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1. Initial Conditions
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)
(P&B 4th Ed. Fig. 9.7;
5th Ed. Fig. 8.7;
7th Ed Fig. 9.7). 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' (P&B 4th Ed.
Fig. 9.8 & Fig. 9.9;
5th Ed. Fig. 8.8 & 8.9;
7th Ed Fig. 9.8 &
Fig. 9.9).
(M&Y
4.6)
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. (M&Y
4.7)
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 (P&B 4th Ed. Fig. 6.3;
5th Ed. Fig. 5.3;
7th Ed Fig. 5.2 ).
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
happiness subject to a budget constraint represented by two
equations:
1. U = f (x, y)
2. I = PxX + PyY
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