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Price Discrimination September 28, 2015

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Elasticity and Demand March 18, 2015

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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.

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.

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.

Opportunities and What They Cost December 23, 2011

Posted by tomflesher in Finance, Micro, Teaching.
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One of the fundamental concepts in economics is that of opportunity cost. In order to understand opportunity cost, though, we need to take a step back and think about costs in a more general way.

The standard example goes like this: I like books, so I want to turn my passion into a job and open a bookstore. To do so, I need to rent a storefront and buy some inventory; for now, I’m going to run the bookstore myself. I’ll be open eight hours a day, so I’ll quit my current job at the box factory and do the bookstore job instead. Easy peasy, right? I even have $100,000 in the bank to get myself started.

Let’s look at the costs. The first thing to consider is the actual money I’m laying down to run this business. Say rent is $1,000 per month. If I don’t want to bother with discounting – and for now, I don’t – then that means I’ve spent $1,000 x 12 = $12,000 on rent this year. Then, imagine that in order to meet demand and still have a decent inventory, I need to spend $43,000 on books. That brings me up to $55,000 worth of cash that I’m laying out – my explicit costs, otherwise known as accounting costs, are $55,000.

But accounting costs don’t show that I had to give up my job at the box factory to do this, and I could have made $45,000. They also don’t account for the interest income I’m giving up by pulling my money out of the bank to live on it. Even if interest rates are only 1.25 APR (that’s annual percentage rate), I’m losing $1,250 in interest income. So, for simplicity (I don’t want to bother with compounding, either), let’s assume that in January I take out this year’s $45,000 in salary and keep it under my mattress. I buy my inventory and pay my rent. I’ve given up $1,250 in interest income and $45,000 in salary, so even though I haven’t laid out that cash, I have to count it as a cost. Accountants won’t write down what I gave up on a balance sheet, but my implicit costs, or opportunity costs, are $46,250.

Total costs are simple – just add implicit and explicit costs. My total costs for starting the business are $55,000 + $46,250 = $101,250.

The key to understanding opportunity cost is that it’s a measure of what you gave up to make a choice, and so it shows how much something is worth to you. If I offer you a free Pepsi, your opportunity cost is zero, so you might as well take it. If I offer you a Pepsi for your Dr. Pepper, we can infer two things:

  1. I value Dr. Pepper at least as much as Pepsi, and
  2. I can figure out how much you value Dr. Pepper, relatively, based on your decision. If you accept, then you must value Pepsi at least as much as Dr. Pepper; if not, you must value Dr. Pepper more (and would thus be rational, since Dr. Pepper is superior to Pepsi).

Opportunity cost is very useful for determining preferences. We’ll talk about that a little more later on. In the meantime, just remember this distinction:

  • Explicit costs are things you paid money for
  • Opportunity costs are how much you’d value your best alternative
  • Total costs are the sum of explicit and opportunity costs.