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?

Expected price ≈ 1.5

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

month 1 start amount =$3287.90 interest=(3287.90x0.0145/12)3.97 total to pay=$3291.81 paid =$1200 balance =$2,091.87

month 2 starting amount= $2,091.87 interest =$25.28 total to pay =$2117.15 paid =$1200 balance $917.15

month 3 starting amount =$917.15 interest =$11.08 total to pay =$928.23 paid =$928.23 balance =$0 total to pay 1200+1200+928.23 = $3328.23 it will take 3 months to pay a total of $3328.23

i'ts proportional. if the inflation rate is 12% for example, the cpi will be 12% less.

hope it ,

bioteacher101