Question

The tables below show the short-run total cost data for each of three firms (A, B, C) which constitute the industry producing X, and the market demand schedule facing the industry. The firms differ in their initial fixed costs.

a. compute the short-run competitive supply schedule for the industry. That is, for each price (use the prices listed for the demand schedule), indicate the amount that would be profitable to produce and supply assuming each firm behaves as a price taker. assume there is no input-price effects.

b. what is the market-clearing price and quantity? what is the output rate and total profit (or loss) for each firm?

Firm A Firm B Firm C Market Demand qa TC qь ТСь qc TCC Р. О. $.80 70 .60 4 0 $1.00 0 $0.25 1 $1.10 1 $0.40 2 1.20 2 0.60 3 1.30 0.85 4 1.45 4 1.15 5 1.60 5 1.50 6 1.75 6 1.90 7 1.90 7 2.60 8 2.05 8 Impossible 9 2.25 10 2.55 11 3.00 12 Impossible 0 $0.00 1 $0.25 2 0.55 3 0.90 4 1.30 5 1.75 6 Impossible .45 .40 .35 .30 .25 .20 9 11 13 16 19 24 05 4

Answer 1

a)

Marginal Cost =Change in TC/Change in q

First we estimate marginal cost at each output level for each of the firms.

Firm A			Firm B			Firm C
qa	TCa	Mca	qb	TCb	MCb	qc	TCc	MCc
0	1.00		0	0.25		0	0.00
1	1.10	0.10	1	0.40	0.15	1	0.25	0.25
2	1.20	0.10	2	0.60	0.20	2	0.55	0.30
3	1.30	0.10	3	0.85	0.25	3	0.90	0.35
4	1.45	0.15	4	1.15	0.30	4	1.30	0.40
5	1.60	0.15	5	1.50	0.35	5	1.75	0.45
6	1.75	0.15	6	1.90	0.40
7	1.90	0.15	7	2.60	0.70
8	2.05	0.15
9	2.25	0.20
10	2.55	0.30
11	3.00	0.45

We know that each firm is a price taker in competitive market. A firm will increase the output level as long as MC is less than or equal to price.

Like in case of A, at a price level of 0.80, firm A's MC is less than price for all possible output levels. Firm will choose to produce 11 units. Supply at a certain price level is equal to the optimal output at that level. Similarly we can determine output levels at different prices for all firms.

At the

Market supply at a particular price is equal to the sum of possible supplies of all firms at that price level.

Px	Qx	qa	qb	qc	Qs=qa+qb+qc
0.80	1	11	7	5	23
0.70	2	11	7	5	23
0.60	4	11	6	5	22
0.50	7	11	6	5	22
0.45	9	11	6	5	22
0.40	11	10	6	4	20
0.35	13	10	5	3	18
0.30	16	10	4	2	16
0.25	19	9	3	1*	13
0.20	24	9	2	0	11
0.15	28	8	1*	0	9
0.10	33	3*	0	0	3
0.05	40	0	0	0	0

*At this point, firm is indifferent to decisions of producing or not producing. I assume firm decides to produce.

b)

Market clearing price is where quantity demanded =quantity supplied

We find that at a price of $0.30, quantity demanded is equal to quantity supplied i.e. 16 units

So, Market clearing price is $0.30 and quantity is 16 units.

In case of firm A

Output =10 units

Total Revenue=Price*output=0.30*10=$3.00

Total Cost=$2.55

Profit (Firm A)=3-2.55=$0.45

In case of firm B

Output =4 units

Total Revenue=Price*output=0.30*4=$1.20

Total Cost=$1.15

Profit (Firm B)=1.2-1.15=$0.05

In case of firm C

Output =2 units

Total Revenue=Price*output=0.30*2=$0.60

Total Cost=$0.55

Profit (Firm C)=0.60-0.55=$0.05