Question

Suppose that the market for some good is competitive and the demand curve can be written as Qd= 200 - 4P and the supply curve can be written as Qs= 20 + 2P

1. What is the equilibrium price and quantity in the market?
2. Suppose that every firm in the market has total costs which can be expressed as TC= 8+10Q+5Q^2.  What is the marginal cost function of each firm?
3. How much will each firm produce?
4. How many firms are currently in the market?
5. What are the profits of the firms?
6. Will the firms produce in the short run?
7. Will the firms produce in the long run?
8. What will happen to the number of firms in the market in the long run?i.
9. What will be the profits of firms in the long run?

Answer 1

a.Given, in a competetive market the demand curve is

Qd= 200 - 4P

and the supply curve can be written as

Qs= 20 + 2P

At equilibrium,

Qd=Qs

200 - 4P= 20 + 2P

180=6P

P=30

Putting P=30 in the supply function we find that,

Q= 20 + 2*30

=80

Answer:The equilibrium price is 30 and quantity is 80 in the market .

b.Given, every firm in the market has total costs TC= 8+10Q+5Q^2

Marginal cost function of each firm is MC=dTC/dQ=10+10Q

Answer:Marginal cost function of each firm is 10+10Q

c.As the given firm is a competitive firm at profit maximization,

P=MC

From part a.we know that P=30 and from part b. we know that MC= 10+10Q.. Putting this we get,

30=10+10Q

Q=2

Answer: Each firm will produce 2 units.

d. From part a.we know that Q=80= Total Production.

Each firm is producing 2 units.

So, the total number of firms 80/2=40

Answer: There are 40 firms in the market.