Question

Suppose the demand function is Q _x^d = 120 - 8P_x - 6P_y - M. If P_x = $1, P_y = $2, and M = $10, what is the cross-price elasticity of good x with respect to the price of good y?

Answer 1

Cross price elasticity of demand tells us the responsiveness of change in quantity demanded of one good (X) by the change in the price of another good (Y). It is given by the following formula:

Cross elasticity of demand = dQx/ dPy * (Py/Qx)

where dQx/dPy is the partial differentiation of Qx with respect to Py.

dQx / dPy = -6

We have the value of Py which is equal to 2, now given other values we will find the value of Qx.

Qx = 120 - 8Px - 6Py - M

Qx = 120 - 8(1) - 6(2) - 10

Qx = 90

Cross price elasticity of demand = dQx/dPy * (Py/Qx)

= -6 *(2/90)

= - 0.133