Question

Suppose that the market for painting services is perfectly competitive. Painting companies are identical; their long-run cost functions are given by:

TC(Q) = 5 q^{3} - 45 q^{2} + 250 q

If the market demand is:

Q^{D} = 7,000 - 6 P

1. What is the quantity of output that minimizes average total cost?

2. What is the long run equilibrium price?

3. Using market demand, what is the equilibrium total industry output?

4. What is the equilibrium number of firms?

Answer #1

1)

The output level at ATC is minimum is found by first differentiation equal to zero.

the q=4.5 units when ATC is minimum.

----------

2)

The long run price is equal to minimum average total cost

P=min(ATC)=5q^2-45q+250

q=4.5

P=5*4.5^2-45*4.5+250

P=$148.75

The long run price is $148.75

-------------

3)

Q=7000-6P

P=148.75

Q=7000-6*148.75

Q=6107.5

the industry output is 6107.5 units

-------------

4)

Number of firms =Q/q=6107.5/4.5

=1357.22222

equilibrium number of firms are 1357

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