Someone was kind enough to help me with this question, but i was still confused on how they helped me with the first part of my question.
The original question was:
You go to an auction and set a maximum price of $100 you are willing to bid on an item. However, you are fortunate and purchase it for $50.
1) Does the lower price alter the marginal utility you originally placed on the item?
The answer that was given me for Number 1 was:
1) Under the most common utility functions, No. Price paid is independent of the marginal utility received.
I am not quite sure if i understand this answer, can someone help me understand it more. Thanks
So, you go the frige and find an apple. You bite into it, and its delicious. You get positive utility. Then you see a grocery receipt lying on the table. Your mother paid $3 per pound for the apples. Does this change the utility you got from eating the apple. (no). Opps, you mis-read the receipt, she actually paid 0.30 cents per pound. Does this change your utility (again no).
Most utility functions are of the form U=f(x1,x2,...xn) where x are the different goods you could consume. Nowhere in the function is the prices of each x. Utility comes from the consumption of the various goods. And more consumption give more utility. (That said, one could have a utility function that included the price paid. But this would be unusual).
Thanks for the clarification, means alot.
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Of course! I'll be happy to help you understand the answer to your question.
In utility theory, marginal utility refers to the additional satisfaction or benefit that a person derives from consuming one more unit of a good or service. It is commonly believed that as the quantity of a good or service consumed increases, the marginal utility derived from each additional unit diminishes.
The answer to your question states that under most common utility functions, the lower price you paid does not alter the marginal utility you originally placed on the item. In other words, the satisfaction or benefit you expected to get from the item remains the same, regardless of the price you actually paid for it.
To explain this further, let's consider the concept of willingness to pay. When you set a maximum price of $100, you are essentially expressing your willingness to pay up to that amount for the item. This willingness is based on the perceived value or utility you expect to receive from the item.
If you are fortunate and purchase the item for $50, it means that you paid less than your maximum willingness to pay. However, this lower price does not change the utility or benefit you associate with the item itself. The satisfaction or utility you expected to derive from the item is independent of the price you paid for it.
In other words, the utility or benefit you originally assigned to the item does not change just because you paid less for it. The value you assigned to the item and the satisfaction you expect to receive from it remain the same, regardless of the actual price paid.
I hope this explanation clarifies the answer for you. Let me know if you have any further questions!