Question

Assume that 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 $1.50, and a one-third probability that it will be $2. His cost function is C(Q) = 0.01Q2. What is the expected price in the world apple market?

Answer 1

Expected price ≈ 1.5

Step-by-step explanation:

Expected Value is the average value of an event , found by summing products of various outcomes with their corresponding probabilities .

E (X) = x p(x1) + x p(x2) + ....... xn p(xn)

Here, probability of price = 1 , 1.5 , 2 = 1/3 , 1/3 , 1/3 each {respectively}

So, Expected Value of price = 1/3 (1) + 1/3 (1.5) + 1/3 (2) = 0.33 (1) + 0.33 (1.5) + 0.3 (2) = 0.33 (1 + 1.5 + 2) = 0.33 x 4.5 = 1.485 ≈ 1.5