Utility: a generalized term for the satisfaction
obtained by an individual from the 'use' of a product (good or service)
measured by the price the individual is willing to pay for the product.
Indifference Curve:
For any level of utility - U' = f (x, y) - there is a locus of commodity
combinations which graphically form an indifference curve, that is, all
combination yield the same level of utility - U' meaning the consumer is
'indifferent' to any combination on the curve.
Usually an indifference curve is 'convex' in shape reflecting the fact
that an increase in x can only be obtained by a reduction in y, and vice versa.
The amount of y that is traded off to obtain an increase in x but maintaining
the same level of utility is called the marginal rate of substitution, i.e.,
MUy/MUx
Furthermore, in a sense, the 'f'
in U = f (x, y) and 'f' is your taste function which is obviously different
than mine or any other consumer and is reflected by different shape of
indifference curves and different MRSs.
Anyone's indifference map will, for normal goods, be convex (opening
away) from the origin. The reason is
diminishing marginal utility, i.e., at some point you are unwilling to give up
x for any more y. This is the point of
inflection for the indifference curve.
The transitivity assumption ensures that curves do not intersect but
rather rise
higher and higher.
c) Budget Line:
Given a specific
level of income, a budget line shows all commodity combinations of x and and y
that can be purchased by a consumer, i.e, .I = PxX + PyY. One cannot consume above it (not attainable
given income and prices) and it would be irrational to consume below it and
pocket the cash. Happiness in this model
is only derived from the consumption of goods & services purchased on the
market. Saving money does not count
other than as a 'good & service' that increases future consumption by
'selling' money for interest. The
maximum amount of x or y one can afford given income and prices is shown as the
intercepts of the budget line and the respective axes.
If income goes up
(and x and y are normal goods) a new higher budget line will be available to
the consumer parallel to the original.
If the price of x
decreases then the angle of the budget line changes and the intercept
increases, that is, the consumer can buy more x with the same income The slope
of the budget line is also the negative of the price ratio, i.e., - Px/Py. Thus the price ratio is NOT the slope of the
line which would be Py/Px (rise over run).
This formulation of the price ratio is a 'convention' or tradition in
economics. However, it also represents
the 'relative price' of x and y at a given point in time, i.e., how many units
of x can be bought with one unit of y at current prices, e.g., $1.00/50 cents =
a relative price of '2'.
d) Equilibrium:
The commodity combination which maximizes a
consumer's utility is the one on the budget line tangent to the highest
indifference curve. In rare cases - a
corner solution - an individual will consume none of a commodity x because no
amount of x is worth the cost. In such
cases the consumer's maximum utility is obtained on the y -axis that is no x is
consumed.
Equilibrium occurs where the Budget Line
just touches (is tangent to) the highest attainable indifference curve. This equilibrium or 'best affordable point' satisfies the
following conditions:
Marginal Rate of Substitution (MRS = MUy/MUx) equals the slope
of the Budget Line or its negative, the price ratio - (Px/Py) therefore in
equilibrium MUy/MUx = - Px/Py
at this point the
'rationale' consumer has equated the MU per dollar of each commodity consumed,
i.e. MUx/Px = MUy/Py Consumers will tend
to remain at this point (or be 'in equilibrium') as long as taste, income and
prices remain fixed. This is called the
'initial equilibrium'. We will now change
these assumption one by one and see what happens to equilibrium.
Maximum utility is
found where the budget line is tangent to the highest attainable indifference curve - that is, where the
negative slope of the indifference curve (or marginal rate of substitution of x
for y) is equal to the slope of the budget line, that is, the marginal rate of
substitution equals the (-) price ratio and here MUx/Px = MUy/Py.
2. Manipulations
From the basic analytic mechanism of the
indifference curve and budget line a range of additional information can be
deduced including:
a) Income-Consumption
Curve
An increase in income increases the
intercepts of the budget line but leaves its slope constant - assuming constant
prices. The locus of tangents of budget
lines with indifference curves forms the 'income-consumption curve' or the set
of commodity combinations (x, y) purchased as income increases - assuming
constant prices and taste.
b) Engel Curve
The amount of a given commodity (x)
purchased at different levels of income, derived from the income-consumption
curve, forms the 'Engel' curve. The
shape of an Engel curve depends on the type of commodity and consumer taste -
assuming constant prices. The quantity
of a commodity (x) purchased will increase at either an increasing or
decreasing rate as income rises - depending on the type of commodity.
c) Price-Consumption
Curve
If the price of one commodity (x) changes a
new set of combinations (x, y) is created between the changing tangents of the
budget line and indifference curves forming the 'price-consumption curve' for
the commodity (x) - assuming constant income and prices of the other commodity
(y). The price-consumption curve shows
how much of a commodity (x) is purchased if its price changes - assuming
constant income and constant prices for the other good (y).
d) Demand Curve
The demand curve for a given commodity (x)
can be derived from the price-consumption curve showing how much of that
commodity (x) is purchased at different prices - assuming constant income and
constant prices for the other good (y) (MBB 10th Ed. Figs 6.5Aa & 6.5Ab;
MBB 11th Ed. A5a & b; PB 4th Ed. Fig. 9.7; 5th Ed. Fig. 8.7). The shape of
the demand curve (x) depends on taste, income and the type of commodity - assuming
constant prices for the other good (y).
e) Substitution &
Income Effects
An increase in the price of a given
commodity (x) causes the slope of the budget line to increase lowering the
level of consumer utility, i.e. a new equilibrium on a lower indifference curve
- assuming constant income and constant prices for the other good (y) . The overall effect is called the 'price
effect'.
If, however, income is increased to
maintain the initial level of utility the quantity of the commodity (x)
consumed will still decrease as the slope of the budget curve increases in
response to the price rise. This
decrease in consumption due to a price increase - varying income to maintain
the initial level of utility - is called 'the substitution effect'. It measures how much less of the now more
expensive commodity (x) will be consumed. The difference between the amount
of the commodity (x) consumed - if
income is not increased to maintain initial utility - and the amount consumed
if income is increased is called the 'income effect'
f) Inferior Goods
The substitution effect is always negative,
that is if the price of a commodity (x) goes up, the quantity consumed goes
down. The income effect can be positive
or negative. For 'normal' goods, an
increase in income results in an increase in consumption - assuming constant
prices. If the quantity decreases when
income increases - assuming constant prices - the commodity is an 'inferior'
good. In most cases, if the price of an
inferior good decreases consumption will still increase if income rises.
3. Consumer Surplus
& Price Index
a) Consumer Surplus
Consumer surplus is the difference between
the maximum a consumer is willing to pay for a total quantity of a commodity (x
) and what the consumer actually pays
b) Consumer Price
Index
A consumer price index measures the
combined income effect of price changes of given commodity combination (x,
y). It measures how much income must
increase or decrease to purchase the same commodity combination (x, y) at
different price levels - through time.
Summary of Demand
In effect, Demand
reduces to constrained maximization of our happiness subject to a budget
constraint represented by two equations:
1. U = f (x, y)
2. I = PxX + PyY