How to Manipulate Your Budget Line for Optimal Purchasing Power

AI Thread Summary
The discussion revolves around determining the price ratio of two goods based on a budget constraint. The budget equations provided indicate that the ratio of the price of good x to good y is 1:2. To find how many units of good x can be purchased with the entire income, one must use the established price ratio and the quantities of goods that can be bought. The conversation highlights the importance of rearranging the budget line equations to isolate the price ratio and clarify the purchasing power of the budget. Ultimately, the focus is on understanding how to manipulate the budget line for optimal purchasing decisions.
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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.
 
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