9-78
個體經濟 之魔法書
Microeconomics
題型 6
Assume that there are n identical firms producing the same product in the market, and each
2
has the same cost function, TCi(qi) = 2q 1 + 10, i = 1, A, n. The market demand function is
P = a − bQ, where P is the market price and Q =
n
/q
i
is the market demand. Let n = 100.
i=1
Please answer the following questions:
(1) Assume that all of these n firms are price takers. What is the equilibrium market price? P
= (2) Assume that all of these n firms are Cournot-type competitors. What is the equilibrium
market price? P = .
(3) Assume that all of these n firms merge into one company, with all other things remain the
same. What is the equilibrium market price? P = .
a
(2) ab + 4a (3) 25ab + a
25b + 1
50b + 1
101b + 4
(1) 完全競爭均衡：
解： (1)
S
P
 個別廠商短期供給曲線：P = MC & P = 4qi & q 1 = 4
S
S
P
 市場短期總供給曲線：Q = 100q i = 100 ` 4 j = 25P
d
S
*
a 1
a
 完全競爭均衡：Q = Q & 25P = - P & P =
b b
25b + 1
(2) Cournot 均衡：
2
Max
ri = [a - b (q1 + q2 + ggq100)] qi - 2q i - 10
F.O.C.
2ri
= a - bq1 - bq2 gg - 2bqi - 4qi = 0 & a = (101b + 4) qi
2qi
a
101b + 4
*
*
a
a
+
Q = 100 8
B = 100+
& P = a - b ; 100a E = ab 4a
101b + 4
101b 4
101b + 4
101b + 4
(3) 合作均衡解：
Q
 多工廠均衡條件：MC1 = MC2 = …MC100 & q1 = q2 = … = q100 & qi = 100
& qi =
因為每家廠商成本結構都相同，因此每家廠商分配相同產量。
 Cartel 總成本： TC = 100 ; 2 c
2
Q 2
Q
m + 10 E =
+ 1000 &
100
50
第九章
獨占市場 9-79
MC =
Q
25
Q
25a
 Cartel 獨佔決策：MR = MC & a - 2bQ = 25 & QC = 50b + 1
PC = a - b ;
25a
25ab + a
E=
50b + 1
50b + 1