Review Questions 1
Yuya Takahashi
7
=
26
=
2018
1. Consider an industry where there is only one °rm. Demand is given by
Q
= 10
°
p:
Assume the °rm±s
cost function is
c
(
Q
) = 2
Q:
Find a competitive equilibrium.
2. Consider a market of homogenous products with two active °rms (the number of °rms is °xed). Demand
is given by
Q
(
p
) = 40
°
p:
Two °rms are identical and the total cost function is given by
TC
(
q
) = 10
q:
(a) Find a competitive equilibrium (i.e., °nd
p
°
and
Q
°
).
(b) Find a Cournot-Nash equilibrium (i.e., °nd
p
C
; q
C
1
;
and
q
C
2
).
(c) Find an equilibrium for a sequential game where °rm 1 moves °rst and °rm 2 moves second. (i.e.,
°nd
p
S
; q
S
1
;
and
q
S
2
).
(d) Find a Bertrand-Nash equilibrium (i.e., °nd
p
B
; q
B
1
;
and
q
B
2
).
(e) Compare four di/erent equilibria. Order the price levels and explain why you obtain that result.
3. Consider a market with demand given by
Q
(
p
) = 100
°
p:
The total cost function is given by
TC
(
q
) =
50 + 2
q
2
+ 5
q:
Firms are identical. Let
n
denote the number of °rms. Note that
P
n
i
=1
q
i
=
Q:
(a) Derive the average cost function,
AC
(
q
)
and marginal cost function,
MC
(
q
)
.
(b) Assume there are now 25 °rms.
Consider the short run such that the number of °rms is °xed.
Find a competitive equilibrium (i.e., °nd
p
°
; q
°
; Q
°
). Are °rms making a positive, zero, or negative
pro°t?
(c) Find a competitive equilibrium in the long run (i.e., °nd
p
°
; q
°
; Q
°
; n
°
). Hint: °rms enter and exit
until each °rm earns zero pro°t.
4. Consider a market with inverse demand function
p
= 14
°
Q
. Firms have constant marginal cost 2 and
°xed cost 2. Firms compete by simultaneously choosing quantities.
(a) Suppose there are
n
°rms in this market. Derive the Nash equilibrium prices, quantities and pro°ts.

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- Spring '08
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- Economics, Supply And Demand