Answer to Question #259069 in Microeconomics for Sahlah Ahmed

Question

Each firm in a competitive market has a cost

function of C = q + q2 + q3. The market has an

unlimited number of potential firms. The market

demand function is Q = 24 - p. Determine the

long-run equilibrium price, quantity per firm, market quantity, and number of firms. How do these

values change if a tax of $1 per unit is collected from

each firm? (Hint: See Solved Problem 8.4.) M

Answer 1

Solution:

In the long-run equilibrium price, the profits are zero, therefore: P = MC = ATC

MC = $\frac{\partial TC} {\partial Q} = ​$1 + 2q + 3q²

ATC = 1 + q + q²

Set: MC = ATC

1 + 2q + 3q² = 1 + q + q²

q = 0.5

Q = 0.5

The long run equilibrium output per firm = 0.5 units

The long run equilibrium price is = MC = 1 + 2q + 3q² = 1 + 2(0.5) + 3(0.5²) = 2.75

The long run equilibrium price = 2.75

 

The market quantity is determined through the market demand, Q = 24 – p

Q = 24 – 2.75 = 21.25

The number of firms = $\frac{21.25}{0.5} = 43$ firms