Question

Suppose the demand for good X can be represented by the following equation: Q_X = 35 - 2P. Furthermore, suppose that the demand for good Y can be represented by    Q_Y = 25 - 0.1P.

a. Find the elasticity of demand for both good X and good Y when the price of X is $15 and the price of Y is $10.

b.If the community’s goal is to raise tax revenue as efficiently as possible, what should be the ratio of the tax on X to the tax on Y?

Answer 1

a) Qx = 35 - 2P = 35 - 2(15) = 5

Elasticity of demand for good X = (∆Qx / ∆Px) * (Px / Qx)   [Where, ∆Qx / ∆Px is the price coefficient in the demand function]

                                                   = -2 * (15 / 5)

                                                   = -6

The absolute value of PED is 6. Since the PED is greater than 1, therefore, good X has elastic demand.

b) Qy = 25 - 0.1P = 25 - 0.1(10) = 24

Elasticity of demand for good Y = (∆Qy / ∆Py) * (Py / Qy)   [Where, ∆Qy / ∆Py is the price coefficient in the demand function]

                                                   = -0.1 * (10 / 24)

                                                   = -0.04

The absolute value of PED is 0.4. Since the PED is less than 1, therefore, good Y has inelastic demand.

b) Since good Y has inelastic demand, imposing tax on good Y will lead to increase in tax revenue. On the other hand, since good X has elastic, imposition of tax on good X will not lead to increase in tax revenue. Thus, the ratio of the tax on X to the tax on Y will be less than1. It means more tax is imposed on good Y and less tax on good X.