Download Chapter 6 - University of Puget Sound

Problem set 3
49.5 total points
Chapter 6 PROBLEMS
1.
Use Figure 6.4 to determine:
a.
How many baskets of fish should be harvested at market prices of
i.
$17
ii.
$13
iii.
$9
b.
How much total revenue is collected at each price?
c.
How much profit does the farmer make at each of these prices?
(a)
(b)
(c)
(d)
4.
1 pt
(i)
(ii)
(iii)
(i)
(ii)
(iii)
(i)
(ii)
(iii)
5 baskets of fish.
1 pt
4 baskets of fish.
1 pt
3 baskets of fish.
1 pt
Total revenue = P x Q = $17 x 5 = $85.
1 pt
Total revenue = P x Q = $13 x 4 = $52.
1 pt
Total revenue = P x Q = $9 x 3 = $27.
1 pt
Total profit = Total revenue – Total cost = $85 - $61 = $24.
Total profit = Total revenue – Total cost = $52 - $44 = $8.
Total profit = Total revenue – Total cost = $27 - $39 = -$12.
Graph the market behavior described in the Headline on p. 144.
Price per
Laptop
S1
S2
P1
P2
D
Q1
Q2
Q of Laptops
1 pt
1 pt
1 pt
5. Suppose that the monthly market demand schedule for Frisbees is:
Price
Quantity Demanded
$8
1,000
$7
2,000
$6
4,000
$5
8,000
$4
16,000
$3
32,000
$2
64,000
$1
150,000
Suppose further that the marginal and average costs of Frisbee production for every
competitive firm are
Rate of Output 100
200
300
400
500
600
Marginal Cost $2.00 $3.00 $4.00 $5.00 $6.00 $7.00
Average Cost
2.00
2.50
3.00
3.50
4.00
4.50
Finally, assume that the equilibrium market price is $6 per Frisbee.
a.
Draw the cost curves of the typical firm and identify its profit maximizing rate of
output and its total profits.
b.
Draw the market demand curve and identify market equilibrium.
c.
How many Frisbees are being sold in equilibrium?
d.
How many (identical) firms are initially producing Frisbees?
e.
How much profit is the typical firm making?
f.
In view of the profits being made, more firms will want to get into Frisbee
production. In the long run, these new firms will shift the market supply curve to
the right and push the price down to average total cost, thereby eliminating
profits. At what equilibrium price are all profits eliminated? How many firms
will be producing Frisbees at this price?
(a)
Cost Curves
8
Cost Per Unit
7
MC
6
5
ATC
4
3
2
1
0
0
100
200
300
400
Quantity
1 pt
500
600
700
If the market price is $6, then each individual profit maximizing firm
would produce an output of 500 units (1 pt)where MC= MR=P. Total profits are
$1,000: ($6 - $4) x 500. (1 pt)
b.
Price per Unit
Market Demand
9
8
7
6
5
4
3
2
1
0
A
0
20000
40000
60000
80000
100000
120000
140000
160000
Quantity
1 pt.
c.
d.
e.
f.
At $6 per Frisbee, market equilibrium is 4,000 units. 1 pt
Since there is an equilibrium quantity sold of 4,000, there is room for eight
firms. 1 pt
Profits of a typical firm are $1,000. 1 pt
The long run price equals the minimum ATC, $2 in this case 1 pt, at which point
economic profits will equal zero. At this price, 64,000 units are demanded and
individual firms will produce only 100 units. Thus there will be 640 firms in the
industry in the long run. 1 pt
Chapter 7 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. 1 pt
The MR is equal to $7 at 4 units of output. 1 pt Price, the maximum price
consumers are willing and able to pay, at 4 units of output is $10. 1 pt
If output is increased beyond 4 units of output, MC>MR. 1 pt 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 (corresponding to a quantity of 1). 1 pt
At a price of $13, the firm could sell 1 basket of fish for total revenue of $13. 1 pt
As shown in the table in Figure 7.1, as price is reduced from its maximum level,
the total revenue increases. 1 pt
Marginal revenue is still positive as price declines but is decreasing in value. 1 pt
Total revenue is maximized at a price of $7 1 pt
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.
e.
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?
Graph the demand and MR curves.
a.
Price (per unit)
Quantity demanded
(Units per day)
Total Revenue
Marginal Revenue
$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
½ pt each above (9.5 total)
b.
c.
d.
e.
Total revenue, P x Q, is maximized at 15 units of output. 1 pt
Marginal revenue is less than price at all levels of output. 1 pt
Marginal revenue becomes negative at 16 units of output. 1 pt
1 pt
Market for Catfish
$25
Price per unit
$20
$15
Demand
$10
$5
$0
($5)
0
5
10
15
20
Marginal
Revenue
($10)
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.
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?
c.
d.
e.
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
Quantity (Units per day)
1 pt
This chart of numbers helps answer the rest of the question
P
20
19
18
17
16
15
14
13
12
11
Q
10
11
12
13
14
15
16
17
18
19
TR
200
209
216
221
224
225
224
221
216
209
MR
9
7
5
3
1
-1
-3
-5
-7
MC
3
5
7
9
12
15
18
21
29
33
20
c & d. The monopolist produces where MC=MR at 12 units of output 1 pt and charges a
price of $18. 1 pt
e.
5.
If the market were competitive, price would equal $15 1 pt and quantity would
also equal 15. 1 pt 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
Units demanded
Marginal revenue
Price per unit
Units demanded
Total Revenue
Marginal Revenue*
½ pt each (3 total)
$40 $36 $32 $25 $2o $12 $4
10
12
14
17
25
50 150
$40
10
$400
----
$36
12
$432
16
$32
14
$448
8
$25
17
$425
-7.667
$2o
25
$500
9.375
$12
50
$600
4
$4
150
$600
0