Suppose the demand for good X
Suppose the demand for good X can be represented by thefollowing equation: QX = 35 – 2P. Furthermore,suppose that the demand for good Y can be represented by QY = 25 – 0.1P.
a. Find the elasticity of demand for both good X and good Y whenthe price of X is $15 and the price of Y is $10.
b.If the community’s goal is to raise tax revenue as efficientlyas possible, what should be the ratio of the tax on X to the tax onY?
Answer:
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 thedemand 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 thedemand 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 inelasticdemand, imposing tax on good Y will lead to increase in taxrevenue. On the other hand, since good X has elastic, imposition oftax on good X will not lead to increase in tax revenue. Thus, theratio of the tax on X to the tax on Y will be less than1. It meansmore tax is imposed on good Y and less tax on good X.
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