You have been appointed to look into the elasticity of toothpaste and toothpicks

Question

You have been appointed to look into the elasticity of toothpaste and toothpicks, two products the government is considering taxing. Which product would be a better candidate to tax if the government wishes to raise revenue? Why?

Price of toothaste before the tax: $1.50 where Quantity Demanded is 1,000,000 tubes per week

Price of toothpaste after the tax: $3.50 where Quantity Demanded is 950,000 tubes per week

_____

Price of toothpicks before the tax: $1.00 where Quantity Demanded is 50,000 tubes per week

Price of toothpaste after the tax: $1.50 where Quantity Demanded is 10,000 tubes per week

_____

My calculations:

E = |(% change in Quantity Demanded)/(% change in Price)|

E_ToothPaste = |((950,000 - 1,000,000)/(950,000))/((3.50-1.50)/(3.50))| --> approx. |-0.09| ---> 0.09 and since 0.09 < 1, toothpaste is inelastic

E_ToothPicks = |((10,000 - 50,000)/(10,000))/((1.50-1.00)/(1.50))| --> |-12| --> 12 and since 12 > 1, toothpicks are elastic.

Which product is the better product to choose if the government wanted to raise revenue and why?

Explanation / Answer

Ed = % change in quantity demaned / % change in price

% change in quantity demanded = (q2 - q1)/q1 x 100

% change in price = (p2 - p1)/p1 x 100

Ed for toothpaste = [(950,000 - 1000,000)/1000,000 x 100] / [(3.50 - 1.50)/1.50 x 100]

= - 0.05/0.5 = - 0.1 < 1 so demand for toothpaste is inelastic.

Ed for toothpicks = [(10,000 - 5000)/5000 x 100] / [(1.50 - 1)/1 x 100]

= 1/0.5 = 2 > 1 so demand for Tooth Picks is elastic.

If government wanted to raise revenue then it will choose to produce good with inelastic demand because change in price does not change the quantity demanded of inelastic demand. So, government will produce ToothPaste.

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