Consider the classical problem of supply and demand of some commodity. At time n, let The demand d[n], which is a function of the price p[n], is given by Because the production of a commodity (corn,...

The demand d[n], which is a function of the price p[n], is given by

Because the production of a commodity (corn, for instance) is not instantaneous but takes time to produce, the producer bases production on the price during the previous period. Thus,

s[n] = s₀
+ bp[n − 1],

where s₀
is usually a negative constant. Finally, the prevailing price must be such that supply equals demand during any period.

(a) Construct the model (equation) for the prevailing price during the nth period.

(b) Determine a block realization of this system.