Answer to Question #173546 in Math for ANJU JAYACHANDRAN

Question

2. (a) Find the equilibrium price in a perfectly competitive market with the supply function

( ) ( 3/)4

2

S p = − p + and the demand function D( p) = − p + .2 Using the static

criterion of Walras, determine whether the price is stable or not.

Answer 1

$$S(p)=(-p^2+4)/3$$

$$D(p)=(-p+2)$$

To find the intersection of the two curves set supply equal to demand and solve for $p$.

$$(-p^2+4)/3=-p+2$$

$$3(2-p)-(2-p)(2+p)=0$$

$$(2-p)(1-p)=0$$

$$p_1=1, p_2=2$$

$$dS/dp=-2p/3$$

$$dD/dp=-1$$

$$p=1: |dS/dp|=2/3<1=|dD/dp|$$

The price $p=1$ is stable.

$$p=2: |dS/dp|=4/3>1=|dD/dp|$$

The price $p=2$ is unstable.