2. (12 points) Suppose there are n identical firms in a market. Each firms cost
ID: 1095330 • Letter: 2
Question
2. (12 points) Suppose there are n identical firms in a market. Each firms cost function is given by C = 648 + 8q2, where q is the amount that an individual firm produces. This means that an individual firms marginal cost is given by MC = 16q. Also, the market demand is given by P = 306 3Q, where Q is the total amount of the good produced by all of the firms combined. Therefore, Q = n*q.
a) How much output will each firm produce?
b) What will be the market price?
c) How many firms will there be in long run equilibrium?
Explanation / Answer
a) How much output will each firm produce?
in equilibrium market demand = supply=Q
Each firm produces at min point of AC
Ac= 648/q +8q
To minimize Ac
dAC/dq= -648/q2 +8=0
q^2= 648/8= 81
q= 9
b) What will be the market price?
P will be the value of Minimum AC
min AC= 648/9 + 8*9= 72+72=144
c) How many firms will there be in long run equilibrium?
in equilibrium demand = supply
put P=144 to get
144= 306-3*Q
Q= (306-144)/ 3= 162/3= 54
Now Q=9*n
N= 54/9= 6
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