可以請問這題怎麼算嗎 算好久 - 經濟

※ 引述《zs71928 (中肯之王)》之銘言：
: In a perfect competition market, every firm has the same long run total cost
: function as
: TC=q平方+16 and the demand function of the market is Q=1200-20P
: Please answer the
: following questions :
: (a) If the government allow only 200 firms to supply the market in the long
: run, what are the
: market equilibrium price, quantities each firm produced and profit each firm
: made in the long
: run?

supply function: P=MC=2q ---> qs=0.5P
Market supply function: Qs = 200q = 100P

market equilibrium: Qs=Qd --> 100P = 1200-20P --> P*=10


: (b) If the government allows firms to free enter or exit the market, what are
: the market equilibrium
: price, quantities each firm produced and the number of the firms in the long
: run?

題目已經說是完全競爭了
政府允許商廠自由進出變成贅述

由於廠商自由進出
因此長期下僅能賺取正常利潤

留在產業的廠商
必然在MES處生產

故一般都列式： min LAC = q + 16/q

f.o.c. dLAC/dq = 0 --> 1 - 16/q^2 = 0 ---> q* = 4

P* = LAC* = 4 + 4 = 8

Q = 1200 - 20*8 = 1040

n = 1040/4 = 260

------------------------------------------

: 第一題我算出來 q=5 Q=1000 P=10 每家廠商利潤9

: 第二題是我卡住的地方 q跟p跟廠商家數都變動 Q總產量應該不會也變動吧
: 有三個變數實在不知道怎麼算
: 徵求高手解答
: 謝謝

--
無心擁有 何嘆失去

無心真正追尋過的擁有 便無須矯情怨失去

若是無悔追尋過 烙在心頭上 又怎能失的去

--