Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

22 DEMAND, SUPPLY, AND EQUILIBRIUM: AN OVERVIEW [CHAP. 2
(a)
What was said in Section 2.1 can be expressed in simple mathematical language as follows:
Qd x ¼ f (P x , M, P 0 , T)
(b)
where Qd x ¼ the quantity of commodity X P x ¼ the price of commodity X
demanded by the individual, M ¼ the money income of the individual
over the specified time period P 0 ¼ the prices of other commodities
f ¼ a function of, or depends on T ¼ the tastes of the individual
By keeping constant the individual’s money income, the prices of other commodities, and the individual’s
tastes, we can write
Qd x ¼ f (P x , M, P 0 , T)
where the bar on top of M, P 0 , and T means that they are kept constant. The last mathematical expression is
usually abbreviated as
Qd x ¼ f (P x )cet: par:
This reads: The quantity of commodity X demanded by an individual over a specified time period is a function
of or depends on the price of that commodity while holding constant everything else that affects the individual’s
demand for the commodity.
2.2 (a) What is the relationship between the expression Qd x ¼ f(P x ) cet. par. and the expression
Qd c ¼ 8 2 P x cet. par. in Example 1?
(b) What is the relationship between “need” or “want” and “demand”?
(a)
(b)
The expression Qd x ¼ f (P x ) cet: par: is a general functional relationship indicating simply that Qd x is a
function of or depends on P x when everything else that affects the individual’s demand for the commodity
is held constant. The expression Qd x ¼ 8 2 P x cet. par. isaspecific functional relationship indicating
precisely how Qd x depends on P x . That is, by substituting various prices of commodity X into this specific
demand function, we get the particular quantity of commodity X demanded by the individual per unit
of time at these various prices. Thus, we get the individual’s demand schedule and from it, the demand
curve.
The demand for a particular commodity arises because of its ability to satisfy a need or a want. However,
the demand for a commodity, in an economic sense, arises when there is both a need for the commodity
and consumers have the money to pay for it. Thus, demand really refers to effective demand rather than to
simple need.
2.3 From the demand function Qd x ¼ 12 2 2P x (P x is given in dollars), derive (a) the individual’s demand
schedule and (b) the individual’s demand curve, (c) What is the maximum quantity this individual will
ever demand of commodity X per time period?
(a) Table 2.7
P x ($) 6 5 4 3 2 1 0
Qd x 0 2 4 6 8 10 12
(b)
It should be noted that in economics, contrary to usual mathematical usage, price (the independent or
explanatory variable) is plotted on the vertical axis while the quantity demanded per unit of time
(the dependent or “explained” variable) is plotted on the horizontal axis (see Fig. 2-7). The reason
for the negative slope of the individual’s demand curve will be explained in Chapter 4.