Question

8. Suppose that there are 100 identical firms in a perfectly competitive industry. Each firm has a short-run total cost curve of the form C(q) = 1/300q3 +0.2q2 + 4q + 10

(d) A perfectly competitive market has 1,000 firms. In the very short

run, each of the firms has a fixed supply of 100 units. The market

demand is given by

Q = 160, 000 - 10,000P

(e) Calculate the equilibrium price in the very short run.

(f) Calculate what the equilibrium price would be if one of the sellers

decided to sell nothing or if one seller decided to sell 200 units.

Answer 1

e)

If there are 1000 firms and each firm supplies 100 units. Then market supply is given as

Qs=100*1000=100000

Set Qd=Qs for equilibrium

160000-10000P=100000

10000P=60000

P=$6 (equilibrium price)

Equilibrium quantity=Qd=Qs=100000 units

f)

If one seller supplies nothing then market supply is given by

Qs=100*999=99900

Set Qd=Qs for equilibrium

160000-10000P=99900

10000P=60100

P=$6.01 (equilibrium price)

Equilibrium quantity=Qd=Qs=99900 units

If one seller supplies 200 units then market supply is given by

Qs=100*999+200=99900+200=100100

Set Qd=Qs for equilibrium

160000-10000P=100100

10000P=59900

P=$5.99 (equilibrium price)

Equilibrium quantity=Qd=Qs=100100 units