Question

in a perfect competition, the cost function of each of 100 firms is given as . C = q^3\300 + 0.2q^2+4q+10 . the market demand function is given by Q= 8000-200P

Answer 1

Solution:

The correct answer is a.) 15

C = $\frac{1}{300}q^{3} +0.2 q^{2}+4q+10$

Derive the short-run marginal cost:

MC = $\frac{\partial TC} {\partial Q} = \frac{q^{2} } {100} + 0.4q+4$

Calculate the short-run supply function:

Short run supply function is where P = MC(Q):

$P = \frac{q^{2} } {100} + 0.4q+4$

Multiply both sides by 100:

100P = q² + 40q + 400

Q = 10√P – 20

Short run supply function (Qs) = 10√P – 20

Derive the market or industry short run supply curve:

Qs = 100q = 100(10√P – 20) = 1000√P – 2000

The market short-run supply curve (Qs) = 1000√P – 2000

Finally, derive the short run equilibrium price and quantity:

At equilibrium: Qd = Qs

Qd = 8000 – 200P

Qs = 1000√P – 2000

8000 – 200P = 1000√P – 2000

1000√P – 200P – 10000 = 0

P + 5√P – 50 = 0

(√P + 5/2)² = 225/4

P = 25

Equilibrium price = 25

Substitute in the demand function to get the equilibrium quantity:

Qd = 8000 – 200P = 8000 – 200(25) = 8000 – 5000 = 3000

Equilibrium quantity = 3000