MSc Economic Evaluation in Health Care
Welfare Economics
Topic 2. Welfare of the household
Objective
In welfare economics (and the economic evaluation of health care programmes) we are interested in being able to rank different social states (or allocations of resources).
Society’s welfare ultimately depends on the welfare of its constituent households. Therefore to make value judgements of the desirability of different social states to society we need to have a theory of household behaviour. Put another way, we are interested in how households rank different social states.
Two key assumptions
Welfarism = social welfare depends only on the welfare of households, which depends on the bundle of commodities consumed.
Non-paternalism = individualism = the welfare of the household must correspond with the household’s own view of its welfare, or at least be consistent with the household’s preferences = social welfare must respect household preferences (If this were not the case welfare economics would not be very interesting!)
Measuring utility (or how much satisfaction does a consumer derive from a commodity or bundle of commodities?)
Ordinality = the ability to (only) rank alternatives according to the utility they provide = sufficient for household utility maximisation
Cardinality = indicate the magnitude of the change in utility in moving from one alternative to another (like a temperature scale)
Preference orderings over alternative bundles of commodities
Simple economic model = a household must choose how to spend its income on different goods. This is the household’s utility maximisation problem.
The household chooses among available bundles of commodities on the basis of its preferences.
Commodity bundles
x = (x1, x2, …., xn ) [1]
Initially it is assumed that the household can compare any two commodity bundles and declare that one is at least as good as another (= ordinality).
xRy = x is at least as good as y
xRy and yRx = the household is indifferent between x and y
Rationality
It is assumed that the household is rational. So, we assume that following:
1. Reflexivity = xRx
2. Completeness = xRy or yRx or both, for any two commodity bundles x and y
3. Transitivity = if xRy and yRz then xRz
4. Continuity = household preferences can be represented by a utility function u(x), which will be a suitable representation of household preferences provided that u(x)³u(y) whenever xRy for any two commodity bundles x and y
5. Non-satiation = formally, utility is non-decreasing in any commodity and is increasing in at least one. Informally, more is preferred to less (so indifferences curves are downward sloping)
6. Strict convexity = formally, the marginal rate of substitution is diminishing. Informally, an indifference curve lies above a tangent line drawn at any point on the indifference curve
Utility functions
The utility function depicts the relationship between the level of satisfaction reached by a household and the amounts of different commodities it consumes.
U = u(x1, x2, …., xn ) [2]
The utility function can be used to compare any number of commodity bundles.
Indifference curves
Indifference curves provide a locus of points representing combinations of two commodities (x1 and x2) between which the consumer is indifferent (i.e. has equal utility).
There are an infinite number of indifference curves, each corresponding to a given level of utility, and they cannot intersect.
Marginal rate of substitution (MRS)
MRS = the amount of good x2 that must be given up per unit of x1 gained if the consumer is to remain at the same level of utility
MRS = slope of the indifference curve at any one point = [3]
Convexity of indifference curves = diminishing MRS
The budget set and budget constraint
A household receives an income y and faces a set of prices p for commodities given by
p = p(p1, p2, …., pn ) [4]
for each good x = (x1, x2, …., xn )
The budget constraint is given by
[5]
The budget set is the set of different bundles that it is feasible to consume so that
[6]
A formal statement of the utility maximisation problem
Maximise U = u(x1, x2, …., xn ) [7]
Subject to
The solution to the utility maximisation problem requires that the MRS between goods must equal their price ratio. E.g.
MRS = [8]
The demand function
Each time the budget constraint changes (due to changes in prices or incomes) there will be a new equilibrium. This can be used to derive a relationship between the optimum amount of a good purchased (i.e. quantity demanded) and prices and income.
The demand function is given by
xi = x(p1, p2, …, pn, y) [9]
The demand function can be thought of as the solution to the household utility maximisation problem. Given the prices and income facing the household the demand functions determine the bundles of goods that yield the highest value of the utility function.
The indirect utility function
If those demand functions are substituted into the utility function, the results is the indirect utility function, which shows the maximum utility that can be achieved for any set of prices and income.
v(p, y) = v[x1(p, y), x2(p, y), …., xn(p, y)] [10]
Summary
Consumer choice theory seeks to predict how the utility-maximising household acts. In summary, the household is confronted by a social state characterised by a budget constraint from which the consumer can choose a bundle of commodities. The budget constraint is determined by the prices of the commodities and the income of the household. The household then chooses the most preferred bundle in the budget set, or the one that maximises the utility function. As prices and incomes change, so does the bundle chosen. We characterise the choice of the household as a set of demand functions, one for each commodity, each depending on prices and incomes. The demand function can be thought of as the solution to the household utility maximisation problem.
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