5. A competitive industry currently has 1000 identical firms. Each firm has cost
ID: 1116750 • Letter: 5
Question
5. A competitive industry currently has 1000 identical firms. Each firm has costs TC(q) = 8 + 4q + q2 and MC-q + 4, minimum AC-8, and is reached when the firm produces q-4. Please answer the following a. Find the individual firm's supply curve. b. Find the industry short-run supply curve c. Currently, the industry demand is Q- 20,000 -1,000P. Find the short-run equilibrium price P, market quantity Q, and individual firm quantity q. d. What is the profit of an individual firm? e. Suppose there are thousands of similar firms outside of the market and ready to enter Find the long-run equilibrium price P, market quantity Q, individual firm quantity q, and number of firms n.Explanation / Answer
a)
TC = 8 + 4q + q2/2
MC = 4 + q
supply curve
P = MC
P = 4 + q
q = p - 4
b) number of firm n = 1000
industry supply curve Qs = nq
= 1000(p - 4)
= 1000P - 4000
Qs = 1000P - 4000
c)
Qd = 20000 - 1000P
short run equilibrium is given by
Qs = Qd
1000P - 4000 = 20000 - 1000P
2000P = 24000
P = 12
Q = 20000- 1000P
= 20000 - 1000(12)
= 8000
Individual firm quantity q = Q/n
= 8000/1000
= 8
d)
TC = 8 + 4q + q2/2
= 8 + 4(8) + 82/2
= 8 + 32 + 32
= 72
Profit = Pq - TC
= 12(8) - 72
= 96 - 72
= 24
e )
IN long run AC = MC = P
AC = MC
AC = TC/q
= 8/q + 4 + q/2
MC = q + 4
8/q +4 + q/2 = q + 4
8/q = q - q/2 + 4 - 4
8/q = q/2
q2 = 16
q = 4
so individual firm quantity q = 4
P = MC
MC = q + 4
= 4 + 4
= 8
P = 8
Long run euq. price P = 8
Q = 20000 - 1000P
= 20000- 1000(8)
= 12000
So market quantity Q = 12000
number of firms n = Q/q
= 12000/4
= 3000
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