An apple farmer must decide how many apples to harvest for the world apple market.He knows that there is a one-third probability that the world price will be $1, a one-third probability that it will be $1.5, and a one-third probability that it will be $2.His cost function is C(Q) = .01Q².If the farmer is risk neutral:

Question

Quizplus · Accepted Answer

The expected profit maximizing quantity can be calculated as follows:
Expected price = (1/3)*$1 + (1/3)*$1.5 + (1/3)*$2 = $1.5
Q = (P-MC)/PUP = ($1.5-0.01Q)/(1+2Q) 
Q = 1500/7 
Expected profit = (1/3)*($1.5-0.01*(1500/7))/(1+2*(1500/7))*(1500/7) = $535.71
Since the farmer is risk neutral, he will strictly prefer to produce rather than not produce. Therefore, the best choice is to produce the expected profit-maximizing quantity, which is 1500/7 units of apples.

An Apple Farmer Must Decide How Many Apples to Harvest