Consider the market for sweeteners. Here, we characterize a two-commodity market in which the two commodities are sugar and corn syrup, which we will hereafter call commodities 1 and 2, respectively. We will assume that these two are substitutes.

So, in parametric form, we have:

QD1 - QS1 = 0

QD1 = a0 + a1P1 + a2P2

QS1 = b0 + b1P1 + b2P2

QD2 - QS2 = 0

QD2 = 0 + 1P1 + 2P2

QS2 = 0 + 1P1 + 2P2

In this numerical example, we will use the following supply and demand functions:

QD1 = 6 -P1 + 2P2

QS1 = -4 + P1

QD2 = 9 -2P1 + P2

QS2 = -2 + P2

c0 = 6-(-1) = 7 c1 = -4 - 1 = -5

c2 = 2 - 0 = 2

y0 = 9-(-2) = 11

y1 = -2 - 1 = -3

y2 = 1 - 0 = 1

So we have:

P1* = (c2y0 - c0y2)/(c1y2 - c2y1) = (15)/(1) = 15

P2* = (c0y1 - c1y0)/(c1y2 - c2y1) = (34)/(1) = 34

Q1* = 59

Q2* = 13

1. Graph the supply and demand curve of sugar and corn syrup
2. Verify that the cross price elasticity for the two goods is elastic and positive.