2. In the local cabbage market, there are 5,000 producers that have identical short-run cost functions. They are: where q is the number of bushels produced each period. Out of the fixed cost, 50% is sunk and 50% is non-sunk. The short-run marginal cost function for each producer is: MC(q) = 0.05q. (3*2.5 = 7.5) a) If the local cabbage market is perfectly competitive, what is each cabbage producer's short-run supply curve? Derive the local market supply curve of cabbage. b) Suppose the market demand is Q=560,000-40,000P. What is the equilibrium price and quantity that will be produced in the market? c) How much will individual firm produce?
Answer:
a) In a perfectly competitive market, the short-run supply curve of the firm = P = MC
The marginal cost of each producer = 0.05q, Therefore the supply curve of each producer = 0.05q
There are around 5000 producers, the local market supply curve = 5000(0.05q) = 250q
b) Given market demand: Q = 56,0000 - 40,000 P
The marginal revenue (MR) = dQ / dP = -40,000
Equilibrium Quantity (q) in perfect competition: MC = MR
0.05q = 40,000
q = 80,0000
Subsituting the value of q into direct demand function, we can obtain price (p).
P = -((56,0000 - Q)/ 40,000)
= -((56,0000 - 80,0000) / 40,000)
= 6
c) So individual firm will produce quantity equivalent to P=MC
Knowing that P = 6 and MC = 0.05q, the total quantity produced will be: 0.05q = 6
q = 6/0.05 = 120
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