Question

We have three types of firms in the market. Type 1 firms has the total cost of production as T C1 = Q2 1 + 100 and the fixed cost of production as F C1 = 19. Type 2 firms has the total cost of production as T C2 = Q2 2 + 64 and the fixed cost of production as F C2 = 15. Type 3 firms has the total cost of production as T C3 = Q2 3 + 36 and the fixed cost of production as F C3 = 11. The short run market demand is P = 100− 5 6Q. The long run market demand is P = 35− 3 5Q. There are a total of 3 type 1 firms, 4 type 2 firms, and 5 type 3 firms in the market in the short run. a. Characterize the ATC, AVC for each type of firm. Characterize the minimum ATC and AVC for each type of firm. b. Draw the ATC, AVC and MC curves for each type of firm. Make sure to label it carefully. c. Calculate and plot the market supply curve in the short run. Then characterize the equilibrium price and quantity in the market in the short run. d. Calculate and plot the market supply curve in the long run. Then characterize the equilibrium price and quantity in the market in the long run.

a. Characterize the ATC, AVC for each type of firm. Characterize the minimum ATC and AVC for each type of firm.

b. Draw the ATC, AVC and MC curves for each type of firm. Make sure to label it carefully.

c. Calculate and plot the market supply curve in the short run. Then characterize the equilibrium price and quantity in the market in the short run.

d. Calculate and plot the market supply curve in the long run. Then characterize the equilibrium price and quantity in the market in the long run

Answer 1

a) Firm 1

TC1 = Q1² +100

FC1 = 19

TC1 = FC1+VC1

Therefore VC1 = Q1² +100 -19 = Q1² +81

Now ATC1 = TC1/Q1 = Q1+100/Q1

AVC1 = VC1/Q1 = Q1+81/Q1

TO get the minimum of ATC, and AVC, we derive the first order condition

For ATC1 = 100/Q1 = 0, Q1 = 100

For AVC1 = Q1 = 81, therefore mimium ATC is at the point where Q1 = 100, and minimum AVC is at the point where Q1 = 81

Similarly for firm2

TC2 = Q2² +64

FC2 = 15

TC = FC+VC

Therefore VC 2= Q2² +64-15 = Q1² +49

Now ATC = TC/Q = Q2+64/Q2

AVC = VC/Q = Q2+49/Q2

TO get the minimum of ATC, and AVC, we derive the first order condition

For ATC2 = 64/Q2 = 0, Q2 = 64

For AVC2 = Q2 = 49, therefore mimium ATC2 is at the point where Q2= , and minimum AVC2 is at the point where Q2 = 49

Also for Firm 3

TC3 = Q3² +36

FC = 11

TC = FC+VC

Therefore VC3 = Q3² +36 -10 = Q3² +25

Now ATC3 = TC/Q = Q3+36/Q3

AVC3 = VC/Q = Q3+25/Q3

TO get the minimum of ATC, and AVC, we derive the first order condition

For ATC3 = 36/Q3 = 0, Q3 = 36

For AVC3 = Q3 = 25, therefore mimium ATC3 is at the point where Q3 = 36, and minimum AVC3 is at the point where Q3 = 25

b)

Firm 1
Q	TC	ATC	VC	AVC	MC
5	125	25	106	21	0
10	200	20	181	18	75
20	500	25	481	24	300
30	1000	33	981	33	500
40	1700	43	1681	42	700
50	2600	52	2581	52	900
60	3700	62	3681	61
Firm 2
Q	TC	ATC	VC	AVC	MC
5	125	25	106	21	0
10	164	16	149	15	39
20	464	23	449	22	300
30	964	32	949	32	500
40	1664	42	1649	41	700
50	2564	51	2549	51	900
Firm 3
Q	TC	ATC	VC	AVC	MC
5	125	25	106	21	0
10	136	14	125	13	11
20	436	22	425	21	300
30	936	31	925	31	500
40	1636	41	1625	41	700
50	2536	51	2525	51	900

The firms will produce at a point where the ATC is minimum, thus the firms will produce 10 units of product

c) There are 3 firms of type 1, each firm is producing 10 units, thus total quantity is 30 units of type 1 firm,

4 firms of type 2, each producing 10 unitd, total quantity is 40 units

firms of type 3, each producing 10 units, total is 50 units

Market Supply = 30+40+50 = 120 units

In short run,the supply curve for each firm will be the marginal cost curve that is above the minimum of the average variable cost. The minimum AVC is at 10 units for each firm, therefor the MC curve is beyond the minimum AVC is the supply curve of the market.

At equilibrium quantity of 10 units, the market price according to demand curve = P = 100-5/6Q

P = 92, Q = 10 units in the short run.

d) in the long run, the firm's supply curve is the marginal cost fucntion which lies above its long run ATC function. In case the firm is not able to cover its minimum ATC, the firm will shut down in the long run. Th markt long-run supply curve is the increasing MC curve above the minimum of its long run average cost.

The equilibrium quantity will b again 10 units, the price will be P = 35-3/5Q

P = 35-3/5*10, P = 29