CHAPTER TEN
Answers to Self Test Questions
1.
At a fare of $1.50 the quantity demanded is 100 000, of which each company would serve 50 000. The
average cost of servicing 50 000 riders is $2.50. This means that each company would make a loss of
$1.00 for each fare, for a total loss of 50 000 x $1.00 equals $50 000 per day.
2.
The monopolist’s total revenue at a price of $50 is $75 000 (1500 x $50). At a price of $45, the total
revenue is $76 500 (1700 x $45). The extra 200 units produces extra total revenue of $1500. The
marginal revenue is therefore $1500/200 = $7.50. The demand is price elastic over this range since the
drop in price caused an increase in total revenue. The elasticity co-efficient is equal to:
ε = %∆Q
%∆P
3.
= 12.5
10.5
= 200/1600 x 100
5/47.5 x 100
= 1.19
See Table AK 42.
Table AK 42
Quantity
Price (=AR)
Total Revenue (TR)
Total Costs (TC)
20
21
22
23
24
25
26
27
28
29
$100
98
96
94
92
90
88
86
84
82
2 000
2 058
2 112
2 162
2 208
2 250
2 288
2 322
2 352
2 378
$2060
2080
2112
2142
2177
2216
2257
2322
2417
2530
Total Profit
(T -60
-22
0
20
31
34
31
0
-65
-152
Break-even outputs occur at 22 and 27. Profit-maximizing output occurs at an output of 25 (profit =$34).
4.
See Table AK 43
Table AK 43
Quantity
1
2
3
4
5
6
7
8
9
10
11
12
Marginal Marginal Revenue (MR) Marginal Profit
Cost
(MC)
$20
$8
18
$10
6
16
10
4
14
10
8
12
4
10
10
0
13
8
-5
15
6
-9
17
4
-13
19
2
- 17
21
0
- 21
23
-2
-25
53
The firm will maximise profits by continuing to produce as long as marginal profits are positive, i.e. up to
an output of 6. This confirms the profit-maximizing output from Text Table 10.3.
5.
See Table AK 44
Table AK 44
Quantity Price Total Revenue Total Costs
(TR)
(TC)
20
$100
$2000
$2067
21
98
2058
2087
22
96
2112
2112
23
94
2162
2142
24
92
2208
2177
25
90
2250
2216
26
88
2288
2257
27
86
2322
2322
28
84
2352
2417
29
82
2378
2530
Average Costs Marginal Costs
Marginal
(AC)
(MC)
Revenue (MR)
103.35
99.38
20.00
58.00
96.00
25.00
54.00
93.13
30.00
50.00
90.71
35.00
46.00
88.64
39.00
42.00
86.81
41.00
38.00
86.00
65.00
34.00
86.32
95.00
30.00
87.24
113.00
26.00
A) Break even occurs at outputs of 22 (total revenue = total costs = $2112) and 27 (total revenue = total
costs = $2322). At an output of 22, average cost = price = $96. At an output of 27, average cost =
price = $86.
B) Profit maximizing output is where MR = MC. In general, a firm should continue to produce as long
as marginal profit is positive, i.e. as long as MR exceeds MC. In the above table this means up to an
output of 25. The price charged would be $90, and the total profit is $34 ($2250 minus $2216).
6.
Total revenue for the perfectly-competitive industry is $800 000 ($4 times 200 000). Total revenue for
the monopolist industry is $825 000 ($5.50 times 150 000). It wouldn’t charge the same price. It would
restrict output and push up the price.
7.
See Table AK 45
Table AK 45
Output
10
11
12
13
14
15
16
17
18
19
20
21
22
Price
(=AR)
$30
29
28
27
26
25
24
23
22
21
20
19
18
Total
Rev.
300.00
319.00
336.00
351.00
364.00
375.00
384.00
391.00
396.00
399.00
400.00
399.00
396.00
Marg.
Rev.
19.00
17.00
15.00
13.00
11.00
9.00
7.00
5.00
3.00
1.00
-1.00
-3.00
54
Total
Costs
$258
268
280.3
293
306
319.5
334
350
368
389
414
444
482
Av.
Costs
25.80
24.36
23.36
22.54
21.86
21.30
20.88
20.59
20.44
20.47
20.70
21.14
21.91
Marg.
Costs
10.00
12.30
12.70
13.00
13.50
14.50
16.00
18.00
21.00
25.00
30.00
38.00
Total
Profit
42.00
51.00
55.70
58.00
58.00
55.50
50.00
41.00
28.00
10.00
-14.00
-45.00
-86.00
A) Monopoly output is where MC = MR, i.e., at 14. Price is $26. Total profits are $58.
B) Perfectly competitive industry output is where supply (MC) = demand (which is AR or price). This
occurs at an output of 19. Price is $21. Total profits are $10.
C) Given similar costs, a monopolist will produce a smaller output, charge a higher price and make
greater economic profits than a group of firms in a competitive industry.
8.
A) An unregulated monopolist would produce an output where MC = MR. This would be at an output
of 4 (MC = MR = $70). The price would be $115. Total revenue would be equal to 4 x $115 = $460.
Total cost would be 4 x $105 (average cost) = $420. Total profit therefore would be the difference of
$40.
B) The socially-optimum price is where P = MC. This occurs at an output of 6. The price is $85.
Total revenue would be equal to 6 x $85 = $510. Total cost would be 6 x $97.50 (average cost) = $585.
Total loss therefore would be the difference of $75.
C) The fair-return price is where P = AC. This occurs at an output of 5. The price is $100. Total
revenue would be equal to 5 x $100 = $500. Total cost would be 5 x $100 (average cost) = $500. The
monopolist would break even and make only normal profits.
Answers to Study Guide Questions
Are You Sure?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
True.
True.
False: it is always less than the average revenue.
True.
False: the price will be above the marginal cost.
True.
False: a lump-sum tax will have no effect on the price or output.
False: it is set equal to the average cost, but not necessarily the lowest cost.
True.
True.
Choose the Best
11. a
12. b
13. b
14. c
15. a
16. c
17. a
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
c
a
b
b
a
d
b
55
d
c
e
b
c
c
Problems
31. See Table AK 46
Table AK 46
Quantity
per period
0
1
2
3
4
5
6
7
8
9
10
b) P = $40; Q = 6;
c)
Price
TR
MR
MC
TC
ATC
50
48
46
44
42
40
38
36
34
32
50
96
138
176
210
240
266
288
306
320
50
46
42
38
34
30
26
22
18
14
35
30
25
20
25
30
35
40
45
50
25
60
90
115
135
160
190
225
265
310
360
60
45
38.3
33.75
32
31.67
32.14
33.13
34.44
36
Tp= + $50.
Q = 13; TR = $338.
32. See Table AK 47
Table AK 47
Q
1
2
3
4
5
6
7
8
9
10
11
12
P
16
15
14
13
12
11
10
9
8
7
6
5
TR
16
30
42
52
60
66
70
72
72
70
66
60
Figure AK 42
56
MR
16
14
12
10
8
6
4
2
0
-2
-4
-6
b)
c)
d)
e)
f)
Quantity = 9 (TR = $72); Marginal revenue = 0
1.
9.
Elastic.
A monopolist will always produce an output where the demand is elastic.
33. See Table AK 48
Table AK 48
a) Sales revenue
maximization
b)Profit
maximization
c)Socially
optimum price
d) Fair return price
34. a) - d)
(1)
Price ($)
8
(2)
Output
8
(3)
Total Revenue ($)
64
9
7
63
(4)
Total Profit ($)
Between 12 and
14
14
5
11
55
– 11
6
10
60
0
See Figure AK 43
Figure AK 43
57
Translations
2
4
6
8
10
Quantity of drums per period
Figure AK 44
Key Problem
a)
First work out the total revenue (TR) by multiplying the price by the quantity demanded (column 1 times
column 2). The marginal revenue (MR) is the difference in total revenue from one output level to the
next, i.e., TR at quantity of 1 is $28, at quantity 2 it is $52; therefore the marginal revenue of the 2nd unit
is the difference between $52 and $28, or $24. Similarly, marginal cost (MC) is the difference in total
cost (TC) from one output level to the next. Total profit is the difference between total revenue and total
cost at each level of output. Average total cost (ATC) is equal to TC divided by quantity of output. The
completed table is as follows:
Table AK 49
Price
$30
28
26
24
22
20
18
16
14
12
Quantity
Demanded
0
1
2
3
4
5
6
7
8
9
TR
MR
MC
TC
$0
28
52
72
88
100
108
112
112
108
$28
24
20
16
12
8
4
0
−4
$20
11
8
16
17
18
20
25
30
$28
48
59
67
83
100
118
138
163
193
Total Profit
− $28
− 20
−7
+5
+5
0
− 10
− 26
− 51
− 85
ATC
$48
29.5
22.3
20.75
20
19.7
19.7
20.4
21.4
Since the marginal cost of the industry is synonymous with its supply curve, you need to relate the marginal
cost data with the quantities to plot the supply curve. In this case, for both the demand and supply curves,
begin with the quantities on the horizontal axis and plot the dollar price and marginal cost, e.g., at a quantity
of 1, the price is $28 and the marginal cost (supply) is $20; at a quantity of 2, the price is $26, the marginal
cost (supply) is $11, and so on. This gives:
58
Figure AK 45
b) From the graph in Figure AK 45, or looking at Table AK 49, you can see that the price is equal to MC at
a quantity of 6. Price (equals the marginal cost) of $18. At this level of output, there is a loss of $10.
c)
To maximize profits, a monopolist will produce that output where marginal revenue is equal to marginal
cost. The two curves intersect, which is confirmed in Figure AK 49, at an output of 4. This is confirmed
in Table AK 42. This quantity will be sold at a price of $22. The table shows that at this output, total
profit is equal to 5.
d) See Figure AK 45. To locate a price equal to average cost, find where the demand curve intersects the
average cost curve. This is identified as point a on the graph. To locate a price equal to marginal cost,
find where the demand curve intersects the marginal cost curve. This is identified as point b on the graph.
e)
A tax of $5000 is a fixed cost to Irina. Therefore it will have no effect on the marginal costs. It will
increase the total costs and reduce profits by $5000 at every output level. The best output level is the
same as before; she would simply be making $5000 less profit at this output, i.e., reducing it to zero. You
have already located the P = AC level on the graph. Figure AK 45 shows that the price and average cost
are equal at an output of 5. The P = MC level you have previously identified as the perfectly competitive
solution. The results are summarized below.
Table AK 50
Price
Tax of $5000
$22
20
P = AC
18
P = MC
Irina’s choice:
Quantity Traded Profit/Loss
4
$0
5
0
6
− 10
Either option 1 or 2 (probably 2, since she might object to paying a tax to the
government. This latter is the fair return price, guaranteeing Irina normal profits only.)
Government’s choice:
If their sole interest is in raising revenue, then option 1.
Coronans' choice:
Option 3, which is the socially optimal price giving consumers the lowest price
and the highest quantity.
59
More of the Same
a)
See Table AK 51.
Table AK 51
Price
($)
50
48
46
44
42
40
38
36
34
32
30
Quantity
demanded
0
1
2
3
4
5
6
7
8
9
10
TR
($)
0
48
92
132
168
200
228
252
272
288
300
MR
($)
MC
($)
48
44
40
36
32
28
24
20
16
12
33
27
24
20
24
28
32
34
40
50
Figure AK 46
b) P = $34; Q = 8 000;
TΠ = $14 000 loss.
c)
P = $38; Q = 6 000;
TΠ = $ 8 000.
d) P = $38; Q = 6 000;
TΠ = $ 2 000.
e)
P = $34; Q = 8 000;
TΠ = $14 000 loss.
f)
P = $36; Q = 7 000;
TΠ =
0
60
TC
($)
64
97
124
148
168
192
220
252
286
326
376
T
($)
-64
-49
-32
-16
0
+8
+8
0
-14
-38
-76
ATC
($)
97
62
49.33
42
38.40
36.67
36
35.75
36.22
37.60