Question

9.7 Newsprint (the paper used for newspapers) is produced in a perfectly competitive market. Each identical firm has a total variable cost TVC(Q) = 40Q+ 0.5Q², with an associated marginal
cost curve SMC(Q) = 40 + Q. A firms’s fixed cost is entirely nonsunk and equal to 50.
(a) Calculate the price below which the firm will not produce any output in the short run.
(b) Assume that there are 12 identical firms in this industry. Currently, the market demand for newsprint is D(P) = 360- 2P, where D(P) is the quantity consumed in the market when the price is P . What is the short-run equilibrium price?

Answer 1

TVC = 40Q + 0.5Q²

AVC = TVC/Q

= (40Q + 0.5Q²)/Q

= 40 + 0.5Q

MC = 40 + Q

The minimum price below which firm will not produce any amount in short run is given by

P = min AVC

AVC is minimum when MC = AVC

40 + Q = 40 + 0.5Q

Q - 0.5Q = 40 - 40

0.5Q = 0  

Q = 0  

So min AVC = 40 + 0.5(0)

= 40

Thus, P = 40 which means , If P    40 then firm will not produce any amount

We can also find it from short run supply function which is given by P = MC

P = 40 + Q  

Q = P - 40  

clearly Q = P - 40 , P > 40

= 0 , P 40

b)  short run supply function is given by P = MC

P = 40 + Q

P - 40 = Q

Q = P - 40

since there is 12 identical firms thus, industry supply curve is

S(P) = nQ

= 12(P - 40)

= 12P - 480

D(P) = 360 - 2P

short run equilibrium is given by   

S(P) = D(P)  

12P - 480 = 360 - 2P

12P + 1P = 360 + 480

14P = 840

P = 840/14

= 60

thus, short run equilibrium price is 60