Suppose that the weekly demand for a good in a competitive market is Q = -40.1592P...

Suppose that the weekly demand for a good in a competitive market is Q = -40.1592P + 401592. Further suppose that the typical long-run weekly cost curve for a company in the market is: C(q) = .75q^3- 54q^2 + 4500q + 4000

a) What is the long-run equilibrium price of the good (to two decimal places)

b) How many companies will operate in the market (to two decimal places)?

Expert Solution

a)

Long run equilibrium price is where MC=ATC
MC= ATC
2.25Q^2-108*Q+4500 = 0.75Q^2-54Q+4500+4000/q
(1.5Q^2-54Q)Q = 4000
1.5Q^3-54Q^2 = 4000
Solving the equation we get Q= 37.86
So, Price = MC = 25*37.86^2-108*37.86+4500 = 3636.22

b)

Replacing price in the market demand equation we get,
Market demand, Q=-40.159*3636.22+401592 = 255565.04
No of firms = 255565.04/3636.22 = 70.28

Rahul Sunny answered 2 years ago

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