Question

Suppose the demand for good X can be represented by the following equation: QX = 50 - 1.25P. Furthermore, suppose that the demand for good Y can be represented by QY = 20 - 0.5P. a. Find the elasticity of demand for both good X and good Y when the price of X is $10 and the price of Y is $15. 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? (Hint: You can use the regular elasticity formula to calculate the elasticity. Elasticity at a given price can also be found using the formula: elasticity = - (1/s)(P/QX), where s is the slope of the inverse demand curve, QX is the quantity demanded, and P is the price. )

Answer 1

(a) The elsticity of X would be as or or or or , and for the price $10 and quantity , we have the elasticity as or .

The elsticity of X would be as or or or or , and for the price $15 and quantity , we have the elasticity as or .

(b) The after tax demand would be and , and the tax revenues would be and . The tax revenue maximization problem would be to maximize with respect to tx and ty.

The FOCs would be as below.

or or or .

or or or .

Solving for the FOCs, we have , which is the optimal ratio of tax on X and tax on Y that maximizes the total revnue T.