Assigning Money between Goods for Maximum Utility

We have seen how to get the most amount of utility out of a limited budget of $10 on two goods, which in our example were hamburgers and orange juice. To start off you need to consider the two extreme options, which are to spend all the money on hamburgers or on orange juice. Keep in mind that the hamburger costs $1 and the orange juice is $2 per jar.

If you were to spend all the $10 on hamburgers, you will be able to buy 10 hamburgers and that would give you a total utility of sixty-four units of utility. On the other hand, if you spend $10 on the orange juice, you can buy five jars at $2 each and obtain eighty units of utility.

There is another option that can be done here though. You can obtain an even higher utility if you were to combine the two options wisely and spend one part of your money on hamburgers and the other on orange juice.

The best way to get the most utility with the $10 you have is very simple, all you have to do is take each one of these ten dollars and spend it on what provides you with the most amount of utility. This means that you are not actually buying yourself hamburgers and orange juice but rather buying utility. For each dollar that you spend you will want to buy a much utility as is possible and it does not matter if the utility comes from the hamburgers or the orange juice.

The only thing that makes this process of spending each dollar on a good that provides you with the most amount of utility more difficult, is the fact that you have decreasing marginal utility for both the hamburgers and the orange juice, in other words the amount of utility you will be able to buy with each additional dollar depends on how many hamburgers you have already bought or how many cups of orange juice you have drunken.

So what should you do with the first dollar? Well, in the fourth line of the hamburger chart you can see that if you spend the first dollar on the hamburger, you will be able to buy twenty units of utility. On the other hand, the forth line of the orange juice chart says that if you spend that first dollar on orange juice along with one other dollar since it costs $2, you will get ten units of utility. So the obvious thing in this case would be to use the first dollar to buy a hamburger instead of a jar of orange juice.

In the case of the second dollar, if you were to buy another hamburger you would obtain sixteen units of utility. If you buy orange juice with that second dollar – along with another dollar since it costs $2, you would only obtain ten units of utility for that second dollar because you would spend on buying the first jar of orange juice. So once again, the best would be to use the second dollar on a hamburger instead of getting a jar of orange juice.

You will probably also want to spend the third dollar on another hamburger since you will obtain fourteen units of utility.

In the case of the fourth and fifth dollar, things become a bit different. If you spend one dollar on a hamburger, it would provide you with eight units of utility, whereas if you were to spend the fourth dollar (along with the fifth) on a jar of orange juice, you would get ten units of marginal utility per dollar (per each dollar spent). So you would want to spend the fourth and fifth dollar in buying the first jar of orange juice.

In the case of the sixth and seventh dollars you will also want to spend them on a jar of orange juice, because you will obtain a marginal utility of nine units of utility per dollar for the second jar of orange juice, whereas you would only get eight units of utility if you spent the sixth dollar on a fourth hamburger.

In the case of the eight dollar, the marginal utility per dollar is the same. If you were to use this dollar to buy a fourth hamburger, you would obtain eight units of utility. The same would apply if you spent the dollar on a third jar of orange juice. So what you should do is spend your last three dollars on a fourth hamburger and a third jar of orange juice.