Question

11. Problems and Applications Q11

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

Total Cost: TC = 50 + $0.5q^{2}$

Marginal Cost: MC = q

The market demand curve for this product is:

Demand

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

What is each firm's variable cost?

0.5q

50+0.5q

q

$0.5q^{^{2}}$

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

50q

50+0.5q

$\frac{50}{q} + 0.5q$

0.5q

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
6
7
8
9
10
11
12
13
14
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?

50−q

120−0.5$q^{2}$

0.5$q^{2}$

q

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

Answer 1

Answer 1. Variable cost=0.5q^2

Reason- Variable cost depends on quantity.

Answer 2. Average Total cost=50/q+0.5q

Reason- Average total cost= Total cost/ Quantity= (50+0.5q^2)/q= 50/q+0.5q

Answer 3.

q	MC=q	ATC=50/q+0.5q
5	5	12.5
6	6	11.8
7	7	10.6
8	8	10.2
9	9	10.05
10	10	10
11	11	10.04
12	12	10.16
13	13	10.3
14	14	10.5
15	15	10.8

Answer 4. ATC is minimum when Q=10.

Answer 5. q

Reason- MC is the short run supply curve above the price level.

Answer 6. In the long run firm will remain in the market and produce if q≥10.

As As q=10, ATC is minimum.

Answer 2

A) FC: $50 B) VC: 1/2q^2 C) ATC: 50/q +1/2 q MC:5,6,7,8,9,10,11,12,13,14,15 ATC: 12.50, 11.33, 10.64, 10.25, 10.06, 10.00, 10.05, 10.17, 10.35, 10.57, 10.83 D) ATC at min equals 10 E) q F) q>10 G) $12, 108 units, 12 units H) $22 I) Enter J) $10, 110 units, 11 firms, 10 units