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Elasticity and Demand March 18, 2015

Posted by tomflesher in Micro, Teaching.
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The price-elasticity of demand measures how sensitive consumers are to changes in price. There are two primary formulas for that. Most commonly, introductory courses will use \frac{\% \Delta Q^D}{\% \Delta P}, where \% \Delta means the percentage change. This means the numerator is \frac{\Delta Q^D}{Q_0}, where Q_0 is the original quantity demanded and \Delta Q^D is the change in quantity demanded. The denominator is \frac{\Delta P}{P_o}. Through the properties of fractions, that ratio is equal to \frac{\Delta Q^D}{\Delta P} \times \frac{P_0}{Q_o}, and a lot of students find that formula much easier to use.

A graph of demand and price-elasticity of demand

A graph of demand and price-elasticity of demand

Take note of the shape of that formula, and keep in mind the Law of Demand, which states that as price increases, quantity demanded decreases. At high prices, quantities are relatively low, meaning that a small change in price yields a relatively big change in quantity demanded. If the percentage change in quantity demanded is bigger than the percentage change in price, then demand is elastic and consumers are price-sensitive. On the other hand, at low prices, quantities are relatively high, meaning that a small change in price yields an even smaller change in quantity demanded. That means demand is inelastic.

This pattern of high prices corresponding to elastic demand and low prices corresponding to inelastic demand holds for most goods. At a very high price, firms can make a small change in price to try to encourage new buyers to buy their product, whereas at a very low price, firms can jiggle the price up a little bit to try to snap up some extra revenue without dissuading most of their buyers from purchasing the product.

A slightly more accurate formula for price-elasticity of demand is \frac{dQ}{dP} \times \frac{P}{Q}, which looks surprisingly like the previous formula but doesn’t depend on choosing an original value.

The graph in this post shows market demand Q^D = 1000 - P in blue and elasticity in orange. Note the high elasticity at high prices and low elasticity at low prices.

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Elasticity (SPROING~!) March 17, 2015

Posted by tomflesher in Micro.
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When we think about elasticity in the real world, we often think about the properties of things like rubber bands or the waists of sweatpants. If a solid has high elasticity, that means it’s very sensitive to having forces applied to it – so while something like Silly Putty or latex is very elastic, other materials like steel or titanium are not. A small amount of force yields a lot of deformation for Silly Putty, but not much at all for steel.

Elasticity in economics works the same way. It measures how responsive one measurement is to a small change in some other measurement.

When economists say “elasticity” without any qualifiers, they typically mean the price-elasticity of demand, which measures how sensitive purchases are to small changes in price. Elasticity, \epsilon, is expressed as a ratio:

\epsilon = \frac{\% \Delta Q^D}{\% \Delta P}

where \% \Delta Q^D refers to the percentage change in quantity demanded1 (the actual change divided by the starting value) and \% \Delta P refers to the percentage change in price (again, the actual change in price divided by the starting value).2 This leads to three cases:

  1. \% \Delta Q^D > \% \Delta P – a small price change yields a big change in quantity demanded. This means that buyers of the good are price sensitive, and (equivalently) demand for the good is elastic. Note that in this case, \epsilon > 1.
  2. \% \Delta Q^D < \% \Delta P – a small price change yields an even smaller change in quantity demanded. This means that buyers of the good are not price sensitive, and demand for the good is inelastic. Here, \epsilon < 1.
  3. \% \Delta Q^D = \% \Delta P – a small price change yields exactly the same change in quantity demanded. The term for this type of demand is unit-elastic. When demand is unit-elastic, \epsilon = 1.

It’s tempting to treat elasticity as very complicated, when it has a really simply mathematical interpretation. It answers the question “Which change is bigger – price, or quantity?”

Also interesting is the question of why some goods are demanded elastically and some are demanded inelastically. Typically, goods with many alternatives are demanded elastically. Alternatives can come in many forms. Most commonly, they’ll show up as substitute goods, or goods which you can use instead of another good. For example, bread has many substitutes (naan, grits, cornbread, rice, tortillas, English muffins….), and so if the price of bread rose significantly, you’d see many people substituting away from using bread. However, there are other forms of alternatives, too. You may see elastic demand for goods that cost a large proportion of the buyers’ income or that can be purchased over a longer timescale. A college education is an example of both of these – a small change in the level of tuition can lead to big changes in the behavior of students, who will often take a year off to earn money.

Anything with few alternatives will typically be demanded inelastically. Salt is the classic example, because it has no alternatives – it’s necessary for flavoring food, allowing our bodies to function properly, and (in the case of iodized salt) preventing certain illnesses. However, anything that is addictive (like tobacco or heroin), necessary for many uses (like cell phone plans), or difficult to switch away from (it’s not like you can put diesel fuel in your gas-engine car!) will typically have inelastic demand.

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1 Quantity demanded means the number of goods people are willing to buy at a certain price.
2 Usually one of these will be negative and the other positive, because of the Law of Demand; economists, ever economical with their notation, simply ignore this and use the absolute value.

Anecdote Alert: Do restaurant deposits depress attendance? January 1, 2015

Posted by tomflesher in Examples.
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Last night I spent New Year’s Eve at one of my favorite restaurants, Verace in Islip, New York. I actually did New Year’s Eve there last year, too, and there were three very interesting changes. The upshot is that the restaurant, though it had a fantastic menu, was significantly less full than it was last year, and the crowd skewed slightly older.

First, the price of the dinner was $65 last year and $85 this year. That corresponds to about a 30% price hike. That might deter some people, but I’m skeptical. The price-elasticity of demand for restaurant meals is about 2.3, or very elastic. (That means that if the price of a restaurant meal changes by 1%, the quantity of restaurant meals sold would drop about 2.3%.) If that’s the correct elasticity to apply here, that would explain a 69% drop in attendance, but I’m not so sure that restaurant meals on New Year’s are as elastic as restaurant meals during the rest of the year. The well-known Valentine’s Day Effect causes price elasticity for certain goods (cut roses) to drop on Valentine’s Day, and since a meal at home isn’t a close substitute for a restaurant meal on a special occasion, I’m skeptical that this price change would explain the precipitous drop in attendance.

Second, the restaurant required a deposit this year – $50 per person, returned at the beginning of the meal as a gift card. This was my first hypothesis, but I’m not sure it’s much of an explanation. For one thing, I put down my deposit on Monday, so there was no real loss of value. $50 per person to hold a spot is well within the income for most demographics that you see at Verace most nights [more on this in a moment], especially since it operated as a credit on the bill. No dice here, really.

Third, this might be the big one – Verace is part of the Bohlsen Restaurant Group, which operates a couple of restaurants at slightly different price points. This year, BRG made a big deal of advertising different, keyed experiences at their different restaurants. Specifically, Teller’s was a much more expensive steakhouse offering, Verace was a meal only, but Monsoon – their lower-priced, Asian fusion restaurant – had a modular menu with options of $75 for a meal (a bit cheaper than Verace, but not much) and $75 for an open bar. The open bar and Monsoon’s dance floor almost surely made it more attractive to younger revelers. That also explains the shift in demographics – Verace’s younger crowd may have been cannibalized by another BRG restaurant.

In the alternative, our waiter’s hypothesis: The manager did a great job seating people. “This guy,” says he, “is a magician.” He may be, but I’m more interested in seeing Monsoon’s numbers.