How to Manipulate Your Budget Line for Optimal Purchasing Power

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Homework Statement



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?

Homework Equations



Budget line: p1x1 + p2x2 = m

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


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.
 
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4/12 does not equal 6/2. Reread the problem.
 
I meant 4/12:6/2, since it's supposed to be a ratio.
 
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.
 
Alright, so the ratio is 1/2. But I still don't understand how you find what your income is.
 
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.