Question
Assume Pork and chicken market in China is perfectly competitive and 1000 firms are producing the...
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
Answers
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
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