Answer to Question #279346 in Microeconomics for Easter

Question

In a perfectly competitive and constant cost industry, all firms are identical. If the market demand function is:Q^D=600-P, a typical firm’s cost function is:

TC=q³- 20q² +120q

1. In the long run, what is the firm’s equilibrium production decision?
2. In the long run, what is the market equilibrium price and quantity? What is the industry’s long run supply curve?
3. In the long run, how many firms will stay in the industry?
4. If the government decide to impost a $7 tax per unit, what is the new long run equilibrium market price and quantity? 
5. How many firms are producing after the tax? 

Answer 1

In the long run, what is the firm’s equilibrium production decision?

In the long run, a firm achieves equilibrium when it adjusts its plant/s to produce output at the minimum point of their long-run Average Cost (AC) curve

TC=q³- 20q² +120q

ATC=q²-20q+120

In the long run, what is the market equilibrium price and quantity? What is the industry’s long run supply curve?

At equilibrium; ATC=MC

q²-20q+120=3q²-40q+120

2q²-20q=0

Equilibrium quantity;

q=10

Equilibrium price;

ATC=q²-20q+120=P

=10²-20(10)+120

=20

Long run supply curve is; q=10

In the long run, how many firms will stay in the industry?

When p=20, QD;

=600-20=580

Thus each firm is supplying 10 units and industry demand is 580 units.

Let there be n firms thus Total market supply = 10n.

So, At equilibrium, Total Market supply = Total Market demand

10n=580, therefore n=58

Hence, In the long run equilibrium, Number of firms in the industry are 58

If the government decide to impost a $7 tax per unit, what is the new long run equilibrium market price and quantity?

Long run equilibrium market price would be;

$\$20+\$7=\$27$

Long run equilibrium quantity would be;

QD=600-27

= 573

How many firms are producing after the tax? 

So, At equilibrium, Total Market supply = Total Market demand

10n=573, therefore n=57

Hence, In the long run equilibrium, Number of firms in the industry are 57