Coffee farmers operate in a competitive market with free ent

Coffee farmers operate in a competitive market with free entry where the cost function for each of the existing 100 farms that are currently operating in the area is given by C(q)=25+30q+q^2. q represents each bag of 8 kilograms of coffee that each farmer brings to the market

a. What is MC?

b. What is the competitive supply behavior (as a function of market price) of the typical firm in this market? And given this behavior, what is the supply for the entire market?

c. Suppose that market demand is given by Q^d=4500-100P. What is the market price (per bag of 8 kilograms of coffee) in equilibrium, how much will be exchanged in the market?

d. How much will each farm produce and what will be the profits for each farm?

Solution

a)marginal cost is obtained by differentiating the total cost function with respect to quantity.

MC= dC(q)/dQ = 30+q

b) the variable cost, vC=30q+q^2

Avc= vc/q = 30+q

this is the supply function for one firm. for the market with 100 firms it becomes 100 * (30+q)

c. equilibrium is attained at Quantity demanded= quantity supplied

4500-100p = 3000+100q

1500= 200p

p= 7.5

d. At p = 7.5, q= 4500- 100*7.5 = 3750