Assume that the price elasticity of demand for cigarettes is 0.4. If a pack of cigarettes currently costs $6 and the government aims to decrease smoking by 20 percent, by how much should it increase the price?

Alright, let's see what we got here. Assume that the price elasticity of demand for cigarettes is 0.4. If a pack of cigarettes currently costs $6 and the government aims to decrease smoking by 20%, by how much should it increase the price? First thing I wanna note here is that it gave us the price elasticity of demand already. It told us price elasticity of demand is 0.4, right? And what does that mean? It's inelastic, right? So you could probably think that that makes sense for for cigarettes. Consumers are not so affected by price changes, right? Because they have an addiction there, so when the price goes up for cigarettes, the quantity demanded doesn't go down by as much because people still want their cigarettes. So it tells us in this case the price elasticity of demand right. So we had our formula elasticity of demand equals percentage change in quantity demanded over percentage change in price, right? But they just told us what this is. They told us the left hand side of the equation is 0.4, right? So 0.4 is what equals this percentage change in quantity demanded over percentage change in price. And what else do they tell us? They tell us the current price is $6 and they tell us that the government wants to decrease smoking by 20%, right? They want to decrease smoking by 20%. So what does that mean when we think economically, right? In economics, that means they want the quantity demanded of cigarettes to drop by 20%, right? They want 20% less, smoking to happen so they want 20% less demanded. So that's what our numerator is, right? Our numerator is gonna be that 20%. So we have 0.2 which is 20% as our numerator divided by what it's asking us, right? It's telling us how much should the price increase. How much should it increase the price? Well that's what we need to find out. We've been given the other two variables in this formula. What's left is this percentage change in price. They gave us a current price, but they wanted to know how much does it need to change. So let's go ahead and do a little bit of algebra here to percentage change in price. So the easiest thing we can do is we can multiply both sides by x, right? So we'll have 0.4x let me do it in red. 0.4x equals, and these x's are going to cancel, 0.2, and now we can divide both sides by 0.4. I'll do that in black again, divided by 0.4 divided by 0.4, and we're going to get this is gonna cancel. We're gonna get x equals 0.2 divided by 0.4. Put that in our calculator and we're gonna get 0.5. So 0.5 is half. That is what we need the percentage change in price to be, right? So this is our percentage change in price. So our price needs to change by 0.5 which is 50%, right? A 50% price change. Right now, the price is $6. So the last step here is how much do we need to change the price? Well we need to change it by 50% to get this 20% decrease in smoking, so $6 times 50% or 0.5, either 1, is going to give us $3 So $3 is the amount that we're gonna have to change the price, increase the price by $3, and we'll decrease smoking by 20%. Pretty tough one there because it kind of trips you up by giving you the price elasticity of demand, but you just gotta know what information you're given and what information you're looking for. Cool. Let's go ahead and move on.

Assume that the price elasticity of demand for cigarettes is 0.4....

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Assume that the price elasticity of demand for cigarettes is 0.4. If a pack of cigarettes currently costs $6 and the government aims to decrease smoking by 20 percent, by how much should it increase the price?

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