Question

Suppose that each firm in a competitive industry has the following costs:

Total Cost: TC=50+1/2 q²

Marginal Cost: MC=q

where q is an individual firm's quantity produced.

The market demand curve for this product is:

Demand Q_D=160-4 P

where P is the price and Q is the total quantity of the good.

Each firm's fixed cost is $_______ 

What is each firm's variable cost?

1/2 q

50+1/2 q

1/2 q^{2}

q

Which of the following represents the equation for each firm's average total cost?

50/q+1/2 q

50+1/2 q

50/q

1/2 q

Complete the following table by computing the marginal cost and average total cost for q from 5 to 15 .

The average total cost is at its minimum when the quantity each firm produces (q) equals _______ .

Which of the following represents the equation for each firm's supply curve in the short run?

120-1/2 q^{2}

50-q

1/2 q^{2}

q

In the long run, the firm will remain in the market and produce if _______ .

Currently, there are 6 firms in the market.

In the short run, in which the number of firms is fixed, the equilibrium price is $_______  and the total quantity produced in the market is _______  units. Each firm produces _______ units. (Hint: Total supply in the market equals the number of firms times the quantity supplied by each firm.)

In this equilibrium, each firm makes a profit of $ _______  (Note: Enter a negative number if the firm is incurring a loss.)

Firms have an incentive to _______ the market.

In the long run, with free entry and exit, the equilibrium price is $ _______ , and the total quantity produced in the market is _______ units. There are _______ firms in the market, with each firm producing _______ units.

Answer 1

Fixed cost = 50

Variable cost = q²/2

(FC + VC = TC)

Average total cost = TC/q = 50/q + q/2

q	MC	ATC
5	5	12.50
6	6	11.33
7	7	10.64
8	8	10.25
9	9	10.06
10	10	10.00
11	11	10.05
12	12	10.17
13	13	10.35
14	14	10.57
15	15	10.83

MC = q

In the long run, the firm will remain in the market and produce if P > = 10 (min ATC, firm will make zero or positive profits)

In the short run:

firms = 6

for individual firm : P = MC = q

Total supply = 6 x q = Qs

Qs = 6P

Demand = 160 - 4P

Equating both:

P = 16 (equilibrium price)

Q = 96 (equilibrium quantity)

Each firm produces= 96/6 = 16 units

Each firm makes a profit of = P x q - 50 - q²/2 = 256 - 50 - 16²/2 = 78

Firms have an incentive to enter the market (positive profits)

In the long run, the equilibrium price = $ 10 ( = min ATC), total quantity produced = 160 - 4 x 10 = 120 units

There are = 120/10 = 12 firms in the market, with each firm producing 10 units (q = 10 where ATC = $ 10, zero economic profit)