Question

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 1

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