food and clothing. If and represent the money prices of food and
clothing, respectively, and F and C represent the quantities of food and
clothing that Hugh chooses, then his spending on food is equal to
times F, and his spending on clothing is equal to times C. Thus the
equation for the budget line is
The Slope of the Budget Line
Look again at Hugh’s budget line in Figure 6A-3. The vertical intercept
is 60 units of clothing, and the horizontal intercept is 30 units of food.
Thus the slope is equal to The minus sign means that increases in
Hugh’s purchases of one of the goods must be accompanied by decreases
in his purchases of the other. The numerical value of the slope indicates
how much of one good must be given up to obtain an additional unit of
the other; in our example, the slope of means that Hugh must give up
2 units of clothing to purchase 1 extra unit of food.
Recall that in Chapter 3 we contrasted the absolute, or money, price of a
product with its relative price, which is the ratio of its absolute price to
that of some other product or group of products. One important point is
that the relative price determines the slope of the budget line. In terms of
our example of food and clothing, the slope of the budget line is
determined by the relative price of food in terms of clothing, with
the price of food at $24 per unit and the price of clothing at $12
per unit, the slope of the budget line (in absolute value) is 2. [ 12 ]
pF pCpF
pCE=pF×F+pC×C−2.− 2pF/pC;
(pF) (pC)