Answer to Question #263679 in Macroeconomics for David

Question

Elasticity and Tax Revenue

Choco Cookies sell for $40/box, of which $10 consists of tax, and 66,666 boxes are sold every year. The price elasticity of demand for Choco Cookies is -4. All other cookies sell for $30/box (including a $l0 tax), and 40,000 boxes are sold every year. The cross price elasticity of demand for other cookies, with respect to a change in the price of Choco Cookies, is 0.5. The government raises the tax on Choco Cookies from $10 to $l1 per box, all of which is passed through to the consumer in the form of higher prices. Calculate the change in total government revenue. Should the government raise the tax? Why or why not? Explain your answer.

Answer 1

initial tax$=(10\times 66 666)+(10\times 40 000)=\$ 1066660$

an increase in tax by $1(=11-10), price of Choco cookies increase by $1$(=\frac{1}{10}=10\%)$

price elasticity of demand $=\frac{\% \Delta Q}{\%\Delta\space p}$

$-4=\frac{\%\Delta Q}{10\%}\\\%\Delta Q=-4\times 10\%=-40\%(decrease)$

New quantity of choco cookies$=66 666\times 60\%=40000$ (considering integer value for number sold)

new tax revenue from choco cookies$=40 000\times 11=\$440 000$

cross price elasticity of demand

$=\frac{\%\Delta Q}{\%\Delta p}\\0.5=\frac{\%\Delta Q}{10\%}\\\%\Delta Q=0.5\times\%10=5\%(increase)$

new quantity of other cookies$=40 000\times 1.05=42 000$

new tax revenue from other cookies $=42 000\times 10=420 000$

total tax revenue$=440 000+420000=860000$

change in tax revenue$=860000-1066660=-\$206 660$

since increase in tax has deceased total tax revenue ,government should not increase tax