Douglas A. Ruby
A Consumer Optimum
|Demand Curve Derivation
Individual demand curves can be thought of as a set of price-quantity combinations
that each represent a separate consumer optimum for different market prices. This
can be seen in the diagrams below:
Point 'a' in the left diagram represents a bundle of goods (x and y) that
will maximize the consumer's level of satisfaction for a given set of market prices
and income (I0). This same point in the right diagram represents an identical quantity of
good-x demanded at a current price P0x. As the price of good-x declines [click on the
next button] the consumer is willing (substitution effect) and able
(income effect) to purchase more of good-x. The inverse relationship between prices and quantity
trace out the individual's demand for this commodity. The slope of this individual demand relationship
depends on the magnitude of the total effect of the price change and specifically the strength of the
income effect. Stronger income effects (assuming normal goods) lead to flatter demand curves.
Additionally, this reduction in prices makes the consumer better off as shown in the tangencies to higher indifference curves in the
left diagram. This increase in consumer welfare can be measured by the corresponding change in consumer surplus as shown in the below right diagram.
A price change:
We can conclude our discussion by deriving a market demand curve.
This market demand represents a (horizontal) summation of individual
demand curves. Specifically, for each market price, individual
consumers each have their own consumer optimums and corresponding
demand for the good in question. We add up these demand for each
possible market price to calculate the total quantity demanded in
the market. For example:
Thus, we find that in the market, every time the price is
reduced by $0.50, the total quantity demanded (market demand)
increases by 6 units.