10

Ch9 MoreDem9/27/2012

©Armen Alchian 1999

Chapter 9

MORE FEATURES OF DEMAND

You can be sure of the first law of demand: a sufficiently higher price will decrease the quantity demanded, and a sufficiently lower price will increase the quantity demanded. But, price is only one thing that can affect the quantity demanded. Income affects the demand at each price. With greater incomes, the demand at each price is likely to be larger. Age, gender, education, and health, to name a few things, affect the demand at each price. Why, when so many other factors affect the demand, do we concentrate so much on price? After answering that question, this chapter explains some measures of the responsiveness of quantity demanded to changes in the price.

Why So Much Attention to Price?

The question should really be, “Why so much attention to price adjustments? Price adjustments make the aggregate quantity demanded equal the aggregate available supply of a good in a peaceful, non-wasteful way, as we will illustrate later. Certainly, our tastes, preferences or total personal worths don't change to make us desire to have only as much of a good as our income allows. We’ll see how prices change so as to reconcile conflicts of interest for available goods. Later we’ll examine how prices direct production from the less highly to the more highly demanded goods. Still later we’ll look at how prices affect your earnings and the kind of work you will be doing.

It is easy to look around you and see that prices are the common attribute in the vast majority of exchanges, so a few observations about the obvious will help you understand why that is so. For any person, the amount of a particular good they want clearly depends on lots of different factors: the price of the good, the prices of other goods, their wealth and income, etc. Their age, sex, geographic location, also play roles as does their knowledge of the good and their expectations of how that good will affect them if they acquire it. For different people, the list of factors and impacts of each factor will vary…sometimes by a lot! Regardless, the list could go on and on. But, to see the importance of prices of goods in exchange, let’s consider a few examples of those other factors. As one’s wealth increases, the effect on how much is wanted varies not just in magnitude (as does price), but in direction (unlike price) from person to person and good to good. For many goods, consumers generally consume more as their wealth increases, but there are other goods where a significant number of people will consume less as their wealth and income increase. An example for many (though not all!) is boxed macaroni and cheese. As most people become wealthier, they will purchase more higher quality (to you) meals of steak, shrimp, and lobster and eat less macaroni and cheese (at least of the boxed variety). Your desires for specific goods change as you age. You desire more of some goods and less of others. Moving from Minnesota to Miami, Florida will change your demand for snow boots in an opposite direction to someone who is moving the other way. Males buy some different things than females. The effect of a price change of another good depends on whether the two goods are substitutes or complements in consumption (think of Coke and Pepsi versus gasoline and automobiles). Notice that as any of the factors change – other than the price of the good itself – the amount of the good desired may increase, decrease, or stay the same. There is no universal relationship that fits all goods under all circumstances for all people EXCEPT for adjustments in the price of the good. As a consequence, we observe, for example, that different stores cater to different specific demographic characteristics like age, sex, wealth, religion, tastes, etc., but they all operate under the common knowledge that if they increase their prices, they will sell less, and if they lower their prices they will sell more.

Some Changes in Money Prices and Relative Prices

College tuitions have risen in the past 30 years far more than the average, while prices of television, computers, and travel have fallen. Air travel has become cheaper by almost a half relative to other goods and other forms of transportation 30 years ago. These changes in relative prices are results of events that changed the demand or supply of a good relative to the demand and supply of other goods. Of course, almost all goods have changed in quality, but adjusting dollar prices for improvements in quality are difficult to quantify. So the changes in relative prices may reflect relative changes in qualities of goods.

Which Demand?

When looking at "demand", we must distinguish between three demands. (1) There is the demand by one individual person for a good. (2) Another demand is the aggregated demand by all consumers for good, say wheat, from all suppliers. It’s called the market demand. (3) A third demand is the demand a seller sees when offering that good to people in general. This is called the “demand facing a seller.” This one contains your individual demand and the demand by all the other customers of that seller. If we look at the relationship between (2) and (3), you should see that the market demand is the aggregated quantities demanded by everyone from all sellers rather than from a particular selle. It is also clear that (1), the individual’s demand, is the basis for the others.

The Responsiveness of Demanded Quantity to a Change in Price

For all these demands, there are measures of the responsiveness of the quantity demanded to a change in price. This measure of responsiveness is called the "elasticity of demand with respect to the price". We'll explain it first, and then we'll show for what it's useful.

When a seller thinks about the effect changing the price, say cutting the price, the seller expects an increase in the amount demanded by customers. Those increased sales will bring in more sales revenue. But at the same time, the cut in price will reduce what would otherwise have been received on the number of units formerly sold at the old higher price. This loss is often called "market spoilage." Which dominates?...(a) the added sales revenue from the additional units sold at the lower price? Or, (b) the "market spoilage”, the lost revenue on former sales at the higher price? We can state here without proof that there's an easy rule: There's an easy arithmetic summary-type measure of this net effect on quantity sold and hence on the sales revenue. It's called the "elasticity" of demand." It's the ratio of the percentage increase in the amount demanded relative to the price cut, also expressed as a percentage. If the percentage increase in quantity demanded is greater than the percentage decrease in the price, the increase in quantity dominates the decrease in price and the revenue to the seller will increase. But, if the percentage increase in quantity demanded is less than the percentage decrease in the price, the decrease in the price dominates the increase in quantity demanded and the revenue to the seller will decrease. You can use the same thinking process to figure out whether seller’s revenue would increase or decrease when the price is raised.

One easy way of thinking about this is to remember that Total (seller’s) Revenue, TR, is the product of Price (P) and Quantity (Q). In other words, TR = P∙Q. But, we also know that as P increases, Q falls and vice versa. P and Q change in opposite directions. So, if we add up and down arrows to indicate the direction of change and note the relative magnitude of the change with the length of the arrow, for an increase in the price, either (a) P↑ ∙ Q↓ or (b) P↑ ∙ Q↓ will occur. In (a), TR will ↑, while in (b), TR will ↓ with the increase in price. Study Table 1 to make sure you understand this relationship. Understanding this simple relationship will help you avoid making stupid assertions from here on out. You will never again say, “Sellers are always better off by increasing prices.” Or, our favorite, “They can charge any price they want!” (when it is meant to imply that a seller or producer can increase price without limit). Though seller’s costs are also affected by a change in quantity sold, as we shall see, sellers clearly will not be better off if increasing price causes their revenue to fall by more than they save in costs!

Causal Change / Price Direction and Relative Magnitude / Resulting Change in Quantity Demanded / Effect on Seller’s Total Revenue
Increase in Price / P↑ / Q↓ / TR↑
P↑ / Q↓ / TR↓
Decrease in Price / P↓ / Q↑ / TR↓
P↓ / Q↑ / TR↑

Table 1: The relationship between relative changes in price, the resulting relative changes in quantity demanded, and the effect on the seller’s total revenue.

Relative Price Changes Are What Matter!

We stated that it is relative prices that matter rather than the absolute money price. And, again, we emphasize that when it comes to price changes, it is the relative price change that matters. One might ask, “Relative to what?” If a price changes, the change is relative to the price that prevailed before the change. To see the importance of relative price changes consider an absolute price decrease of $1. A seller surely knows that a $1 cut in price from a $10 price down to a price of $9 is a lot more important than a $1 price cut from $100 to $99 -- though each is the same $1 decrease. The first (a price cut from $10 to $9) is a cut of 10% (=$10-$9$10), whereas, the second (a price cut of the same $1 from $100 to $99) is a relatively trivial 1% cut (=$100-$99$100). The same consideration about relative (or percentage) changes applies also to the associated quantities demanded. If quantity demanded increased by 5 units, from 20 units to 25 units, it is a 25% increase. That would be a greater relative increase than if the initial quantity were 100 and increased to 105, only a 5% increase. Certainly, it’s the changes in relative quantity demanded compared to the relative price change that is pertinent, if we are interested in the "total dollar sales revenue" received by the seller.

An example provides an easy explanation.

Suppose the seller is considering a price decrease from $10 to $9. As explained above this is a 10% cut in price. Also, suppose the seller expects quantity demanded (sold) to increase from 100 to 120, a 20% increase in units sold. Quick arithmetic tells us that if this seller’s expectations are correct, sales revenue will increase from $1000 (= $10 × 100) before the price decrease, to $1080 (= $9 × 120) after the price drop. Notice, in the symbols we developed above, P↓ × Q↑ è TR↑. Now, suppose that there is another seller who is considering the same exact price cut from $10 to $9, and this seller also expects the increase in quantity demanded (and sold) to increase by 20 units, only this increase is from 1000 to 1020…a 2% increase. If this seller follows through with the price cut, revenue will fall from $10,000 (=$10 × 1000) to $9,180 (=$9 × 1020)! The absolute changes in quantity demanded were the same (20 units) in these two examples, but the relative changes were dramatically different…and changed revenue in a completely different way. Verify that , P↓ × Q↑ è TR↓ is exactly what occurred in the second situation. We said earlier that the up and down arrows indicate magnitude of relative change. Now you should understand why!

Calculating Percent Changes

We hope that you were able to follow our numerical examples since we picked numbers that (hopefully) were intuitively obvious. But, not all price and quantity relative changes will be as easy to quickly calculate. So, we offer a (very) brief refresher on how to calculate a percentage (or relative) change. If P0 is the initial price and P1 is the new price, the change in price is P0 – P1. We will call that ∆P (where ∆ is the Greek letter “delta”…and is the mathematical symbol to denote “change in”). Note that ∆P is the absolute change. (Also, for convenience sake, we will not worry about whether ∆P is positive or negative, so we will use the absolute value of ∆P if it turns out to be negative. In our symbols, the direction of the arrows tells us whether the change represents an increase or a decrease.) We are interested in the relative or percentage change, so we compare the change as a proportion of the initial price. Mathematically,

The percentage change in price =%∆P=∆PP0

The result from calculating this ratio usually will be a decimal fraction, e.g., when the price falls from $10 to $8, the above ration would equal 0.2. The word “percent” is derived from Latin and means “out of 100” (look it up on Wikipedia!) 0.2 is the same as 0.20, which you learned to read as 20 one-hundredths—or 20%. The easy way to convert from decimal fractions to percentages is to perform the division in the equation above and move the decimal point in the answer to the right by two digits. Thus if the decimal fraction is 0.4673, it is the same as 46.73%.

[Note: Dr. Harris’s students can check their understanding by going to the course page and downloading the “Calculating Percentage Changes” Excel file. It is a tutorial and has exercises you can use to check to make sure you are “up to snuff” on your arithmetic abilities. While it is the concepts that are important, you will struggle with them if you do not understand the basic arithmetic employed. If you are reading this online, follow this direct link to the Excel file: http://www.msubillings.edu/BusinessFaculty/Harris/Percentage%20Changes.xls .]

The Elasticity of Demand

The basic concept of responsiveness is defined and measured with what economists call the “elasticity of demand.” It's measured as the ratio of (a) the percentage change in the quantity demanded in response to (b) a percentage change in price. Again, we emphasize that the elasticity is the ratio of the percentage changes, not the ratio of the absolute changes.