Question

Assume Pork and chicken market in China is perfectly competitive and 1000 firms are producing the pork. Following equations shows the TC for the production for short run and long run.

Qd = 5000-4p

STC(q) = 100 + 10q +q2

TC(q) = 100q – 2q2 + 0.2 q3

13.6 What is the short run shut down price, Ps?

13.7 Given 13.6, what is the equation for the short run supply curve for a producer?

13.8 What is the short run market supply curve?

13.9 Find the short run EQ P* , Q* and q*

13.10 Derive the profit function, π, and calculate the profit

13.11 What will happen in the market and what can you predict the number of firms in the LR

Please show how you get your answers

Answer 1

13.6 Shut down point is where P = AVC

TVC = 10q + q²

AVC = 10 + q

P = 10 + q

P = 10 + 5000 - 4p

5P = 5010

P = 1002

13.7 MC is the supply curve for a producer.

MC = dSTC/dq = 10 + 2q

13.8 Market supply curve = 1000 firms x MC of one firm = 1000(10 + 2q) = 10000 + 2000q

13.9 Equilibrium is where MR = MC

TR = P.Q = (5000 - Q)/4 x Q = 5000Q/4 - Q²/4

MR = dTR/dQ = 5000/4 - Q/2 = 1250 - 0.5Q

MC = 10 + 2Q

Equilibrium: 1250 - 0.5Q = 10 + 2Q

1240 = 2.5Q

Q = 1240/2.5 = 496 units

P = (5000 - Q)/4 = (5000 - 496)/4 = 1126