Suppose that the demand function for good Z is given as a no

Suppose that the demand function for good Z is given as a non-linear function: Qd(P) = aP^b, where a>0 and b<0 are constants and P is the price of good Z.                                                                                            

a) Find price elasticity of demand for Z when P = 1.

b) Find price elasticity of demand for Z when P = 2.

Your answer at (a) and (b) should be the same.

Show Work!                               

Solution

When P =1 Q = a(1)^b

Q = a

EDp = p/q *cofficent of demand curve

codfficent fo demand curve = ab(1)^b-1 = ab (differentiation fo demand function with repsect ot price)

EDp = 1/a*ab = b

When P = 2

Q = a2^b

Cofficient of demand curve = ab(2)^b-1(differentiation fo demand function with repsect ot price)

EDp = P/Q*cofficent of demand curve

2/a2^b*a2^b-1

= b