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Cigarette taxes revenues and elasticity of demand

A few weeks ago the Nicholls Worth ran this article about Jindal’s plan to change the structure of taxation in Louisiana, moving away from income taxes and toward sales taxes.   More recently, more details of the governor’s tax proposals have been released, as we see in this article from the Baton Rouge Advocate.  In particular, notice that after fighting against keeping a 4-cent per pack temporary tax on cigarettes two years ago, Jindal has now proposed almost quadrupling the state’s cigarette tax to $1.41 per pack.  Of course, this time the increase in the cigarette tax is part of a plan to get rid of the income tax in the state.

A discussion of cigarette taxes and revenues seems to be especially in order, since we are now discussing something called the “price elasticity of demand” and the “income elasticity of demand” in two of my classes.  As it happens, I have done some research on estimating the effects of state cigarette taxes (for instance, see here and here).

Basic economic theory suggests that any unit tax (so many cents per unit, not based on selling price) on a specific good, as we see on cigarettes and beer, and we saw in our auction, the tax should either be passed on to buyers in higher prices, with sellers paying the rest of the tax in terms of the price received (after-tax price or price minus the tax).  Since the supply to any single state is a very small part of the total supply of cigarettes, state supply is completely flat and any state cigarette tax is completely passed on to buyers.

In Figure 1 we see the two types of demands noting that the X-axis measures the amount of cigarettes demanded in state j (where j could stand for any state) on a per capita basis, or total quantity demanded divided by the number of people in the state).  Demand 1 shows the demand for cigarettes in a state when prices in that state change, holding the prices of cigarettes in all other states constant, which is what happens when a state changes its tax rates while other states do not.  Demand 2 shows what happens when prices in all states increase the same, as is the case when the tax on cigarettes changes, affecting all states the same.   If the state tax on cigarettes increases, the supply curve shifts up by the amount of the tax, and so, with a flat supply curve, the supply shifts up in the price direction by the amount of the tax, resulting in the price changing (dP = change in price = tax) by the amount of the tax increase.

Figure 1.  Demand when prices rise together in all states and when prices rise in just one state

 fig 1

From Figure 1, using “d” to represent “change in,” b = inverse slope or dQ/dP of Demand 1 and a = inverse slope of Demand 2, or dQ/dP.  The coefficients “a” and “b” are estimated from data on cigarette, prices, cigarette taxes and cigarette sales state by state.  So, a state tax of the amount dP (dP stands here for change in price) will cause the quantity demanded to fall in the state by b*dP, where b is the change in quantity from a one-cent change in price along Demand 1 (what we can call the “state only” demand curve)—note that the change in Quantity Demanded, dQ = b*dP).    Based on Demand 2, where all states’ prices change together (the “all together” demand), we see that increases in cigarette prices because of the tax reduce consumption of cigarettes in the state by a*dP.  So the remaining reduction in cigarette sales in the state will be (b-a)*dP or s*dP.  This is the amount of sales reduced, not because people are cutting back on smoking, but because people are no longer buy cigarettes in this state, but buy them elsewhere.  Remember, the price increase of dP reduces the quantity demanded in the state only by a*dP.   So, we find the effect of a state tax hike in changing cross-state purchases by subtracting the slope coefficient a from the slope coefficient b.

Figure 2 shows the result of a federal or nation-wide cigarette tax increase from $.39 per pack to $1.01 per pack in 2009 as a movement along the blue demand curve, the all-together demand curve.  This all-together demand curve corresponds to Demand 2 in Figure 1.  If this increase in federal cigarette taxes of $.62 per pack is fully passed on to buyers in higher prices, the federal tax increase would boost the state average price for $4.08 to $4.70.  Here, the demand curve in blue, the “all-together” demand, corresponds to Demand 2 in Figure 1, the demand for cigarettes in the state when prices in all states go up together.  The two red demands show the demand when just this one state is raising its taxes, the state-only demand, corresponding to Demand 1 in Figure 1.  The lower state-only demand is the one for which the federal tax is only $.39 per pack, while the higher state-only demand is the one when the federal tax is $1.08  per pack.

Figure 2. Cigarette demand with elasticity estimates

fig 2

The state’s tax revenue gains from a state cigarette hike will be the amount of that tax hike times the number of units purchased after that tax hike, which is the rectangle labeled as the “Revenue rectangle.”  Notice that since the federal tax hike will reduce sales in the state, the same state tax hike generates less state revenue than before the federal tax hike.

The price elasticity of demand for the All-together demand is -0.296.  The price elasticity of demand for the state-only demand when state prices start at $4.08 is -1.085, but is -1.25 when the state price starts at $4.70.  The income elasticity of demand is estimated to be -0.58, meaning that across states, cigarettes are inferior goods.

Figure 3 shows the relationship between a given tax hike in Louisiana and the revenues gained by the state at different tax rate hikes.  Comparing the revenues to those in 2008, which we see as the red dotted line, the upper curve in blue shows the predicted gross revenues for cigarette taxes in Louisiana for various tax hikes (from along the horizontal axis).  Gross revenue is about total collections and has not taken the costs of collection and enforcement into effect.

Figure 3. Predicted Gross Revenues from Various State Cigarette Tax Hikes in Louisiana

fig 3

There are two points worth noting in Figure 3.  The first is that the revenues are predicted to grow with the size of the tax hikes, but that growth is at a decreasing rate.  We see that with blue and dashed green lines which have positive but falling slopes. The other point is that the state revenue gains from a given tax hike are lower after the federal tax hike than before it.

A last point to note is one that seems a contradiction from what we have seen with elasticities and firm revenues and elasticities and state tax revenues that we see here.  Notice from Figure 2, both state only demands are in the elastic range.  This means that an increase in price when demand is in the elastic range would result in lower revenues for sellers.  Yet, when taxes push prices up, they increase state tax revenues, as we see with the two Revenue rectangles.  Why is it that tax revenues go up even though the demand is elastic?  The first person to correctly answer this will get an extra half point for the answer and gets to earn a half point more from the blogs than other students.


18 Responses to “Cigarette taxes revenues and elasticity of demand”

  1. JG says:

    Because Jindal eliminated income tax just means that state tax will go up enough to cover the difference. Raising the tax on cigarettes may deter a few buying but ultimately people who smoke will continue because it becomes addiction. smokers might buy less of another good in order to cover the tax increase of cigarettes.

    • mcoats says:

      I don’t think Jindahl eliminated the income tax. I am still paying it. I just think it is lower. BTW, Jindal approved the legislation, so it was not just Jindal alone.

  2. MF says:

    I am all for sales tax on cigarettes increasing. It’s most definitely a bias view as I am a non smoker but with increasing sales tax on cigarettes, this will give the smokers the opportunity to consider how they spend their money. Especially the working class who have families to support, they will have to ask themselves if its financially viable to keep purchasing cigarettes.

  3. -AC says:

    As the price of something goes up people buy less of that item. So deleting income taxes and just increasing sales taxes, especially cigarette taxes, may not have the effect that Governor Jindal is looking for. Smokers may start to look for substitutes to fill the place of their cigarettes if buying a pack of cigarettes becomes too expensive. Substitutes like chocolate, coffee, and chewing gum may increase instead. Whatever the substitutes may be, smokers will turn to those if the price of cigarettes gets too expensive.

  4. SM says:

    I think raising the tax on cigarette is a great idea. Not only will raising the cigarette tax stop the increase of other taxes, but it will also cause many people to rethink about the importance of smoking. The majority of my family smokes, and here the price for cigarettes is not high enough to make them consider stopping, unlike place like NY were the price of one pack of cigarettes can cost up to $14 dollars.

  5. JL says:

    I agree with raising taxes on cigarettes. I am a non smoker, so this may be biased, however, I do think that if a product is causing an increase in other taxes indirectly, such as medicare, then the tax should be raised for that produc

    • dl says:

      I agree 100% JL. I am also a non-smoker, but I have many family and friends who do smoke. While I don’t mind personally that they do, I do think it should cost them more in taxes to obtain the product. Not only is it raising taxes for us indirectly to pay for things like Medicare like you mentioned, but also they are killing themselves slowly in the process. Maybe if cigarettes cost more, people wouldn’t buy them as much. But that is more of an ethical and moral standpoint of mine. As far as economics is concerned, if they raise the price on cigarettes too much as a means of getting rid of the income tax, and people decide to stop smoking because of it, what have we really achieved?

      • -AC says:

        Raising the tax on cigarettes would really only hurt those who do smoke. They would have to either decide on spending more money for a pack of cigarettes or buying a decent substitute instead. Maybe they should raise the taxes on alcohol too?

        • SP says:

          I agree! Putting tax on cigarette will in a way force people to make choices. Yes, it does have costs in terms of cigarette industries facing huge loss but then the benefit to the society would be greater. If people do stop smoking then there is higher chance for them to not suffer from lung cancer. Same goes to second hand smokers as well. Besides people can make use of nicotine patches. I also think that, the tax collected from the cigarette can be used for something more beneficial for the society. Lastly, if the cigarette factory were to go out of business, it does raise an issue of a number of people suffering unemployment but the governmnt can open up other manufacturing industry and provide them with employment.

        • mcoats says:

          SP, governments don’t produce many private goods, and when they do, the cost is usually about twice the cost of a private business, and so governments usually do not start factories.

  6. MPC says:

    I think that it will not be a bad idea to increase the cost, but not by that amount since it cost $4.08 so if is raised to an amount that is not a dollar more like $4.99 or $4.50 people will still see the 4 bucks praise even if it raised. This is a market strategy used in different business to sell products, and it will lower the change of buyers trying to find other ways to buy the desire product.

    • SM says:

      I agree that the tax they are proposing is not a large enough amount. If people doesn’t see a drastic change in price, they wont stop to consider the importance of consuming the product.

      • MF says:

        I agree with this, increasing cigarette taxes will make the consumers make a decision whether they could be spending their money in more useful things such as food and paying bills!

  7. MW says:

    I think the way our present day economy is we should embrace some of the raise in taxes. It is our generation that will have to suffer and fix this problem, but if we suck it up and deal with it now our future will be more secure. “If this increase in federal cigarette taxes of $.62 per pack is fully passed on to buyers in higher prices, the federal tax increase would boost the state average price for $4.08 to $4.70.” This increase is not substantial enough to stop people from smoking, and with the health risks that do involve smoking and second hand smoke the tax is valid. Our state average tax on tobbacco is much lower still then other states such as California and New York. Whatever means necessary that we need to do to get out of debt now will be instrumental to us as a nation getting out of this econmoic crisis. So I agree with the tax completely.

  8. Scott says:

    With the idea being said that higher tax would cause a decease in smokers is a false statement in my opinion. People who smoke will buy cigarettes no even if the price goes up, and even if sales do go down you’ll begin to see more discounts on cigarettes from producers. If the sales tax of everything goes up, i do believe this will lead to more online shopping wich may cause sales within the state to fall. With falling sales i see an increase in price on products to balance the supply and demand.

    • morris.coats says:

      Scott, that higher taxes cut smoking is not a matter of opinion, but this relationship is supported by about every study on the matter that I have seen, including my own widely cited study on cigarette taxes. One really interesting finding was from William Evans and Jeanne Ringel (http://www.sciencedirect.com/science/article/pii/S0047272798000905), who found that women cut back their smoking more when they find out that they are pregnant in high cigarette tax states than in low cigarette tax states. Maybe not every smoker cuts back, but all in all, both purchases and actual use goes down. When prices go up, because of a sales tax, people look for and find substitutes, cutting back from their original level. When there is a specific tax on something, even with an admittedly low elasticity of demand, people cut back, only not as much as they might with other items.

  9. Paul says:

    I don’t see a problem with Jindal’s tax plan to raise sales tax, because sales tax can be collected from everyone who lives in Louisiana as well as tourists. I also think it’s good that cigarette taxes are being increased, because the number of people who smoke is growing every day and it’s an easy way to earn millions in tax income. For example, in the last fiscal year that ended June 30, the tobacco tax generated $136 million dollars in revenue (http://theadvocate.com/home/4936782-125/la-talks-charging-more-tax). While analyzing your graph you brought out an interesting point for me. I did not think about the fact that people could buy cigarettes in one state and bring them to another, which I feel is what a lot of people do when they visit Louisiana, because our tobacco tax is so low compared to other states. I think that since the demand is elastic in the upper half the linear demand curve, the total revenue moves in the direction of the quantity change.

    • morris.coats says:

      Hi Paul,

      One of the big problems I see with increasing the sales tax is that state businesses (and our state sales tax) already lose a lot of sales to out-of-state businesses through internet sales, increasing the sales tax rate even further would push more people to buy large ticket items online. You are quite correct that a significant part of our cigarette sales in this state is to our neighbors in Mississippi, Texas and Arkansas, so that raising the tax would reduce their purchases in the state.

      Think again about what you have suggested in your last line, that raising the tax and the price would lower total revenues (increase tax increases price, reduces quantity, and if demand is elastic, revenue would drop). Wouldn’t that mean that raising the tax would reduce overall cigarette tax revenues? Or does it? My own estimates is that raising cigarette taxes by $1.05 a pack would bring in about $239 million more in revenues–revenues going up. Which is it, revenues up or down? Why?


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