Practice Problems

4 Consider the supply and demand equations

We conclude that stability depends on the relative sizes of a and c, which govern the slopes of the supply and demand curves. Bearing in mind that we have chosen to consider supply and demand equations in which Q is expressed in terms of P, namely

Qd = -cP + d we deduce that the system is stable whenever the supply curve is flatter than the demand curve when P is plotted on the horizontal axis.

Throughout this section we have concentrated on linear models. An obvious question to ask is whether we can extend these to cover the case of non-linear relationships. Unfortunately, the associated mathematics gets hard very quickly, even for mildly non-linear problems. It is usually impossible to find an explicit formula for the solution of such difference equations. Under these circumstances, we fall back on the tried and trusted approach of actually calculating the first few values until we can identify its behaviour. A spreadsheet provides an ideal way of doing this, since the parameters in the model can be easily changed.

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