Mathematical Notes

1. Because one cannot divide by zero, the ratio cannot be

evaluated when. However, as approaches zero, the

ratio increases without limit:

Therefore, we say that the slope of a vertical line (when

for any ) is equal to infinity.

2. Many variables affect the quantity demanded. Using functional

notation, the argument of the next several pages of the text can

be anticipated. Let represent the quantity of a product

demanded and

represent, respectively, tastes, average household income,

population, income distribution, the commodity’s own price, and

the price of the jth other product.

The demand function is

The demand schedule or curve is given by

ΔY/ΔX

ΔX= 0 ΔX

ΔY/ΔX

ΔlimX→ 0 ΔΔXY =∞

ΔX

ΔY

QD

T,Y ̄ ̄ ̄,N,Yˆ,p,pj

QD=D(T,Y ̄ ̄ ̄,N,Yˆ,p,pj), j= 1 , 2 ,...,n