Answer to Question #263609 in Microeconomics for Mka

Question

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

The total government revenue from the Choco Cookies(CC) is $TR_{1} = 66666 \times 10 = 666660$

The price of CC rises from $\$10 + \$30 = 42$ a box. The price of elasticity of demand is -2.

Therefore, $ed = -2\\$

$ed = \frac{\% change\ in\ Qd}{\%change\ in \ P}$

Now, % chang in P = $\frac{42-40}{40} \times 100 = 5\%$

$-2 = \frac{\% change\ in\ Q}{5 \%}\\ \% change\ in\ Q = -10\%\\ = (1-0.1) \times 66666 = 59,999.$

Then the tax revenue of the government is now TR2 = 719,992.8

Consider all other cookies, the revenue from OC is $Tr_{01} = 40000 \times 10 = 400000$

The price elasticity of demand = 0.75

$\% change\ in \ Q = 0.75 \times 5 = 3.75\%$

Total tax revenue 1134992.8 as oppose to tax revenue before 1066660.

The government should increase tax.