ECONOMICS DEPARTMENT

**Economists have worked out a theory of the consumer which appears to be
a general theory explaining what people buy. In actuality explaining the
the behavior of any specific individual would be too complex a problem and
probably require a psychological approach. But economics is not concerned
with explaining the behavior of any specific consumer; instead it is
concerned with explaining the behavior of markets. In order to explain
the behavior of a typical consumer in a market it is not necessary to have
a completely realistic and detailed model of consumers. All that is
required is a model that captures the market-relevant influences of the
average and allows the individual differences to aveage out.
**

**The economic model of the consumer was originally formulated in terms
of the concept of a utility function and that formulation is still valid.
Unfortunately the concept of utility has some puzzles for beginning
students of economics. The problems are about how utility is measured and
what are its units. If there are two goods whose quantities of consumption
are x and y then a utility function would have the form U(x,y). But any
always increasing function of U, say f(U(x,y)) would an equally valid
utility function.
**

**For beginning students in economics it is better to replace the concept
of utility with the notion of benefit. The benefit function B(x,y) is the
amount of income a person would consider equivalent to the consumption
bundle (x,y); i.e., x units of good X and y units of good Y. A consumption bundle (x,y) has a benefit B is when a person
is given the choice of the bundle (x,y) or some amount of income less than
B that person will choose the bundle but if the amount of income is more
than B that person will take the income. For a choice of (x,y) or B the
person is indifferent, one being consider just as good but no better than
the other.
**

**Now suppose the level of y is held fixed at y _{0} and B is plotted
as a function of x as the diagram below.
**

If the price of the good X is p_{x} then the cost of consuming
an amount x is
p_{x}x. This is plotted in the above diagram as the cost. The net
benefit of
consuming an amount x is the difference between the B(x,y_{0}) and the
cost p_{x}x. The net benefit is shown in the diagram above in red.
A consumer wants to
get the greatest net benefit; i.e., the consumer would choose a level of
consumption of x such that the net benefit is a maximum. Note that when the
net benefit is a maximum the slope of the net benefit curve is zero. This
means that at the level of x where net benefit is a maximum the increase in
benefit from another unit of X is exactly equal to the increase in cost of
consuming another unit of X.

The increase in cost for consuming another
unit of X is just the price of a unit of X. The increase in benefit can
be computed from the benefit function. It is called the *marginal*
benefit of another unit of X. The marginal benefit usually goes down; i.e.
the more X someone is already consuming the less valuable another unit of
X is to the consumer.

The marginal benefit curve for an individual is important because it determines how much that individual would purchase of the good at any price. For any price a horizontal line is drawn in the graph at that level. Where the price line intersects the marginal benefit curve gives the quantity which would be demanded at that price. If the price and quantity data are plotted in a different graph to construct the demand schedule for the individual one finds that the marginal benefit curve is just being replotted. In other words,

The demand curve is exactly the same as the marginal benefit curve. The downward sloping of the demand curve is just the diminishing marginal benefit of the increasing consumption of the good.

While the above tells us that if we know the marginal benefit curve then we can construct the demand curve, the significance of the result is that if know the demand curve then we have the marginal benefit curve.

From mathematics it is known that the change in some quantity, say
benefit, over some interval is equal to the area under the marginal
curve, in this case the marginal benefit curve, over that same interval.
(This is known as the Fundament Theorem of Calculus.) Therefore if we
want to know the benefit consumers get from increasing their consumption
of a good from x_{1} to x_{2} we just need to find the
area under the demand curve from x_{1} to x_{2}.

Furthermore if we want to know the total benefit consumers get from
consuming an amount x_{1} of a good we just need to find the
area under the demand curve for that good from 0 to x_{1}. This
is the total or gross benefit. The net benefit to consumers of being
able to purchase the good at price p_{1} is the gross benefit
they get from the amount x_{1}, which is the amount
they are willing to purchase when the price is p_{1} less the
amount they have to pay for that amount of the good; i.e.,
p_{1}x_{1}. In terms of a graph the gross benefit consumer
get is the area under the demand curve from 0 to x_{1} and the
cost of that consumption is the area of the rectangle with height
p_{1} and width x_{1}. The net benefit is the area
between the demand curve and the price line over the interval from 0 up to
the quantity consumed. This net benefit is usually called
*consumer surplus*. It is the surplus benefit consumers get above the
cost of the consumption.