HKDSE Economics Question Review

Question:

Denote communism as command economy and capitalism as market economy. Prove that they are linearly independent.

Solution:

Method 1 (out of syllabus): Use Indifference curve to illustrate the relationship between these 2 goods/services. Then we can use budget line to link them up.

Method 2: Show that they are inversely related when ceteris paribus holds:

Using the fact that both variables must be non-zero and of positive magnitudes, when they have proportion, we can establish a set of rectangular hyperbolic of Cartesian form xy=c, which is exactly an Indifference curve derived by Dot Product of 2 vectors of phase angle exactly π/2 in radian measure. Q E.D.

rectangular hyperbolas

Note that the 2 vectors must be 2D, as economics is always 2D, even when Iine Integrals are applied in advanced courses.

The reason is simple, the Dot Operation of more than binary means is invalid:

We have a • (b • c) and (a • b) • c,

but no such thing called a • b • c.