Econ Question about utility maximizing rule?
Answer:
the utility maximising rule reflect the point where your consumers indiference curve (a curve plotting all the points of consumption for which the consumer has equal utility) is tangent to your consumers budget constraint (a line plotting all the points of consumption that cost the same). The reason why this represents the point of maximum utility its because you have reached your highest possible indifference curve (representing your highest point of utility) given your budget.
When Marginal Utility equals 0 you have reached maximum utility.
in order to max util subject a budget constaint the rule is to make purchases between the two goods so that:
1) the mu per dollar of each good is equal
2) you spend all your money
algebraic
MU1 / P1 = MU2 / P2
take marginal util of good 1 divide by price of 1 set equal to marginal util of 2 divided by price of 2
How would you know that you have maxed out your utils? When you are at a combination of products X and Y such that any shift from X to Y (or vice-versa) will no longer increase utility.
So let's see: a one-unit shift from X allows you to buy Px/Py more of Y. You lose MUx, but gain MUy * Px/Py. (Remember, MU's all come from incremental one-unit changes). So: If MUx>MUy*Px/Py, you improve; if <, you lose (and should move away from Y towards X). No change in utils if =.
Rearranging: MUx/Px = MUy/Py. (Looks neater that way).
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