Choco Cookies sell for $50 per box, of which $10 consists of tax, and 70,000 box
ID: 1211601 • Letter: C
Question
Choco Cookies sell for $50 per box, of which $10 consists of tax, and 70,000 boxes are sold every year. From previous research, you know that the price elasticity of demand for Choco Cookies is –1.5 (that is 1.5 in absolute value terms). All other cookies sell for $40 per box (which includes $l0 tax), and 40,000 boxes of other cookies 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 1.5. The government raises the tax on Choco Cookies from $10 to $l5 per box, all of which is passed through to the consumer in the form of higher prices of Choco Cookies. The government does not change the tax on other cookies. (a) Using the appropriate elasticity measures (price elasticity of demand and cross price elasticity of demand), calculate the change in total government revenue from the government raising the tax (and hence raising the price). To do this, you must calculate the government revenue before and after the tax change. Show your work. (b) Should the government raise the tax? Why or why not? (c) Explain your answer by showing how you calculated the new P’s and Q’s for Choco and other cookies after the change in tax was levied. (d) Characterize the elasticities by types of goods. (ee) Explain how a different characterization of elasticities would change the outcome.
Explanation / Answer
Choco cookies:
Price $50 / box
Other cookies:
Price $40 / box
Government revenue before tax increase = $10 x 70,000 = $700,000
Price elasticity of demand for Choco cookies = - 1.5
Price of Choco cookies after tax = ($40 + $15) = $55
% change in price = $5 / $50 = 0.1 or 10%
PED: - 1.5 = %change in quantity / 0.1 (10%)
% change in quantity = - 1.5 x 0.1 = - 0.15 or decrease of 15 % in quantity ( - 10,500)
Quantity demanded after tax = 70,000 – 10,500 = 59,500
Government revenue after increase in tax = $15 x 59,500 = $892,500
Other cookies:
Government revenue before tax increase = $10 x 40,000 = $400,000
Government revenue after tax = $10 x 31,000 = $310,000
Total government revenue before increase in tax = $700,000 + $400,000 = $1,100,000
Total government revenue after increase in tax = $892,500 + $310,000 = $1,202,500
a. Change in government revenue after increase in tax = $1,202,500 - $1,100,000 = $102,000
b. In order to maximize revenue, the government needs to levy a tax.
c. Price elasticity of demand for Choco cookies = - 1.5
Price of Choco cookies after tax = ($40 + $15) = $55
% change in price = $5 / $50 = 0.1 or 10%
PED: - 1.5 = %change in quantity / 0.1 (10%)
% change in quantity = - 1.5 x 0.1 = - 0.15 or decrease of 15 % in quantity (- 10,500).
Cross-price elasticity:
XED = % change in the quantity of other cookies / % change in price of Choco cookies
1.5 = % change in quantity of other cookies / -15%
% change in quantity of other cookies = 1.5 x0.15 = - 0.225 or - 22.5%
Quantity demanded of other cookies = 9,000 less of 40,000 = 31,000.
d. As the price elasticity of demand is given as negative, they can be characterized as inferior goods.
e. An inferior good means an increase in income causes a fall in demand. It has a negative YED. But if the elasticity is positive, it means that it is a normal good in that an increase in income causes an increase in demand.
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