Friday, August 07, 2009

An Answer to the Exam Question I Should Have Asked

Former student Michael Duch provides the following answer to the question I posed:

The demand for water is inelastic! The fact that total revenue rose after the price increase implies that the percent change in price > percent change in demand, which gives us an elasticity ratio less than 1.

And the price increases should have been enacted first because they would have reduced the amount of water used while allowing people to maximize their utility. If this failed, which, it probably would have (assuming I'm right about the inelasticity of water) restrictions should have been imposed. I think the conservation of water in a drought takes precedence over allowing someone to maximize utility. But that's just me.
Some comments: Michael is correct in his conclusion that the own-price elasticity of demand for water must be less than one, and his reasoning is correct, too. Own-price elasticity of demand is:

Absolute value ( (percent change in quantity demanded)/(percent change in price) )

...and total revenue is simply Price * Quantity. If price goes up, quantity must go down (that's the Law of Demand), but what if revenue still rises? Then the increase in the price outweighs the decrease in quantity. In terms of elasticity, the denominator must be larger than the numerator, meaning own-price elasticity of demand is between zero and one--which we call inelastic. Good job, Michael!

Regarding the second paragraph, I agree that it would be better to raise the price first, but I would like to elaborate on why that is a good idea. Raising the price allows people to adjust in a variety of ways. For example, someone who has fruit trees in their yard might be willing to pay extra in order to make sure that the trees bear fruit, whereas a simple watering ban doesn't allow that option. Other people might decide it's better to just forgo watering altogether, or to collect rainwater, or take other actions. A price increase allows this variety of responses, while still achieving a given reduction in use.

Watering bans are usually riddled with exceptions for car washes and golf courses; there is no economic justification for this. If the water to be used at a car wash is too valuable for that use, then it shouldn't be used. The car wash, faced with an increase in water costs, will try to pass that cost increase to customers in the form of higher prices. If customers are unwilling to pay it, they won't, and the car wash will shut down. This is exactly what we should want to happen. We should want low-valued uses of water to stop, and allow only high-value uses of water to persist. Simple restrictions on use can't achieve this, but a price increase can.