Hey guys! So I\'ve been trying to solve this question for ages and I\'m complete

Question

Hey guys! So I've been trying to solve this question for ages and I'm completely stuck because I'm not sure how to go about solving it. If someone could help me out and show me all the steps I'd greatly appreciate it:

Suppose the price elasticity of demand for cigarettes is equal to 0.25. Assume that a pack of cigarettes currently costs 10 in dirhams. Assume also that the government wants to reduce tobacco consumption by 25%. By how much (in Dirhams) should the government increase the price of cigarttes?

I know how to solve for elasticity but my algebra skills are very weak so I'm not sure how to rearrange the problem to solve for the price, I really need help with this so I can learn how to do it on my own for the exam. Thank you so much.

Explanation / Answer

It has been provided that government wants to reduce tobacco consumption by 25%. This means government wants to reduce demand by 25%.

Price elasticity of demand = 0.25

Price elasticity of demand is calculated as follows -

Price elasticity of demand = % change in quantity demanded/% change in price

0.25 = 25/%change in price

% change in price = 25/0.25

% change in price = 100

Thus, given the price elasticity of demand for cigarettes being 0.25, the government has to increase the price of pack of cigarettes by 100%, if it wants to reduce consumption by 25%.

Current price of pack of cigarettes = 10 dirham

% increase in price = 100%

Increase in price = 10 * (100/100) = 10 dirham

So, government should increase the price of a pack of cigarettes by 10 Dirhams.

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