Question

Given the demand function Qd = D(p, y0), which is a function of price p and exogenous income y0, the supply function Qs = S(p). Suppose both the D,S functions are not given in specific forms but possess continuous derivatives, if we know that supply function is strictly increasing, and demand function is strictly decreasing w.r.t price but a strictly increasing w.r.t income.

(a) Write the equilibrium condition in a single equation.

(b) Check whether the implicit-function theorem is applicable, if so find dp∗ /dy0 , where p ∗ is the equilibrium price.

Answer 1

Solution:

(a) The equillibrium condition is:

(b) Consider the excess demand function

Since, has continuous derivatives, it implies is continuously differentiable.

Let

Therefore, by implicit function theorem,

(i)

(ii)

Thus if income increases, so does the equillibrium price. This result is also intuitive. If given an equillibrium, income increases, the demand of the commodity (at the initial equillibrium price) exceeds that of supply resulting in excess demand. This increases the price of the good at the new equillibrium. Hence the result!.

** I hope you understand the solution. If yes then please rate me up. If not then please comment for solving doubt. And don’t forget to Rate.