# A simple problem involving Calculus or not

• Jul 29th 2009, 11:08 AM
hoildaze
A simple problem involving Calculus or not
Hii recently ran into this problem and i can't seems to solve it. Can someone enlighten me to the method use to solve it?(Happy)

P = A1P1 + … + A5P5

Where

A1 + … + A5 = 1

Let Ai represent the weight of good i (i will be a number between 1 and 5)

P be the price level

And Pi the price of good i

Example
Let the good and weights be given as follow in the table below

Good ---------- Weight (Ai)

Cake -----------0.4
Oil ------------- 0.2
Transport ----- 0.1
Vacations ----- 0.1
Hospital ------- 0.2

Suppose the prices of the various goods change in the following way

Cake +20% (dp1 = 0.2)
Oil +20% (dp2 = 0.2)
Transport +10% (dp3 = 0.1)
Vacations +40% (dp4 = 0.4)
Hospital +10% (dp5 = 0.1)

Given the weights in the table, how much will the Price Level (P) rise? Express your answer in %.

By the way i was wondering if i couldn't get the answer because my interpretation of the meaning of dp1 to dp5
after the price increase was wrong .

I inferred that dp1 after price increase, had an increment of 0.2 to it original value, and so on and so for, for the rest of the dp.
Meaning the new value of dp1 = Original Value of dp1 + 0.2

Did i made a wrong inference? Help on this part much appreciated
• Jul 29th 2009, 12:46 PM
skeeter
1.2(.4) + 1.2(.2) + 1.1(.1) + 1.4(.1) + 1.1(.2) = 1.19

19% increase overall
• Jul 29th 2009, 07:30 PM
hoildaze

1.2(.4) + 1.2(.2) + 1.1(.1) + 1.4(.1) + 1.1(.2) = 1.19

19% increase overall

Actually the correct ans is 11%. Can i ask how did you get the value the new
dp1 to dp5 price?
• Jul 30th 2009, 07:04 AM
skeeter
Quote:

Originally Posted by hoildaze

1.2(.4) + 1.2(.2) + 1.1(.1) + 1.4(.1) + 1.1(.2) = 1.19

19% increase overall

Actually the correct ans is 11%. Can i ask how did you get the value the new
dp1 to dp5 price?

used the change values you provided ... I guess I misunderstood your notation, sorry.
• Jul 30th 2009, 08:58 AM
hoildaze
By the way i also saw a mistake in the equation i gave.

The original equation was

P = A1P1 + … + A5P5

It should actually be

P = A1p1 + … + A5p5

The highlighted p Should be in Small letter