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The allocation that maximizes total utility will also make the marginal utility per dollar spent on each good equal for all goods. The marginal utility per dollar spent is the marginal utility obtained from the last unit of a good consumed divided by the price of the good. In economics you are often required to calculate the marginal utility per dollar spent during the consumer theory or the utility theory portion of the class. The calculation is easy, as you only need to divide the marginal utility of a good or service by the price of that good or service. If you do not have the marginal utility of the good or service, then you need to figure it out by looking at the difference between total utility amounts at different levels of consumption. The idea behind calculating marginal utility per dollar spent is to find out how effective you are while allocating your budget. For example, if a marginal utility per dollar spent is higher for one good than it is for another good then it means that you are not allocating your budget efficiently. In order to allocate your budget efficiently, you need to have the marginal utility per dollar spent for every good and service be equal to each other.
For example, imagine you are trying to allocate your budget between two goods: apples and oranges. Suppose that the marginal utility of the last apple consumed is four. And that the marginal utility of the last orange consumed was three.
At first it would seem like the apple is preferred to the orange, but this is not true. We still need information about the prices of each of the goods. Now imagine that the price of an apple is $2.00 per apple, and that the price of an orange is only $1.00.
Price of apply = $2
Price of orange = $1
We can figure out what the marginal utility per dollar spent is by taking the marginal utility and dividing by the price. This will give us a marginal utility per dollar spent on an apple as two utility per dollar spent, where the orange has three utility per dollar spent.
Marginal Utility per Dollar Spent = Marginal utility divided by price = MU/P
MU/P of apple = 4/$2 = 2
MU/P of orange = 3/1 = 3
This means that an orange has a higher marginal utility per dollar spent. Therefore an additional budget dollar should be spent on the orange. As more budget dollars are spent on the oranges you would expect the marginal utility of the orange to drop, and continue dropping until the marginal utility of the orange decreases from 3 to 2. If the marginal utility of an orange changes to two, then the marginal utility per dollar spent of an orange would become two. At this point the marginal utility per dollar spent on both apples and oranges would be equal to two and it means that we are using our budget efficiently (by maximizing our utility given our budget). Whichever good has a higher marginal utility per dollar spent, is the good that we should consume more of that good until the marginal utility decreases to the point at which they're both equal.
Ok, what if you are not given the marginal utility of an apple, and are instead given a table showing the different apples amounts consumed that their respective total utilities. The trick here is to calculate the change in the total utility amounts in order to find the marginal utility which you can then use to calculate the marginal utility per dollar spent.
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