Question

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

Total Cost:	TC=50+12q2TC=50+12q2
Marginal Cost:	MC=qMC=q

where qq is an individual firm's quantity produced.

The market demand curve for this product is:

Demand

QD=160−4PQD=160−4P

where PP is the price and QQ is the total quantity of the good.

Each firm's fixed cost is $50.

What is each firm's variable cost?

A: 1/2q^2

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

A: 50/q + 1/2q

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

q	Marginal Cost	Average Total Cost
(Units)	(Dollars)	(Dollars)
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

The average total cost is at its minimum when the quantity each firm produces (q) equals 10.

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

A: q

In the long run, the firm will remain in the market and produce if q is greater or equal to 10.

Currently, there are 16 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

Each firm's fixed cost = $50

Each firm's variable cost = 1/2 q². Hence, option(B) is correct.

Average total cost , ATC= TC/q = (50+ 1/2 q² ) /q

= 50/q + 1/2 q

MC = q

q (units)	MC	ATC
5	5	12.5
6	6	11.33
7	7	10.64
8	8	10.25
9	9	10.05
10	10	10
11	11	10.05
12	12	10.17
13	13	10.35
14	14	10.57
15	15	10.85

The ATC is minimum when the quantity each firm produces (q) equals 10 units.

Firm's short run supply curve is represented by the MC curve i.e q . Hence,option(B) is correct.

In the long run ,the firm will remain in the market and produce if P>ATC i.e P>$10.

Currently there are 16 firms in the market.

In the short run ,in which the number of firms are fixed ,the equilibrium price is $8 and the total quantity supplied in the market is 128 units. Each firm produces 8 units.

Because we know P=MC.

There are 16 firms , So, Q= 16q i.e q= Q/16

So, 40-0.25Q = Q/16

Q =128 units.

P= 40-0.25Q

P= 40-(0.25)(128)= $8

P=MC = $8

q= Q/16 = 128/16 = 8 units.

In this equilibrium ,each firm makes a profit of TR-TC = $[(8)(8)- (50+1/2 (8)² ] = [ 64 - 82] = -$18 . (i.e loss).

Firms have an incentive to exit the market.

In the long run ,with entry and exit ,the equilibrium price is $10 i.e equal to minimum ATC. And the total quantity produced is (Q= 160-4(10))= 120 units. There are 120/10= 12 firms in the market , each firm producing 120/12 = 10 units.