Question
In: Economics
Suppose that the demand for stilts is given by Q=1500-50P and that the long-run total operating costs of each stilt making firm in a competitive industry are given by TC=50+10q+0.5q2 .
Suppose that the demand for stilts is given by Q=1500-50P and that the long-run total operating costs of each stilt making firm in a competitive industry are given by TC=50+10q+0.5q2 .
How many stilts are produced by each firm?
What is the long-run equilibrium price of stilts? What is the long-run equilibrium quantity of stilts produced in the market? How many firms will there be?
Solutions
Expert Solution
TC = 50 + 10q + 0.5q2
dTC/dq = MC = 10 + q
MC = 10 + q
AC = TC/q
= (50 + 10q + 0.5q2 )/q
= 50/q + 10 + 0.5q
In long run equilibrium
P = MC = AC
MC = AC
10 + q = 50/q + 10 + 0.5q
10 - 10 + q - 0.5q = 50/q
0.5q = 50/q
q/2 = 50/q
q2 = 100
q = 10
So stilts produced by each firm is 10
MC = 10 + q
= 10 + 10
= 20
P = MC
= 20
Thus,long run equilibrium price is 20
Q = 1500 - 50P
= 1500 - 50(20)
= 1500 - 1000
= 500
Long run equilibrium quantity is 500
Number of firms, n = Q/q
= 500/10
= 50
Rahul Sunny answered 2 years agoRelated Solutions
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