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Math Help - Question - I've shown the working out I've done thus far.

  1. #1
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    Question - I've shown the working out I've done thus far.

    A consumer's preferences over food (x) and other goods (y) are given by U(x,y) = xy.
    With marginal utilities MUx = y and MUy = x. The consumer's income is $32,400.
    a) Calculate the optimal basket when px = 40 and py = 10.
    b) Calculate the income and substitution effects (in terms of changes in quantity of x demanded) of an increase in the price of food to px = 90.
    c) Calculate the Compensating Variation of the price change.


    So for a) Maximized when y/x=40/10, y=4x.
    Budget line, 40x+10y=32,400,
    40x+10(4x)=32,400
    x=32,400/80=405,y=4(405)=1620.

    b) If px=90, x=180. So %change in price=125%,%change in quantity=56%, elasticity of demand =56/125=0.448. The increase in price has the same effect as a decrease in income.

    Have I done all that I need for b) and how do I do c)?
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  2. #2
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    commerial mathematics???

    Quote Originally Posted by brumby_3 View Post
    A consumer's preferences over food (x) and other goods (y) are given by U(x,y) = xy.
    With marginal utilities MUx = y and MUy = x. The consumer's income is $32,400.
    a) Calculate the optimal basket when px = 40 and py = 10.
    b) Calculate the income and substitution effects (in terms of changes in quantity of x demanded) of an increase in the price of food to px = 90.
    c) Calculate the Compensating Variation of the price change.

    So for a) Maximized when y/x=40/10, y=4x.
    Budget line, 40x+10y=32,400,
    40x+10(4x)=32,400
    x=32,400/80=405,y=4(405)=1620.

    b) If px=90, x=180. So %change in price=125%,%change in quantity=56%, elasticity of demand =56/125=0.448. The increase in price has the same effect as a decrease in income.

    Have I done all that I need for b) and how do I do c)?
    i donot understand a number of things here:1)Marginal utilities2)optimal basket3)substitution effects4)budget line
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  3. #3
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    It's for a microeconomics class - maths applied to economics.
    Hi, I'm still hoping that someone will help me out,
    thanks
    Last edited by brumby_3; March 21st 2010 at 01:59 AM.
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  4. #4
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    I've done b) again and this is what I've got:
    With the new price,

    90x + 10y = 32400
    9x + y = 3240

    and

    9x = y

    y still = 1620, but now x = 180. There has been no substitution effect. The reduced quantity demanded is totally due to income effect.

    I still don't understand c), so please help out!
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