Utility-Maximization-and-the-Demand-Curve-Chapter-6-Material...

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Econ1220 -­‐ Fall 2014Page 1 of 7Utility Maximization and the Demand Curve This write-up is intended to make clear what utility maximization is and how utility maximization under the assumption of diminishing marginal utility results in, all else equal, a negative relationship between the price of a good and the quantity demanded of that good. This negative relationship is represented graphically by a downward sloping demand curve. Utility Maximization In order to maximize utility, consumers must allocate their expenditures (given a limited amount of money, “the budget constraint”) so that they can’t receive higher utility from some other set of choices. When a consumer is maximizing their utility, they are making the best set of choices possible. What do I mean by “set of choices”? Basically, there will be many things that a consumer can choose to do with their resources. If I had an hour of time, I can spend it in many different ways; e.g. a walk or a bike ride. If I had $1 to spend, I could buy many different things; e.g. a bagel or a drink. There will be many different combinations of consumption choices that a consumer can make; a combination of consumption choices is what I am referring to as a “set of choices”. From our examples, the combinations would be: i) go for a walk and buy a drink, ii) go for a walk and buy a bagel, iii) go for a bike ride and buy a drink, and iv) iv) go for a bike ride and buy a bagel. Out of all the combinations of consumption choices, there will be one combination of choices that results in the consumer realizing the highest utility from consuming their limited resources. Therefore, if this consumer were to switch to any of the other combination, their utility would decrease. One complication would be if 2 or more combinations resulting in the highest utility; in this case the consumer could pick any of these “utility-maximizing” combinations – we would say that the consumer is “indifferent” between these combinations. Okay, so a consumer maximizes their utility by making choices that use their limited resources to achieve the highest possible utility. How does this relate to the demand curve? Remember that the demand curve represents the relationship between the price of a good and the quantity demanded of that good, all else equal. Consumers are going to have to consider what they get from a particular quantity of a good (the marginal utility; which is related to the benefit) and the price they pay (this is one of the costs).
Econ1220 -­‐ Fall 2014Page 2 of 7Diminishing Marginal Utility and the Utility Maximizing Condition To get to an understanding the demand curve, we are going to employ the concept of “diminishing marginal utility”. If there is diminishing marginal utility, then each marginal/additional unit of a consumption good will provide a lower marginal utility compared to the previous unit (this is over a fixed time period). This is going to be important to “deriving” the demand relationship.

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