Notes on Social Welfare

Notes on Social Welfare - I. Utility Let us begin with a...

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I. Utility Let us begin with a fundamental question: what is utility? Historical definitions include “the capacity of a good to satisfy a want” and happiness itself. The commonly accepted modern definition is “a preference ordering over states of the world”. In other words, for all possible circumstances, an individual forms a ranking that assigns a numerical value to each outcome. Another fundamental question is whether utility can be summed across individuals. The answer determines whether or not it is theoretically valid to conceive of social utility , which is the central tenant of a branch of economics and philosophy called Social Choice Theory. There exist two primary conceptions of utility, which differ in their level of restriction on the nature of utility as a mental construct. In utility functions which are cardinally measurable, the value of utility itself is meaningful, i.e. “magnitudes matter”. For example, if the utility of state x is 2 and the utility of state y is 4, then state y is twice as good as state x . On the other hand, if utility functions are only ordinally measurable, the magnitude of one state versus another is meaningless. Ordinal utility is a simple ranking where one state may be better than another, but we can not say by how much it is better. In the previous example, we can say that state y is preferred to state x but we can not say it is twice as good. A notable variant on utility as purely cardinal or ordinal is co- ordinal utility, where utility is ordinal for individuals but cardinal across individuals. II. Utility Theory Suppose there are only two goods: Shotgun Shells (S) and Whiskey (W) Suppose you have $50 to spend; whiskey is $10 per bottle, shotgun shells are $5 per box Budget Line - the set of feasible (within your budget) and exhaustive (using your entire available income) combinations of goods, in this case, S and W. In this example, the budget line is all combinations of S and W (assume both are perfectly divisible) such that the bundle of goods costs exactly $50. Bundles such as (4S, 3W) and (6S, 2W) cost $50 and are, thus, on the budget line.
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Indifference Curve – a set of various combinations of goods that yield the same satisfaction (i.e. utility) to the consumer. The indifference curve is a construct in the mind of the consumer. His personal tastes and preferences dictate that, for example, he is equally happy with the hypothetical bundles (1S, 5W), (10S, 1W), and (4S, 3W). The fact that the first two bundles are not affordable is immaterial as indifference curves exist independent of budget constraints. There are an infinite number of such indifference curves. If we assume the previous three bundles lie on the curve IC-1 (see the graph below), the bundle (6S, 4W) must exist on a higher indifference curve, IC-2 , because this new bundle has more of both goods than a bundle on IC-1 , (4S, 3W). We assume that more is always better, thus utility must increase when more of both goods is consumed. The individual’s task is to maximize his utility (i.e. reach his highest indifference curve) given the
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Notes on Social Welfare - I. Utility Let us begin with a...

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