Money in the utility function

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Introduction to the theory of Marginal Utility:

This theory was first developed by the Classical Economist James Marshall (see classical economists), and can be summarized in three points:

Marginal Utility is the utility (or value) that I attach to a single unit's addition/reduction to my existing stock of a commodity

Rule of Declining Marginal Utility: Marginal Utility that I attach on a single unit of a commodity depends on how much of that commodity I already have in stock. It declines as my stock of an item increases, and it increases as my stock of an item declines. (The more I have of a thing the less utility I find in acquiring an addition unit of it and vice-versa)

My current marginal utility of an item defines the price I will pay for acquiring a unit of an item as well as what price I will seek for giving up a unit of an item. '''

It is important to note that marginal utility is assumed bi-directional.. My marginal utility of a unit is the same whether I am adding it to my stock or reducing it from my stock.

Money in the utility function: Money is often thought to be an exception to the rule of Declining Marginal Utility; i.e. no matter how much money one accumulates, one is never less happy from getting yet another unit of it. After all, there's no such thing as too much money!!!

However one can argue that a person with $100 in total savings will be thrilled to receive $10 and devastated at losing it, while someone with $1,000,000 in the bank will not care much either way.

The debate the marginal utility of money is often concluded by saying that money too, has a declining utility - only that the in the case of Money the decline rate is very low, i.e. even a large (say 100%) increase to my money-stock will cause only a small decline (say 1%) in its marginal utility to me.

Recent findings of [Loss aversion] and other experiments seem to suggest Money bucks another trend of the Theory of Marginal Utility - specifically they suggest that the marginal utility function for money does not work the same in both directions. The experiments seem to suggest that the marginal utility assigned by people to the addition of a dollar in their stock of money is much less than the utility of giving up a dollar from their existing stock.

This is used to explain "Loss aversion" - the tendency of people to prefer to avoid losses to making gains.

'''Example: When given a choice between:

* Getting $100 with certainty or
* Having a 50% chance of getting $250  (50% of $250 = $125, the "value" of this option)

people tended to chose a sure-fire $100 gain in preference to the 50% chance of getting $250. This attitude is described as risk aversion.

But it was found that the same people when confronted with a second choice between:

* A certain loss of $100 or
* A 50% chance of no loss or a $250 loss

they often choose the riskier second alternative. The same risk-averse folks now became risk seekers!'''

In terms of Marginal Utility of Money, this shows that people placed a higher value on losing money. Hence in the second choice they were willing to risk losing even more in an effort to save some. Also, in the first choice, they were satisfied with a $100 gain but would not risk losing the $100 gain for a 50% chance at a $250 gain. (Which should mathematically be worth $125).

This shows that people place a higher marginal utility towards the reduction of a unit of money, that towards the addition the same unit, thus adding a new dimension to the Theory of Marginal Utility itself.

Note: The above example is taken from: [link]