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Homework Help: Budget line manipulation

  1. May 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Your budget is such that if you spend your entire income, you can afford either 4 units of good x and 6 units of good y OR 12 units of x and 2 units of y.

    A) What is the ratio of the price of x to the price of y?
    B) If you spend all your income on x, how much x could you buy?

    2. Relevant equations

    Budget line: p1x1 + p2x2 = m

    m = income
    p1 = price of x
    p2 = price of y
    x1 = good x
    x2 = good y


    3. The attempt at a solution

    The two budget lines (which are equal) will be:

    4(p1) + 6(p2) = m
    12(p1) + 2(p2) = m

    So would the ratio be 4/12 = 6/2 ?

    And I have no clue about B). Do I have to solve for anything? Using subsitution doesn't solve anything. I still up end up with variables.
     
  2. jcsd
  3. May 23, 2010 #2
    4/12 does not equal 6/2. Reread the problem.
     
  4. May 23, 2010 #3
    I meant 4/12:6/2, since it's supposed to be a ratio.
     
  5. May 23, 2010 #4
    It is not 4/12:6/2. You were doing fine up to the point where you had 4(p1) + 6(p2) = m = 12(p1) + 2(p2). Now, just rearrange so that you get p1/p2 = ?

    For part (b), you know your income through how much of x1 and x2 you can buy. You also know the ratio p1/p2. So, you can find the price p2 in terms of p1. Substitute.
     
  6. May 24, 2010 #5
    Alright, so the ratio is 1/2. But I still don't understand how you find what your income is.
     
  7. Jun 7, 2010 #6
    You don't need to find what the income is exactly, only how many units of good x you can purchase. How can you find out how many units of x cost the same as 6 units of y from the price ratio? Sorry for letting this question slip through the cracks.
     
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