The federal government is considering placing a federal tax on a product as a me
ID: 1216974 • Letter: T
Question
The federal government is considering placing a federal tax on a product as a means of increasing federal tax revenue. After exhaustive review, the government agency responsible for recommending the tax increase has narrowed its choices for the tax increase to two products: Product A and Product B. The new federal tax will be a flat tax per unit sold and, as a result of the tax, the product’s selling price will increase. Part of the recommendation will be based on the price elasticity of demand for these two products. Given the historical price and quantity demanded data for these products provided in the table below, compute the individual price elasticity of demand coefficient values and indicate which of these two products should be assessed the new tax and explain why. (2 points)
Price
Quantity Demanded
Price
Quantity Demanded
Year 1
Year 1
Year 2
Year 2
Product A
$9.87
150,000
$6.63
213,000
Product B
$11.13
206,000
$10.50
278,000
Price
Quantity Demanded
Price
Quantity Demanded
Year 1
Year 1
Year 2
Year 2
Product A
$9.87
150,000
$6.63
213,000
Product B
$11.13
206,000
$10.50
278,000
Explanation / Answer
The formula for Price elasticity is demand is given as E = [(Q2 - Q1)/(P2 - P1)*P1/Q1].
Where Q2 AND P2 are year2 quantity and price resp.
And Q1 and P1 are the quantity and price of year 1 resp.
NOW FOR PRODUCT A :
E = (213,000 - 150,000)/(6.63 - 9.87 )*9.87/150,000.
E = 63000/-3.24*0.0000658
E = -19444.444*0.0000658
E = -1.279.
FOR PRODUCT B :
E = (278,000 - 206,000)/(10.50 - 11.13)*11.13/206,000.
E = 72,000/-0.63*0.0000540
E = 114285.714*0.0000540
E = -6.171.
Now we know, if the coefficient of elasticity is E >1, then we'd consider the demand to be elastic.
And by elastic demand we mean that the proportionate change in quantity demand is now than the proportionate change in price.
So if the tax is imposed on product B, the prices would rise, leading to a more fall in demand than the increase in price. And as a result the tax revenue collected would not be enough.
But on the contrary, if the tax is imposed on product A, which has relatively less elastic demand, an increase in price would not lead to fall in quantity demanded as it would in case of product B.
Thua imposing a tax on product A would lead to relatively higher revenues.
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