c & d. The monopolist produces where MC=MR at 12 units of output and
charges a price of $18.
e.
5.
If the market were competitive, price would equal $15 and quantity
would also equal 15. This is the output and price that exist where MC =
P=MR.
Compute marginal revenues from the following data on market demand:
Price per unit
$40 $36 $32 $25 $2o $12 $4
Units demanded 10 12 14 17 25 50 150
Marginal revenue
Price per unit
$40
Units demanded
10
Total Revenue
$400
Marginal Revenue*
$36
12
$432
16
$32
14
$448
8
$25
19
$475
5.40
$2o
25
$500
4.17
$12
50
$600
4
$4
150
$600
0
*Remember that Marginal Revenue is calculated as:
(Change in Total Revenue)/(Change in Output)
6.
If the price elasticity of demand for oil were 0.1, by how much would the price of
oil have risen in response to the September 2003 OPEC production cutback? (See
Headline, p. 164)
If the output were cut by 3.5 percent with a price elasticity of 0.1, the price would
change by 35 percent. E=%Q/%P= 3.5%/%P = 0.1. Solving for %P
yields the answer of 35%.
7.
If the on-campus demand for soda is as follows:
Price (per can)
$0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Quantity demanded 100
90
80
70
60
50
40
30
(per day)
and the marginal cost of supplying a soda is 50 cents, what price will students end
up paying in.
a.
A perfectly competitive market?
b.
A monopolized market?
The answer to this question is best illustrated using a graph.
Market for Soda
2.5
2
Price (per can)
1.5
1
MC
0.5
D
0
-0.5 0
20
40
60
80
100
120
-1
-1.5
MR
-2
-2.5
Quantity (per day)
In a competitive market, students would pay $0.50 per Pepsi. Remember that in a
competitive market, the price equals the MC of the last item sold.
In a monopoly market, the monopolist produces at the point where MC=MR. In
this case, MC = MR at 50 cans per day, thus students would pay $1.50 per can.
8.
According to the Headline on p. 167, how much profit per year might the
producers of Cardizem have been making if their average total costs were equal to
that of the generic substitute.
Knowns:
PCardizem: PC=$73/month
PGeneric: PG=$32/month
Under competition P=ATC (in long run), so let's assume ATC=$32/month
(generic price) for the manufacturings of Cardizem.
AR-AC=A π
$73-$32=$41 for 12 months=$492π over one year.
The firm would earn $492/yr. on every individual purchasing Cardizem during
this period of time.
Total sales/Price per unit = $700,000,000/$73 = 9,589,041 units sold.
$492(9.6 million) = $4.7 billion