A function problem involving algbra

[holidaze]

Hi i have being trying to solve this problem, but i am unable to get any result.
Seeking enlightenment on this problem


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

 

[Deleted member 4993]

Hi i have being trying to solve this problem, but i am unable to get any result.
Seeking enlightenment on this problem


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

You don't say - what do you need to calculate?

 

[holidaze]

hi lol. i did. Anyway this is what the problem needs you to find

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

 

[Deleted member 4993]

hi lol. i did. Anyway this is what the problem needs you to find

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

Okay it was lost in the jungle of data!! - Sorry.

Anyway

Existence of terms like "dP" tells me you are supposed to use "calculus" -

are you?

 

[holidaze]

Actually i am not sure. Anything that work should be fine.

I forgot to mention the final answer for percentage increase in P should be express as real number like example 10%.

And i made a mistake in one of the equation

P = A1P1 + … + A5P5

The highlighted P should be in small casing as shown below

P = A1p1 + … + A5p5