Homework Help: Budget line manipulation

1. May 23, 2010

60051

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. May 23, 2010

happyg1

4/12 does not equal 6/2. Reread the problem.

3. May 23, 2010

60051

I meant 4/12:6/2, since it's supposed to be a ratio.

4. May 23, 2010

Tedjn

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.

5. May 24, 2010

60051

Alright, so the ratio is 1/2. But I still don't understand how you find what your income is.

6. Jun 7, 2010

Tedjn

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.