Philadelphia supermarkets and distributors say beverage sales have dropped 30 percent to 50 percent after the city instituted a 1.5-cent-per-ounce tax on sugary and diet drinks. On one hand, these are the same people who want to get the tax repealed, and we don’t have hard numbers yet, so take this with a grain of salt. On the other hand, the whole point of the tax is to reduce consumption of stuff that will kill you anyway, so … good job?

To measure the responsiveness of consumers to price changes, economist use what is called the 'price elasticity of demand.' In simple terms, the price elasticity of demand tells us whether consumers react a little or a lot when the price of a good changes.

In technical terms, the price elasticity of demand is equal to the percentage change in the quantity demanded divided by the percentage change in the price. Because of the law of demand we know that the quantity demanded and the price will move in opposite directions, so the elasticity demand is a negative number. To confuse everyone, we report the price elasticity of demand as a positive number (the absolute value).

If the price elasticity of demand is greater than 1, then we say that demand is elastic and that means that consumers are pretty sensitive to price changes.

If the price elasticity of demand in greater than one, then we say that demand in unit elastic (the percentage change in the quantity demanded is exactly equal to the percentage change in the price).

If the price elasticity of demand is less than one, then demand is price inelastic and that means that consumers are not very sensitive to price changes.

One reason we care about the price elasticity of demand is because there is a relationship between price elasticities and revenues collected. If demand is inelastic, an increase in the price will increase revenues. If demand is elastic, a similar percentage increase in the price will decrease revenues. The reverse is also true.

This is why we see goods with elastic demand (furniture, groceries, clothing) going on sale more than goods with inelastic demand (gas, liquor).

So what does this mean for the sugary drink example above?

Let's look at the numbers (and make some assumptions). The tax imposed on sugary drinks is $0.015 per ounce. For a 12 ounce soda (pop?) that's an increase in the price of $0.18. To make the math easy let's say a 12 ounce soda costs $0.50 ($3.00 a six pack?) before the tax. An $0.18 increase in the price is a 36% increase in the price. That's pretty big.

How much does the quantity demanded react. If grocery stores are to be believed, the quantity demanded fell between 30% and 50% in reaction to the tax increase. That means the elasticity of demand is between 0.83 (30/36) and 1.39 (50/36).

So it looks like demand is slightly inelastic to elastic.

Now we can ask question like:

- If the goal is to raise tax revenues, will an increase in the tax increase, or decrease tax revenues?
- Tax revenues will increase if demand is inelastic and decrease if demand is elastic.

- If the goal is to decrease sugar consumption, how effective will an increase in the sugar tax be?
- It looks like consumers might be price sensitive, so an increase in the tax might be pretty effective at reducing sugary drink consumption

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