Price Theory & Public Policy

2. Consumer Theory (cont'd)

2.2 Utility


1. Terms

2. Assumptions

3. Mechanisms

1. Terms

a) Utility is a generalized term for the satisfaction obtained by an individual from the 'use' of a commodity (goods or services, tangible or intangible).  It is assumed that utility has four basic characteristics:

i - total utility, or the total satisfaction yielded by the consumption of a commodity;

ii - marginal utility, or the increase in utility yielded by one additional unit of a commodity consumed;

iii - diminishing utility, or the decreased  level of utility obtained from consuming an additional unit of a commodity relative to the increase in utility yielded by the preceding unit, i.e. utility increases but at a progressively decreasing rate; and,

iv - maximum utility, or the highest possible level of total utility obtainable subject to income and price constraints.

b) Consumption: the use of a commodity whereby its utility is extracted and usually destroyed, or, alternatively, 'negative production'

c) Complementary Goods: goods are complements if an increase in the quantity demanded of one accompanies an increase in the quantity demanded by another

d) Substitute Goods: goods are substitutes if an increase in the price of one is accompanied by an increase in the quantity demanded of the other

e) Normal Goods: goods whose consumption increases as income increases

f) Inferior Goods: goods whose consumption decreases as income increases

g) Giffen Goods: goods whose consumption increases as their price increases.  This occurs because the substitution effect of a price change is not strong enough  to offset an inferior good's income effect.  The Giffen Effect (after Sir R. Giffen) was first identified when a general price rise, in the case of the poor whose income is fixed, caused an increase in the quantity of staple food, e.g. potatoes, to be consumed despite an increase in price in order to stretch a  fixed income to cover subsistence needs.

h)  Preference or Taste: deriving more utility from one good  than another without regard to price or income.  Determinants of taste and preference include:

i -  education

ii -  experience

iii - demonstration effect

iv - advertising

v -  conspicuous consumption.

i)  Price: the current exchange rate of a commodity for the utility derived by a consumer

j) Income: payment for work used to purchase commodities in order to derive utility

k) Work: physical or intellectual effort made, not for any pleasure derived from the activity itself, to earn income to purchase commodities to obtain utility.  According to Adam Smith work should be rewarded according to its 'disutility'.  Thus work that is at least partially enjoyed for its own sake should receive a lower reward.  The pleasure derived from work is called 'psychic income'.


2. Assumptions

 a) Rationality: consumer chooses between alternative commodity combinations to maximize utility assuming:

i - perfect knowledge, that is, aware of all alternative commodity combinations, their prices and their utility

ii - competent, that is, capable of evaluating the alternatives

iii - transitivity, that is, if A = B and B = C then A = C (meaning that indifference curves do not intersect)

b) Ordinality: consumer is able to order commodity combinations by level of utility, 1st, 2nd, 3rd etc.  Does not require cardinality, that is, the ability to specify the actual numeric level of utility


3. Mechanisms

a) Utility Function:

                U = f (x, y) where:

i - U is the utility derived from consuming commodity combinations of x and y;

ii - U is assumed to be continuous (and has first- and second-order partial derivatives) or, alternatively, there is continuity of commodity combinations of x and y, that is, there is an infinite number of combinations yielding the same level of utility, or alternatively, U is a dense set;

iii - U is not unique, that is, any utility number - say U1 - assigned to a given commodity combination indicates only that it is preferable or superior to all combinations with a lower number and inferior to those with a higher number, in other words, U1 does not possess any cardinal meaning; and,

iv - U is defined for consumption within a specified timeframe - long enough to allow substitution among existing commodity combinations but short enough to insure constancy of taste or preference.

b) Indifference Curve:

For any level of utility, say U1, there is a set of commodity combinations which graphically form an indifference curve representing all combinations yielding the same level of utility - U1.  Indifference curves are sometimes called preference curves, i.e. a curve reflecting a constant level of preference, or isoquants, i.e. a curve reflecting a constant quantity of satisfaction or utility.

On U1 the consumer is indifferent to different commodity combinations.  Usually, i.e. for normal goods, an indifference curve is convex reflecting the fact that an increase in x can only be obtained by a reduction in y, and vice versa (M&Y 10th Fig.3.4; M&Y 11th, Fig. 2.4; B&Z Fig. 3.1; B&B Fig. 3.9).  When a set of indifference curves is presented an indifference or preference map  is created showing all possible levels of satisfaction.  The map consists of an infinite number of curves rising from the origin outwards.  If viewed from above the map would resemble a mountain whose peak is technically called 'the bliss point'. 

The amount of y that must be traded off to obtain an increase in x while maintaining the same level of utility is called the marginal rate of substitution (M&Y 10th Fig.3.4; M&Y 11th, Fig. 2.4; B&Z Fig. 3.1; B&B Fig. 3.9) or MRS = (y2 - y1)/(x2 - x1) or, alternatively, the slope of the indifference curve that changes continuously as one moves along the curve.

The indifference curves for:

i -  perfect complements are right-angled to a 45 degree line drawn from the origin.  Increased consumption of x without increasing the consumption of y would not increase utility; and,

ii - perfect substitutes are straight lines connecting the axis. A consumer will always give up a unit of y for a fixed number of units of x (M&Y 10th Example 3.1; M&Y 11th Fig. 2.5; B&Z Fig. 3.7; B&B Fig. 3.12 & 3.13).


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