Question

Consider a firm whose total costs are given by TC(q) = 300 + 6q + 3q2.

a) What is the minimum price at which the firm will produce positive output?

b) What is the firm’s supply curve? If there are currently 300 firms in the market, what is the market supply curve?

c) The market demand for this firm’s product is QD = 10800 - 50P. What is the shortrun market equilibrium price and quantity?

d) Given the equilibrium you found in part c, and assuming that all firms face the same costs, how many units does each firm produce? How much profit does each make?

e) Given your answer in part d, what do you expect to happen in this market in the long-run? What will be the long-run market equilibrium price and quantity?

f) How much will each firm produce in this long-run equilibrium? What will each firm’s profits be? How many firms will there be in the market?

Answer 1

a)

TC = 300 + 6q + 3q2  

MC = 6 + 6q  

VC = 6q + 3q2

AVC = VC/q  

= (6q + 3q2 )/q

= 6 + 3q

Minimum price at wcich firm will produce poitive output is given by P = minAVC and AVC is minimum where

AVC = MC

6 + 3q = 6 + 6q

6 - 6 = 6q - 3q  

0 = 3q

q = 0

Therefore min AVC = 6 + 3(0) = 6

Thus P = 6 is the minimum price at wcich firm will produce poitive output

b) A single firm's supply curve is given as

P = MC  

P = 6 + 6q

P - 6 = 6q

q = (P - 6)/6

= P/6 - 1

So firm's supply curve is q = P/6 - 1

Market supply Qs = 300q

= 300(P/6 - 1)

= 50P - 300

c)

Qd = 10800 - 50P  

Qs = 50P - 300

Qd = Qs   

10800 - 50P = 50P - 300

10800 + 300 = 50P + 50P

11100 = 100P

P = 111

Q = 50(111) - 300

= 5550 - 300

= 5250

d) we have

q = P/6 - 1

= 111/6 - 1

= 18.5 - 1

= 17.5

Profit = Pq - TC  

= 111(17.5) - 300 - 6(17.5) - 3(17.5)2  

= 1942.5 - 300 - 105 - 918.75  

= 618.75

Therefore each firm produces 17.5 units of output and makes a positive profit of $ 618.75