Industrial Economics (30L201), Tilburg University, 2023 1
Tutorial 1 - Solutions
Perfect competition & Monopoly
Question 1: Consider a perfectly competitive firm with short-run total costs of C(q) =
4q3–20q2 + 20q + 40.
a) If the market price is 52, how much will the firm produce and what will be the firm’s
profits?
b) Under which price does the firm shut down (stops to produce in the short run)?
Question 2: * Suppose that each firm in a perfectly competitive market has the following
long-run total cost function T C(Q) = 10Q3 20Q2 + 60Q. The market demand is QD =
600 8P .
a) What is the equilibrium output per firm?
b) What is the long-run competitive equilibrium price?
c) What is the equilibrium number of firms in the market?
Question 3: Suppose that the inverse demand is given by: P = 80 –10Q. A monopolist
has the following marginal cost function:
M C2 (Q) = 8 + 4Q
Determine the profit-maximizing price and the output of the monopolist.
Price discrimination
Question 4: * A monopolist sells its goods in two markets: Utrecht and Amsterdam. The
monopolist has constant marginal costs of 20 and no fixed costs. Inverse demand in Utrecht
and Amsterdam are given by: PU = 70–QU and PA = 100 2QA .
a) Suppose that selection by indicators is possible. Which prices would the monopolist set
and what would be its profit? Illustrate your answer with a graph.
,Industrial Economics (30L201), Tilburg University, 2023 2
b) Suppose that the Dutch government prohibits this form of price discrimination and the
monopolist is forced to set the same price in both towns. Which price would it set and
what would be the monopolist’s profit? Illustrate your answer with a graph.
c) Suppose the Dutch government wants to maximize the total surplus. Should it forbid
selection by indicators in this case?
Question 5: * Consider a local fast-food restaurant. Suppose there are two types of cus-
tomers depending on the maximum willingness-to-pay for hamburgers and fries.
• Type A customers are willing to pay at most 4 for a hamburger and 6 for fries.
• Type B customers are willing to pay at most 5 for a hamburger and 2 for fries.
Both of them are willing to pay at most 9 for a menu with hamburger and fries. There are
100 customers of each type. Marginal costs for hamburgers and fries are constant and given
by cH 0 and cF 0, respectively.
a) Suppose that selection by indicators is not possible, and the fast-food restaurant cannot
sell menus. If marginal costs are zero, i.e. cH = 0 and cF = 0, which prices for hamburgers
and fries would maximize profits?
b) How would your answer to question a) change for values cH > 0 and cF > 0?
c) Consider general values of cH 0 and cF 0. What would profit be if the restaurant
o↵ered only menus?
d) Is there a combination of cH and cF that would make it profitable for the restaurant to
engage in mixed bundling?
Question 6: In the market for headphones there are two types of headphones: noise-
canceling and regular headphones. There is a monopolist that produces both headphones at
equal and constant marginal costs of 30. The firm has no fixed costs. There are also two types
of consumers: snobs and cheapos. There are 1000 consumers of each type. Snobs are willing
to pay at most 400 for a noise-canceling headphone and 150 for a regular headphone. Cheapos
are willing to pay at most 80 for a noise canceling headphone and 50 for a regular headphone.
Consumers always buy at most one headphone and buy the headphone that maximizes their
surplus (willingness to pay – price paid).
,Industrial Economics (30L201), Tilburg University, 2023 3
a) Suppose that selection by indicators is not possible. Which prices will the headphone
producer set for the two types of headphones?
b) The competition authorities now impose that headphones that are produced at the same
cost should be sold at the same price. Which headphones will the firm sell and at what
price?
c) Do you agree with the decision of the competition authorities? Motivate your answer.
, Tutorial 1
question + a Cral=4q-209 209
+
40
+
p 52
=
-b
=
4ac
-
129 409 +
20 52
=
abC: 2a
129 -
409 -
32 = 0
40 w.32
=
9 2.12
9 4
=
-
g
k.n.
=
x 4.52
= -
14.43 -
20.4 20.4
+
40
+
-152
b. shut down is AVC?
AVC: 149 -209 209
+
40)/9
+
-
49 209 +
20
p mc
=
1292 -
409 20
+
492 -
209 20
+
1292
= -
489 20
+
209 0q
=
invullen in mc since p mc
=
q 2.5
=
so shut-down price is: 12.2.5" -40.2.5 + 20 = -
5
question 2 a. TC/ar= 109 209 - +
609 ·
total rew:TC
DD 600 =
-
COP
9.p 109 200
=
-
609
x
-
op 600
p 109 209 60
=
9
=
- +
MR mC
p 75
=
-
= ·
a
MR 15
=
-
q p 3092
=
-
409 60
+
Mc 309
=
-
409 60 +
75
-
q 3092= -
409 60
+
109 -
200 + 60 309
= -
409 60
+
3092 394q
=
15
+
209 =
209
1
=
q
b. filling in gives:
P 30.
=
- 40.1 60
+
-50
C. demand:op 600
market = -
0.50 200=
each firm produces 1 ->
q 1
=
200/1 200
=
firms
Tutorial 1 - Solutions
Perfect competition & Monopoly
Question 1: Consider a perfectly competitive firm with short-run total costs of C(q) =
4q3–20q2 + 20q + 40.
a) If the market price is 52, how much will the firm produce and what will be the firm’s
profits?
b) Under which price does the firm shut down (stops to produce in the short run)?
Question 2: * Suppose that each firm in a perfectly competitive market has the following
long-run total cost function T C(Q) = 10Q3 20Q2 + 60Q. The market demand is QD =
600 8P .
a) What is the equilibrium output per firm?
b) What is the long-run competitive equilibrium price?
c) What is the equilibrium number of firms in the market?
Question 3: Suppose that the inverse demand is given by: P = 80 –10Q. A monopolist
has the following marginal cost function:
M C2 (Q) = 8 + 4Q
Determine the profit-maximizing price and the output of the monopolist.
Price discrimination
Question 4: * A monopolist sells its goods in two markets: Utrecht and Amsterdam. The
monopolist has constant marginal costs of 20 and no fixed costs. Inverse demand in Utrecht
and Amsterdam are given by: PU = 70–QU and PA = 100 2QA .
a) Suppose that selection by indicators is possible. Which prices would the monopolist set
and what would be its profit? Illustrate your answer with a graph.
,Industrial Economics (30L201), Tilburg University, 2023 2
b) Suppose that the Dutch government prohibits this form of price discrimination and the
monopolist is forced to set the same price in both towns. Which price would it set and
what would be the monopolist’s profit? Illustrate your answer with a graph.
c) Suppose the Dutch government wants to maximize the total surplus. Should it forbid
selection by indicators in this case?
Question 5: * Consider a local fast-food restaurant. Suppose there are two types of cus-
tomers depending on the maximum willingness-to-pay for hamburgers and fries.
• Type A customers are willing to pay at most 4 for a hamburger and 6 for fries.
• Type B customers are willing to pay at most 5 for a hamburger and 2 for fries.
Both of them are willing to pay at most 9 for a menu with hamburger and fries. There are
100 customers of each type. Marginal costs for hamburgers and fries are constant and given
by cH 0 and cF 0, respectively.
a) Suppose that selection by indicators is not possible, and the fast-food restaurant cannot
sell menus. If marginal costs are zero, i.e. cH = 0 and cF = 0, which prices for hamburgers
and fries would maximize profits?
b) How would your answer to question a) change for values cH > 0 and cF > 0?
c) Consider general values of cH 0 and cF 0. What would profit be if the restaurant
o↵ered only menus?
d) Is there a combination of cH and cF that would make it profitable for the restaurant to
engage in mixed bundling?
Question 6: In the market for headphones there are two types of headphones: noise-
canceling and regular headphones. There is a monopolist that produces both headphones at
equal and constant marginal costs of 30. The firm has no fixed costs. There are also two types
of consumers: snobs and cheapos. There are 1000 consumers of each type. Snobs are willing
to pay at most 400 for a noise-canceling headphone and 150 for a regular headphone. Cheapos
are willing to pay at most 80 for a noise canceling headphone and 50 for a regular headphone.
Consumers always buy at most one headphone and buy the headphone that maximizes their
surplus (willingness to pay – price paid).
,Industrial Economics (30L201), Tilburg University, 2023 3
a) Suppose that selection by indicators is not possible. Which prices will the headphone
producer set for the two types of headphones?
b) The competition authorities now impose that headphones that are produced at the same
cost should be sold at the same price. Which headphones will the firm sell and at what
price?
c) Do you agree with the decision of the competition authorities? Motivate your answer.
, Tutorial 1
question + a Cral=4q-209 209
+
40
+
p 52
=
-b
=
4ac
-
129 409 +
20 52
=
abC: 2a
129 -
409 -
32 = 0
40 w.32
=
9 2.12
9 4
=
-
g
k.n.
=
x 4.52
= -
14.43 -
20.4 20.4
+
40
+
-152
b. shut down is AVC?
AVC: 149 -209 209
+
40)/9
+
-
49 209 +
20
p mc
=
1292 -
409 20
+
492 -
209 20
+
1292
= -
489 20
+
209 0q
=
invullen in mc since p mc
=
q 2.5
=
so shut-down price is: 12.2.5" -40.2.5 + 20 = -
5
question 2 a. TC/ar= 109 209 - +
609 ·
total rew:TC
DD 600 =
-
COP
9.p 109 200
=
-
609
x
-
op 600
p 109 209 60
=
9
=
- +
MR mC
p 75
=
-
= ·
a
MR 15
=
-
q p 3092
=
-
409 60
+
Mc 309
=
-
409 60 +
75
-
q 3092= -
409 60
+
109 -
200 + 60 309
= -
409 60
+
3092 394q
=
15
+
209 =
209
1
=
q
b. filling in gives:
P 30.
=
- 40.1 60
+
-50
C. demand:op 600
market = -
0.50 200=
each firm produces 1 ->
q 1
=
200/1 200
=
firms
