Question

14.

Let Qd, Qs and P be the quantity demanded, quantity supplied and price, respectively, of a certain 1

commodity. We assume that

Qs =c1 +w1P +u1P′ +v1P′′

Qd =c2 +w2P +u2P′ +v2P′′

where the primes denote derivatives with respect to t, time.

Now let c=c1−c2; u=u1−u2; v=v1−v2; w=w1−w2.

1. (a) Using the typical Economics assumption that demand equals supply i.e. Qs = Qd, derive a

   non-homogenous O.D.E for P.

2. (b) Given that w > 0 and c < 0, what is the equilibrium price?

   (Hint: The equilibrium price is a constant. In fact it is a particular solution to the O.D.E. above)

3. (c) If v > 0, w > 0 and c < 0, what extra conditions on u,v,w guarantee that the price oscillates,

   with a constant amplitude, about the equilibrium price?

4. (d) If v > 0, w > 0 and c < 0, what other conditions on u, v, w guarantees that the price approaches the equilibrium price?

Answer 1

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