Question

The demand curve for X goods is Xd=100-10P and the supply curve is MCx=1. The demand curve for Y goods is Yd=100-20P and the supply curve is MCy=1. A tax of $2 per unit on goods X and no tax on goods Y.
a. Calculate tax revenues and excesses in X goods.
b. Explain the total tax revenue and excess burden if you reduce the tax on goods X to one dollar and impose one dollar per unit on goods Y.
c. Explain which tax system is more desirable.

Answer 1

Part (A)

when no tax is imposed on good X

equilibrium at point when demand equals supply

at free market equilibrium of good X, 90 units of good X are sold at price of $1

tax of $ 2 per unit is imposed on good X

Sellers receive $ 1 for each unit of good X while buyers pay $ 3 for each unit of good X

Part (B)

in case of $ 2 , a tax of $ 1 is imposed on good X

Sellers receive $ 1 for each unit of good X while buyers pay $ 2 for each unit of good X

when no tax is imposed at equilibrium demand equals supply

at free market equilibrium of good Y, 80 units of good Y are sold at price of $1

tax of $ 1 per unit is imposed on good Y

Sellers receive $ 1 for each unit of good Y while buyers pay $ 2 for each unit of good Y

Part (C)

when tax of $ 2 is imposed on good X and no tax is imposed on good Y

when tax of $ 1 is imposed on both good X & good Y

tax revenue is equal for both tax systems but deadweight loss is lower in case of second tax system (part B)

so tax system 2 (part B) is more desirable