We have dealt with market equilibrium in various sections of the main text. Our focus has been the mathematical representation of market equilibrium for a particular good – the price level and the quantity traded in the market when they are settled – per se. We did give a verbal explanation as to how the price adjusts when there is excess demand (or excess supply) in the market, but we did not pay much attention to the mathematical representation of the price adjustment process. This appendix provides an introduction to difference and differential equations that will allow us to shed light on such dynamics.

We will start by introducing the cobweb model of price adjustment, which describes the dynamics of the price adjustment. In our example, it turns out the price adjustment can be represented by a linear first-order autonomous difference equation in terms of the price. We will study how to solve this type of difference equation in general. In turn, the linear first-order autonomous differential equation – a continuous-time version of the same form of difference equation – will be introduced and examined in the context of the demand and supply analysis.

The cobweb model of price adjustment

One of the implicit assumptions in the demand and supply analysis is that sellers make their supply decisions after they know the price of the good. But in reality, in most markets sellers tend to be in the situation where they must commit to a supply decision before they know the price of the good in question.