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

- What is the equilibrium price and quantity in the market?
- 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?
- How much will each firm produce?
- How many firms are currently in the market?
- What are the profits of the firms?
- Will the firms produce in the short run?
- Will the firms produce in the long run?
- What will happen to the number of firms in the market in the long run?i.
- 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.**

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