Answer to Question #259067 in Microeconomics for Sahlah Ahmed

Question

Each of the 10 firms in a competitive market has a

cost function of C = 25 + q2. The market demand function is Q = 120 - p. Determine the equilibrium

price, quantity per firm, and market quantity. M

Answer 1

Solution:

Derive MC:

TC = 25 + q²

MC = $\frac{\partial TC} {\partial Q} = 2q$

TR = P $\times$ Q

P = 120 – Q

TR = (120 – Q) Q = 120Q – Q²

MR = $\frac{\partial TR} {\partial Q} = 120 - 2q$

Set: MR = MC

120 – 2q = 2q

120 = 2q + 2q

120 = 4q

Q = 30

Equilibrium price = MC = 2q = 2 $\times$ 30 = 60

Equilibrium price = 60

 

Market quantity: Q = 120 – P

Q = 120 – 60 = 60

Market quantity = 60

 

Quantity per firm = $\frac{60}{10} =$ 6 units.