Suppose the demand for good X can be represented by the following equation: X d = 22 - (1/4)P. Furthermore, suppose that the demand for good Y can be represented by Y d = 50 - P.
(A) Find the elasticity of demand for both good X and good Y when the price is $10.
(B) Suppose that an ad valorem tax is placed on both goods. Good Y is taxed at a rate of 5%.
To ensure that the inverse elasticity rule holds, what must be the rate at which good X is
taxed?
Reminder: Elasticity at a given price is found using the formula ? = -(1/S)(P/X), where S is the
slope of the demand curve, X is the quantity demanded, and P is the price.
(A) ?x = (1/4)(10/19.5) = 0.128. ?y = (1/1)(10/40) = 0.25.
(B) To ensure t x /t y = ? x /? y , given t y = 0.05, solve tx/0.05 = 0.25/0.128 = 0.0975 or 9.75%.
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