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Slope of a budget constraint

The normal way i've been calculating slope is via 'the rise over the run' - i.e slope = changeinY/changeinX

for budget constraints, the textbook lists the slope as being

slope = -price of good X/price of good Y

in the one example I have, the two different calculations of the slope yield the same answer..soo i was wondering whether they always gave the same answer or whether this was just a concidence?

it also gives another formula,

changeinX = (changeinY x price of good Y)/ price of good X

i was wondering how this formula gave the change in X? is there some simple algebra behind it that proves it that i'm missing?

thanks
redkopite
The normal way i've been calculating slope is via 'the rise over the run' - i.e slope = changeinY/changeinX

for budget constraints, the textbook lists the slope as being

slope = -price of good X/price of good Y

in the one example I have, the two different calculations of the slope yield the same answer..soo i was wondering whether they always gave the same answer or whether this was just a concidence?

it also gives another formula,

changeinX = (changeinY x price of good Y)/ price of good X

i was wondering how this formula gave the change in X? is there some simple algebra behind it that proves it that i'm missing?

thanks
Should really post in the econ help forum, but anyhow... All of the above are the same thing...

change(X) = (change(Y)*Py)/Px
change(X)*Px = change(Y)*Py
change(Y)/change(X) = -Px/Py (you have to stick a minus in because budget constraints are downward sloping).

Take this example. You can work the budget eq as: y = -2x + 200, where Px=2 and Py=1. Slope = -Px/Py = -2, which is the same as dy/dx = -2

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