Firms, Prices & Markets
Timothy Van Zandt
© August 2012
Chapter 4
Competitive Supply and Market Price
SOLUTIONS TO EXERCISES
Exercise 4.1. Suppose that a firm has no fixed cost and that its marginal cost equals 10 + 2Q. (Its cost curve
is c (Q) = 10Q + Q2 .)
a. Write the equation for the firm’s supply curve. Graph the supply curve with price on the vertical axis.
Solution: Because there is no fixed cost and the marginal cost is increasing, the supply
curve is the solution to P = MC. Solving P = 10 + 2Q yields Q = 12 P − 5. This holds for
P ≥ 10; if instead P < 10 then Q = 0. See Figure S1.
Figure S1
P
50
s(P )
40
30
20
10
2
4
6
8
10
12
14
16
18
Q
b. Calculate the firm’s output and profit when P = 20 and when P = 30. For P = 30, illustrate the output
decision, the cost, and the profit on the graph of the supply curve.
Solution:
Table S1
Price
Output
Revenue
Cost
Profit
General
P = 20
P = 30
P
−5
P ×Q
10Q + Q2
R−C
20
5
100
75
25
30
10
300
200
100
1
P
2
Firms, Prices & Markets • Solutions for Chapter 4
(Competitive Supply and Market Price)
These amounts are illustrated in Figure S2 for P = 30.
Figure S2
P
50
s(P )
40
30
Profit
20
10
Cost
2
4
6
8
10
12
14
16
18
Q
Exercise 4.2. Consider the firm in Exercise 4.1 (its variable cost is 10Q+ Q2 and its marginal cost is 10+ 2Q),
but now suppose it has a fixed cost FC = 100 that can be eliminated by shutting down. Thus, its cost curve is
c (Q) = 100 + 10Q + Q2 , the same as in Exercise 3.4.
a. If the firm does not shut down, how much does it produce?
Solution: Contingent on not shutting down, it has the same supply curve as without the
fixed cost: Q = 12 P − 5.
b. In Exercise 3.4, you calculated the quantity that minimizes the average cost and determined the minimum
average cost. Write these numbers again. For what prices should the firm shut down?
Solution:
P < ACu .
We calculated Qu = 10 and ACu = 30. The firm should shut down whenever
c. Graph the average cost curve and the marginal cost curve for quantities between 0 and 20. (using e.g. Excel
or simply by hand). Draw in the supply curve.
Solution: The firm shuts down if P < 30; for prices above 30, the firm’s supply curve
is the one shown in Figure S1. Figure S3 shows the graph of this supply curve.
2
Firms, Prices & Markets • Solutions for Chapter 4
(Competitive Supply and Market Price)
Figure S3
P
50
s(P )
40
AC
30
20
MC
10
2
4
6
8
10
12
14
16
18
Q
Exercise 4.3. Consider a competitive market with N identical firms. Each firm has the cost curve given in
Exercises 3.4 and 4.2:
c (Q) = 100 + 10Q + Q2 .
The demand curve is
d(P ) = 1600 − 20P.
The following steps show you how to find the equilibrium price and equilibrium profit per firm as a function of
N, and then determine how many firms would enter if there were free entry.
a. In order to calculate the equilibrium price when there are N firms, we must find the aggregate supply curve.
Since the firms are identical, aggregate supply is equal to N times the supply of an individual firm. The fixed cost
affects only entry or exit decisions, which we initially take as given. Thus, the individual supply depends only on
marginal cost. In fact, you already found the individual supply curve for this marginal cost in Exercise 4.1. Take
your answer from that exercise, which we denote by si (P ), and multiply it by N to get the aggregate supply curve:
s(P ) = N × si (P ).
Solution: The individual supply curve is si (P ) = 12 P − 5. The aggregate supply curve
is thus s(P ) = N2 P − 5N.
b. Solve s(P ) = d(P ) for P to derive the equilibrium price as a function of N.
Solution:
We solve
N
P − 5N = 1600 − 20P
2
N
P + 20P = 1600 + 5N
2
NP + 40P = 3200 + 10N
P =
3200 + 10N
N + 40
3
Firms, Prices & Markets • Solutions for Chapter 4
(Competitive Supply and Market Price)
4
c. Use a spreadsheet to complete the exercise. You should create the following columns:
1.
2.
3.
4.
5.
6.
N, which ranges from 1 to 150.
P , calculated from N using the formula in the part b.
Qi , the output per firm; this equals si (P ).
Ri , an individual firm’s revenue; this equals P Qi .
Ci , an individual firm’s cost including the fixed cost; this equals c (Qi ).
Πi , an individual firm’s profit; this equals Ri − Ci .
Scan down the last column. As long as the profit is positive, more firms would enter. If it is negative, firms would
exit. Find the point where the profit is 0 or where it switches from positive to negative. This is the equilibrium
number of firms when there is free entry. What is the price? How much does each firm produce?
Solution: Profit is zero at N = 100. The price is 30. Each firm produces 10 units. See
the following spreadsheet.
N
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B11
B12
B13
B14
B15
B16
B17
B18
B19
B20
B21
B22
B23
B24
B25
B26
B27
B28
B29
B30
B31
B32
B33
B34
B35
B36
B37
B38
B39
B40
B41
B42
B43
B44
B45
B46
B47
B48
B49
B50
B51
B52
B53
B54
B55
B56
B57
B58
B59
B60
B61
B62
B63
B64
B65
B66
B67
B68
B69
B70
B71
B72
B73
B74
B75
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
P
Qi
78.29
76.67
75.12
73.64
72.22
70.87
69.57
68.33
67.14
66.00
64.90
63.85
62.83
61.85
60.91
60.00
59.12
58.28
57.46
56.67
55.90
55.16
54.44
53.75
53.08
52.42
51.79
51.18
50.58
50.00
49.44
48.89
48.36
47.84
47.33
46.84
46.36
45.90
45.44
45.00
44.57
44.15
43.73
43.33
42.94
42.56
42.18
41.82
41.46
41.11
40.77
40.43
40.11
39.79
39.47
39.17
38.87
38.57
38.28
38.00
37.72
37.45
37.18
36.92
36.67
36.42
36.17
35.93
35.69
35.45
35.23
35.00
34.78
34.56
34.35
34.15
33.33
32.56
31.82
31.11
30.43
29.79
29.17
28.57
28.00
27.45
26.92
26.42
25.93
25.45
25.00
24.56
24.14
23.73
23.33
22.95
22.58
22.22
21.88
21.54
21.21
20.90
20.59
20.29
20.00
19.72
19.44
19.18
18.92
18.67
18.42
18.18
17.95
17.72
17.50
17.28
17.07
16.87
16.67
16.47
16.28
16.09
15.91
15.73
15.56
15.38
15.22
15.05
14.89
14.74
14.58
14.43
14.29
14.14
14.00
13.86
13.73
13.59
13.46
13.33
13.21
13.08
12.96
12.84
12.73
12.61
12.50
12.39
12.28
12.17
Ri
Ci
i
2,673.41
2,555.56
2,445.65
2,342.98
2,246.91
2,156.90
2,072.43
1,993.06
1,918.37
1,848.00
1,781.62
1,718.93
1,659.67
1,603.57
1,550.41
1,500.00
1,452.14
1,406.66
1,363.40
1,322.22
1,282.99
1,245.58
1,209.88
1,175.78
1,143.20
1,112.03
1,082.20
1,053.63
1,026.25
1,000.00
974.81
950.62
927.38
905.04
883.56
862.88
842.98
823.80
805.32
787.50
770.31
753.72
737.70
722.22
707.27
692.81
678.82
665.29
652.19
639.51
627.22
615.31
603.77
592.58
581.72
571.18
560.95
551.02
541.37
532.00
522.89
514.03
505.42
497.04
488.89
480.95
473.23
465.71
458.38
451.24
444.28
437.50
430.89
424.44
418.15
1,607.44
1,544.44
1,485.61
1,430.58
1,379.01
1,330.62
1,285.15
1,242.36
1,202.04
1,164.00
1,128.07
1,094.08
1,061.91
1,031.41
1,002.48
975.00
948.88
924.02
900.34
877.78
856.25
835.69
816.05
797.27
779.29
762.08
745.58
729.76
714.58
700.00
685.99
672.53
659.58
647.11
635.11
623.55
612.40
601.64
591.27
581.25
571.57
562.22
553.19
544.44
535.99
527.80
519.87
512.19
504.75
497.53
490.53
483.74
477.15
470.76
464.54
458.51
452.64
446.94
441.39
436.00
430.75
425.64
420.67
415.83
411.11
406.51
402.04
397.67
393.41
389.26
385.20
381.25
377.39
373.62
369.94
1,065.97
1,011.11
960.03
912.40
867.90
826.28
787.28
750.69
716.33
684.00
653.56
624.85
597.76
572.15
547.93
525.00
503.26
482.64
463.06
444.44
426.74
409.89
393.83
378.52
363.91
349.95
336.62
323.88
311.68
300.00
288.81
278.09
267.80
257.93
248.44
239.34
230.58
222.16
214.05
206.25
198.73
191.49
184.51
177.78
171.28
165.01
158.95
153.10
147.44
141.98
136.69
131.57
126.62
121.82
117.17
112.67
108.31
104.08
99.98
96.00
92.14
88.39
84.75
81.21
77.78
74.44
71.19
68.04
64.97
61.98
59.08
56.25
53.50
50.82
48.20
N
B76
B77
B78
B79
B80
B81
B82
B83
B84
B85
B86
B87
B88
B89
B90
B91
B92
B93
B94
B95
B96
B97
B98
B99
B100
B101
B102
B103
B104
B105
B106
B107
B108
B109
B110
B111
B112
B113
B114
B115
B116
B117
B118
B119
B120
B121
B122
B123
B124
B125
B126
B127
B128
B129
B130
B131
B132
B133
B134
B135
B136
B137
B138
B139
B140
B141
B142
B143
B144
B145
B146
B147
B148
B149
B150
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
P
Qi
34.14
33.93
33.73
33.53
33.33
33.14
32.95
32.76
32.58
32.40
32.22
32.05
31.88
31.71
31.54
31.37
31.21
31.05
30.90
30.74
30.59
30.44
30.29
30.14
30.00
29.86
29.72
29.58
29.44
29.31
29.18
29.05
28.92
28.79
28.67
28.54
28.42
28.30
28.18
28.06
27.95
27.83
27.72
27.61
27.50
27.39
27.28
27.18
27.07
26.97
26.87
26.77
26.67
26.57
26.47
26.37
26.28
26.18
26.09
26.00
25.91
25.82
25.73
25.64
25.56
25.47
25.38
25.30
25.22
25.14
25.05
24.97
24.89
24.81
24.74
12.07
11.97
11.86
11.76
11.67
11.57
11.48
11.38
11.29
11.20
11.11
11.02
10.94
10.85
10.77
10.69
10.61
10.53
10.45
10.37
10.29
10.22
10.14
10.07
10.00
9.93
9.86
9.79
9.72
9.66
9.59
9.52
9.46
9.40
9.33
9.27
9.21
9.15
9.09
9.03
8.97
8.92
8.86
8.81
8.75
8.70
8.64
8.59
8.54
8.48
8.43
8.38
8.33
8.28
8.24
8.19
8.14
8.09
8.05
8.00
7.95
7.91
7.87
7.82
7.78
7.73
7.69
7.65
7.61
7.57
7.53
7.49
7.45
7.41
7.37
Ri
412.01
406.02
400.17
394.46
388.89
383.44
378.12
372.93
367.85
362.88
358.02
353.28
348.63
344.09
339.64
335.30
331.04
326.87
322.79
318.79
314.88
311.04
307.29
303.61
300.00
296.46
293.00
289.60
286.27
283.00
279.79
276.64
273.56
270.53
267.56
264.64
261.77
258.96
256.20
253.49
250.82
248.20
245.63
243.11
240.63
238.19
235.79
233.43
231.11
228.83
226.59
224.39
222.22
220.09
217.99
215.93
213.90
211.90
209.94
208.00
206.10
204.22
202.37
200.56
198.77
197.00
195.27
193.56
191.87
190.21
188.58
186.97
185.38
183.81
182.27
Ci
366.35
362.84
359.41
356.06
352.78
349.57
346.44
343.37
340.37
337.44
334.57
331.76
329.00
326.31
323.67
321.08
318.55
316.07
313.63
311.25
308.91
306.62
304.37
302.16
300.00
297.88
295.79
293.75
291.74
289.77
287.84
285.94
284.08
282.24
280.44
278.68
276.94
275.23
273.55
271.90
270.28
268.69
267.12
265.58
264.06
262.57
261.10
259.66
258.24
256.84
255.47
254.11
252.78
251.47
250.17
248.90
247.65
246.41
245.20
244.00
242.82
241.66
240.51
239.38
238.27
237.18
236.09
235.03
233.98
232.94
231.92
230.92
229.92
228.94
227.98
i
45.66
43.18
40.76
38.41
36.11
33.87
31.69
29.55
27.47
25.44
23.46
21.52
19.63
17.78
15.98
14.21
12.49
10.80
9.16
7.54
5.97
4.43
2.92
1.44
-1.41
-2.80
-4.15
-5.48
-6.78
-8.05
-9.30
-10.52
-11.72
-12.89
-14.04
-15.17
-16.27
-17.36
-18.42
-19.46
-20.48
-21.49
-22.47
-23.44
-24.39
-25.32
-26.23
-27.13
-28.01
-28.87
-29.72
-30.56
-31.37
-32.18
-32.97
-33.75
-34.51
-35.26
-36.00
-36.73
-37.44
-38.14
-38.83
-39.51
-40.17
-40.83
-41.47
-42.11
-42.73
-43.35
-43.95
-44.55
-45.13
-45.71
Firms, Prices & Markets • Solutions for Chapter 4
(Competitive Supply and Market Price)
Exercise 4.4. Consider a competitive market with free entry. Each potential firm has the cost curve given in
Exercises 3.4, 4.2, and 4.3:
c (Q) = 100 + 10Q + Q2 .
The demand curve is
d(P ) = 1600 − 20P.
Use the values of
Qu
u
and AC that you calculated for Exercise 3.4 as your starting point.
a. Find the equilibrium price.
Solution:
P ∗ = ACu = 30.
b. How much does each firm produce?
Solution:
Q∗i = Qu = 10.
c. What is the total output?
Solution:
Q∗ = d(P ∗ ) = 1600 − (20 × 30) = 1000.
d. How many firms are in the market?
Solution:
N ∗ = Q∗ ÷ Q∗i = 1000 ÷ 10 = 100.
Exercise 4.5. Consider a competitive industry with free entry and a U-shaped average cost curve. (You may
assume a fixed cost and increasing marginal cost.) Suppose the government imposes a per-unit tax. What happens
to the following?
a. The price of the product.
Solution: I use ˆ to differentiate values after the tax from values before the tax. Denote
the amount of the tax by Τ.
We model the tax as being paid by the firm, so the price of the product includes the tax.
The key step is to recall what we learned in Exercise 3.5. Such a per-unit tax does not
affect the efficient level of production; it raises the minimum average cost by exactly the
ˆ u = ACu + Τ.
amount of the tax. That is: Q̂u = Qu and AC
Therefore, our first answer is that the price of the product goes up by Τ.
b. The output of each firm that stays in the market.
Solution:
Q∗i = Qu and Q̂∗i = Q̂u . Therefore, output per firm does not change.
c. Total output.
Solution:
Since the price goes up, demand goes down.
d. The number of firms in the industry.
Solution: The total output goes down, yet the output per firm remains the same. Therefore, there must be fewer firms in the market following the tax.
Exercise 4.6. Consider a competitive industry with free entry and a U-shaped average cost curve. (You may
assume a fixed cost and increasing marginal cost.) Suppose the government imposes a yearly license fee on any
5
Firms, Prices & Markets • Solutions for Chapter 4
(Competitive Supply and Market Price)
firm in the market (the same for all firms, and independent of a firm’s level of output). What happens to the
following?
a. The price of the product.
Solution: I use to denote values after the tax has been imposed; without means the
values when there is no license fee. Denote the value of the license fee by L.
The key step is to recall what we learned in Exercise 3.6. Such a license fee is an
increase in the firm’s fixed cost. The efficient scale of production rises: Q̂u > Qu . ACu also
increases, though by less than L/Qu .
Therefore, our first answer is that the price of the product goes up by less than L/Qu .
b. The output of each firm that stays in the market.
Solution:
It increases from Qu to Q̂u .
c. Total output.
Solution:
u
).
It decreases from d(ACu ) to d(AC
d. The number of firms in the industry.
Solution: Both total output falls and the output per firm increases. Therefore, the number off firms must fall.
Exercise 4.7.
(Competitive supply) Evaluate: “In a competitive market, a firm sets its price equal to its
marginal cost.”
Solution: No. A competitive firm is a price taker. It sets its quantity (output level) where
its marginal cost equals the price.
Exercise 4.8.
(Profit and diseconomies of scale) Evaluate: “A firm in a competitive market without free
entry is better off having diseconomies of scale, because only then can it earn a positive profit in equilibrium.”
Solution: It sounds better to have constant average cost rather than increasing average
cost. Yet we concluded that firms with constant average cost earn zero profit and firms with
diseconomies of scale earn positive profit.
To understand this apparent contradiction, we should remember that the market price
is determined by the market competition of all the firms. Our conclusion is not that it is
better for a firm to have diseconomies of scale, but rather that it is better for the firm to
be in an industry with diseconomies of scale. In the absence of free entry, competition
does not necessarily dissipate all profits. However, if all the firms in the market have the
same constant marginal cost, competition is fierce and drives the price down to the constant
marginal cost.
Exercise 4.9.
(The need for patent protection) Suppose that each pharmaceutical company in a competitive
drug market knows that, with $100 million of R&D, it can develop a cure for hay fever. The medicine will cost
$20 per dosage to manufacture. However, there is no patent protection and so, once the drug is developed, any
firm can also produce it at $20 per dosage. What will happen?
6
Firms, Prices & Markets • Solutions for Chapter 4
(Competitive Supply and Market Price)
Solution: Once the drug is developed, the price will be driven down by competition
to the marginal cost. Each firm will earn zero profit, not taking into account sunk R&D
expenditures. Whichever firm invested in the R&D will have made a loss.
Each firm anticipates that this will happen, and hence it does not invest in R&D.
This illustrates why patent protection is important. By providing a temporary monopoly,
it provides firms the incentive to invest in R&D.
Exercise 4.10.
(Supply with U-shaped average cost) Assume that your firm operates in a perfectly competitive market. Your total cost function is c (Q) = 100 + Q2 and hence your marginal cost is mc(Q) = 2Q. If the
market price is 60, then how much should you produce and what is your profit?
Solution: There is a fixed cost and increasing marginal cost. Therefore, the cost curve
is U-shaped. We need to find the optimal output ignoring the fixed cost and then determine,
taking into account the fixed cost, whether it is better to shut down.
We find the optimal output ignoring the shut-down option by solving
MC = P
2Q = 60
Q = 30
If we operate, profit is
Π = R−C
= P × Q − c(Q)
= (60 × 30) − (100 + 302 )
= 1800 − 1000 = 800
It is best to operate. The profit is 800.
Exercise 4.11.
(Free entry) Consider a perfectly competitive market with free entry. (There are firms and
potential firms with access to the same technology and hence with the same cost curve.) The AC and MC curves
for the common technology are given by
ac(Q) =
50
+ Q,
Q
mc(Q) = 3Q .
Find the (approximate) equilibrium price and the output of each firm that is active in the market.
Solution: The equilibrium price is the minimum average cost ACu and the output per
firm is the quantity Qu that minimizes this average cost. (These values are approximate
because, depending on the demand curve, they might require there to be 17.6 firms in the
market; rounding of the number of firms would then change the actual price and quantity
per firm by a small amount.)
7
Firms, Prices & Markets • Solutions for Chapter 4
(Competitive Supply and Market Price)
We find Qu by solving
MC = AC
3Q = 50/Q + Q
2Q2 = 50
Q = 5.
Then ACu = ac(Qu ) = (50/5) + 5 = 15.
Thus, the equilibrium price is 15 and each active firm produces 5.
Exercise 4.12.
(Integrating different cost structures) Consider a perfectly competitive market in which the
firms are grouped into two sectors, which use different technologies. The technologies cannot be replicated: entry
is not possible and a firm in one sector cannot adopt the technology of the other sector.
The two production sectors and the demand for the good have the following properties:
Production Sector A. Each firm in Sector A has the same cost curve, which has a constant marginal cost of
100.
Production Sector B. Each firm in Sector B has the same cost function, which exhibits diseconomies of scale.
The aggregate supply curve for this sector is as follows (we use M to denote “million”):
Price
50
75
100
125
150
175
200
Supply
1M
2M
3M
4M
5M
6M
7M
Demand. The demand curve for this market has these values:
Price
50
75
100
125
150
175
200
Demand
10M
9M
8M
7M
5M
4M
3M
The following questions ask you to determine the competitive equilibrium under various assumptions regarding (i) whether only one of the sectors or both the sectors serve the market and (ii) the presence of taxes.
a. Suppose the market is served only by Sector A. (Sector B does not exist.) What is the equilibrium price?
How much is traded at that price? Do the firms earn a profit? Explain.
Solution: P = 100: Because in an industry in which all firms have no economies of
scale, the competitive equilibrium price equals the constant marginal cost.
Output = demand = 8M, which is the demand when P = 100.
Profit is zero: Because P = MC (competitive equilibrium) and MC = AC (no economies of scale).
Commentary It is not enough to say that profit equals zero because P = MC .
b. Suppose the market is served only by Sector B. (Sector A does not exist.) What is the equilibrium price?
How much is traded at that price? Do the firms earn a profit?
Solution: P = 150: because this is the price at which supply equals demand.
Output = demand = 5M at this price.
There is positive profit: Firms produce at a point where marginal cost equals price.
Because the sector has diseconomies of scale, the average cost is lower than the marginal
cost. Hence, firms earn positive profit.
8
Firms, Prices & Markets • Solutions for Chapter 4
(Competitive Supply and Market Price)
c. Suppose the market is served by both sectors. What is the equilibrium? How much is produced by each
sector? Do any of the firms earn a profit?
Solution: The equilibrium price must be 100: below a price of 100, Sector A would
produce nothing, Sector B would produce less then 3M, and the demand would be greater
than 8M; above a price of 100 Sector A would want to produce an infinite amount.
At the price of 100, demand is 8M and Sector B supplies 3M. The output from Sector
A is the difference of 5M.
Firms in Sector A have zero profit; same explanation as in part (a).
Firms in Sector B have positive profit; same explanation as in part (b).
d. Suppose that the market is served only by Sector A and that a $25 (per-unit) sales tax is imposed. What is
the new equilibrium price charged by the firms? How much is produced/consumed at that price? Who “bears the
burden of the tax” (i.e., who pays more than the equilibrium price without the tax)?
Solution: The price received by firms in Sector A must be 100: below 100, these firms
would produce nothing; above 100, these firms would want to produce an infinite amount.
Hence, the price paid by the customers must be 125. Demand at this price is 7M, and so
this is the amount produced by the firms.
The consumers bear the burden of the tax: the tax is 25 and they pay 25 above the no-tax
equilibrium price, whereas firms receive the same with or without the tax.
e. Suppose that the market is served only by Sector B and that a $50 (per-unit) sales tax is imposed. What is
the new equilibrium price charged by the firms? How much is produced/consumed at that price? Who bears the
burden of the tax?
Solution: We need to find a price Pf received by the firms and a price Pc paid by the
consumers whose difference equals the tax of $50, such that the firms supply at Pf equals
the consumers’ demand at Pc . This holds for Pf = 125 and Pc = 175; then supply =
demand = 4M.
The tax is born equally by the consumers and producers; the consumers pay 25 more
than without the tax, whereas the producers receive 25 less than without the tax.
f. Briefly compare your answers about the tax burden in the previous two parts and relate the difference to the
elasticities of supply.
Solution: Keeping the demand curve fixed, the more elastic is supply the more the burden of the tax falls on the customers. In part (d), the supply of Sector A is perfectly elastic
and firms bear no burden of the tax. In part (e), the supply of Sector B has finite elasticity
(hence less elasticity than Sector A) and firms and consumers share the burden of the tax.
9