1. A firm called Crain Farms produces corn in a perfectly competitive market in which monthly demand...

Question

1. A firm called Crain Farms produces corn in a perfectly competitive market in which monthly demand is given by the equation Q = XXXXXXXXXX104P and monthly supply is given by the equation Q = XXXXXXXXXX116P, where P is the price per unit of corn in dollars and quantities are in bushels per month.
a. Calculate the market equilibrium price and quantity of corn.
b. Using the "algebraic formula," calceulate the price elasticity of demand that prevails at equilibrium in this market.
C. Crain Farms incurs total costs according to the equation TC = 144 + 3q + q2 and marginal costs according to the equation MC = 3 + 2q, where q is the monthly quantity produced by Crain Farms. Calculate the profit-maximizing quantity of corn produced by Crain Farms.
d. If Crain Farms produces its profit-maximizing output level, how much economic profit (or loss) will it earn in a typical month?
e. In light of the total cost function given in part c, write an algebraic expression for average total costs.
f. Suppose long-run entry into this corn market forces Crain Farms to produce at the minimum average total cost. What level of output will Crain Farms produce?

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Robert · Accepted Answer

a) At equilibrium,
QD = QS
6200 – 104P = 3700 + 116P
220P = 9900
P = 9900/220 
P = 45
Q = 6200 – 104 (45) = 1520
b) Q = 6200 – 104P
Now, find the derivative
dQ/dP = -104
Elasticity = dQ/dP*P/Q
              = -104*45/1520     
              = -3.

1. A firm called Crain Farms produces corn in a perfectly competitive market in which monthly demand is given by the equation Q = XXXXXXXXXX104P and monthly supply is given by the equation Q =...

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