Results 1 to 3 of 3

Math Help - How much has price and quantity increased from year 1 to year 2?

  1. #1
    Newbie
    Joined
    Aug 2011
    Posts
    2

    How much has price and quantity increased from year 1 to year 2?

    We sell two products.

    Product A:
    ---------------------------
    price y1 = 10
    quantity y1 = 2
    sales y1 = 20 (price*quantity)

    price y2 = 10
    quantity y2 = 1
    sales y2 = 10 (price*quantity)


    Product B:
    ---------------------------
    (p) price y1 = 5
    (q) quantity y1 = 2
    (s) sales y1 = 10

    (p) price y2 = 1
    (q) quantity y2 = 2
    (s) sales y2 = 2

    Analysis:
    ---------------------------
    I want to know by how much our prices and quantities have increased for all products in total (or maybe rather on average) from year 1 to year 2.

    Let's use capital letters for the total profit, quantity and sales per year: S, P, Q.

    I know that S = P * Q.

    I want to measure the price and quantity change. So let's set the capital letters to ratios of year 1 values: S1=1, P1=1 and Q1=1. I know that S2 = 12/30.

    What are P2 and Q2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: How much has price and quantity increased from year 1 to year 2?

    Hi there, I'm not following this too well, but i'll give it a shot.

    Consider quantity alone. The sum of products in the 1st year was 2+2=4 and in the second 1+2=3.

    The change therefore in volume of product is -1 and in percentage is a decrease by 25%, as (4-3)/4 = 0.25

    How is that?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2011
    Posts
    2

    Re: How much has price and quantity increased from year 1 to year 2?

    That's good. But I'd like the % change to be volume weighted. So that decreases in quantity influence the change in quantity level more from year 1 to year 2 when the quantity decreases for a high priced product than when it decreases for a low priced product.

    If the quantity of product A (price y1 = 10) increases that should have a more significant impact on sales (S=P*Q) than if the quantity of product B (price y1 = 5) increases with the same amount.

    I tried to solve it like this:

    Price level Article A Year 1 = 10/10 = 1
    Price level Article B Year 1 = 5/5 = 1
    Price level Article A Year 2 = 10/10 = 1
    Price level Article B Year 2 = 1/5 = 0.2
    Sales Article A Year 1 = 20
    Sales Article B Year 1 = 10
    Sales Article A Year 2 = 10
    Sales Article B Year 2 = 2

    I then calculated the volume weighted price level for year 2 for all articles combined as:
    P2 = (1*20+0.2*10)/(20+10) = 0.7333323 [(relative price level article A * sales article A + relative price level article B * sales article A)/(sum sales)]

    I calculated the volume weighted quantity level for year 2 for all articles combined the same way:
    P2 = (0,5*20+1*10)/(20+10) = 0,6666667

    S2 = 12/30 = 0.4

    Now I expect P2*Q2=S2,

    but S2 = 0.4 and P2*Q2=0.4888889




    So if the price decreases of a product I want it to affect the "price level" more if that product is sold in high quantities. If the quantity decreases of a product I want it to affect the "quantity level" more if that product is sold at high prices.

    Is this doable?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: February 3rd 2013, 11:11 AM
  2. Replies: 2
    Last Post: February 3rd 2013, 06:48 AM
  3. Replies: 3
    Last Post: November 12th 2011, 10:57 AM
  4. Convert Annuity from 5 year periods to 1 year
    Posted in the Business Math Forum
    Replies: 0
    Last Post: March 29th 2010, 08:25 PM
  5. Multiple choice price and quantity
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 18th 2009, 10:12 PM

Search Tags


/mathhelpforum @mathhelpforum