No Such Thing as a Free Lunch: Principles of Economics (Part 22)

Economics is not an exact science. It's a combination of an art and elements of science. And that's almost the first and last lesson to be learned about economics: that in my judgment, we are not converging toward exactitude, but we're improving our data bases and our ways of reasoning about them.

Paul Samuelson

Demand and Supply Applications and Elasticity

(Part E) 

by

Charles Lamson

Elasticity

The principles of supply and demand enable us to make certain predictions about how households and firms are likely to behave in both national and international markets. When the price of a good rises, for example, households are likely to purchase less of it and firms are likely to supply more of it. When costs of production fall, firms are likely to supply more---supply will increase, or shift to the right. When the price of a good falls, households are likely to buy fewer substitutes---demand for substitutes is likely to decrease, or shift to the left.

The size, or magnitude, of these reactions can be very important. You have already seen in Part 18 of this analysis that during the oil embargo of the early 1970s, OPEC succeeded in increasing the price of crude oil substantially. Because this strategy raised revenues to the oil-producing countries, we might expect this strategy to work for everyone. If the banana exporting countries (OBEC), had done the same thing, the strategy would not have worked.

Why? Suppose the OBEC decides to cut production by 30 percent to drive up the world price of bananas. At first, when the quantity of bananas supplied declines, the quantity demanded is greater than the quantity supplied, and the world price rises. The issue for OBEC, however, is how much the world price will rise. That is, how much will people be willing to pay to continue consuming the bananas? Unless the percentage increase in price is greater than the percentage decrease in output, the OBEC countries will lose revenues. A little research shows us that the news is not good for OBEC. There are many reasonable substitutes for bananas. As the price of bananas rises, people simply eat fewer bananas and eat more pineapples or oranges. Many people are simply not willing to pay a higher price for bananas. the quantity of bananas demanded declines 30 percent---to the new quantity supplied---after only a modest price rise, and OBEC fails in its mission; its revenues decrease instead of increase.

The quantity of oil demanded is not nearly as responsive to a change in price because no substitutes for oil are readily available. When the price of crude oil went up in the early 1970s, 130 million motor vehicles, getting an average of 12 miles per gallon and consuming over 100 billion gallons of gasoline each year, were on the road in the United States. Millions of homes were heated with oil, and industry ran on equipment that used petroleum products. When OPEC cut production, the price of oil rose sharply. quantity demanded fell somewhat, but price increased over 400 percent (Case & Fair, p. 85). What makes the cases of OPEC and OBEC difference is the magnitude of the response in the quantity demanded to a change of price.

The importance of actual measurement cannot be overstated. Without the ability to measure and predict how much people are likely to respond to economic changes, all the economic theory in the world would be of little help to policy makers. In fact, most of the data that measure behavior research being done in economics today involves the collection and analysis of quantitative data that measure behavior. This is a dramatic change in the discipline of economics that has taken place in the last 45 years.

Economists commonly measure responsiveness using the concept of elasticity. Elasticity is a general concept that can be used to quantify the response in one variable when another variable changes. If some variable A changes in response to changes in another variable B, the elasticity of A with respect to B is equal to the percentage change in A divided by the percentage change in B:

We may speak of the elasticity of demand or supply with respect to price, of the elasticity of investment with respect to the interest rate, or of the elasticity of tax payments with respect to income. We begin with a discussion of price elasticity of demand.

Price Elasticity of Demand

Slope and Elasticity The slope of a demand curve may in a rough way reveal the responsiveness of the quantity demanded to price changes, but slope can be quite misleading. In fact, it is not a good formal measure of responsiveness.

Consider the two identical demand curves in Figure 10. The only difference between the two is that quantity demanded is measured in pounds and the graph on the left and in ounces in the graph on the right. When we calculate the numerical value of each slope, however, we get very different answers. The curve on the left has a slope -1/5, and the curve on the right has a slope of -1/80, yet the two curves represent the exact same behavior. If we had changed the dollars to cents on the Y-axis, the two slopes would be -20 and -1.25, respectively.

The problem is that the numerical value of slope depends on the units used to measure the variables on the axes. To correct this problem you must convert the changes in price and quantity to percentages. The price increase in Figure 10 leads to a decline of 5 pounds, or 80 ounces, in the quantity of steak demanded---a decline of 50 percent from the initial 10 pounds, or 160 ounces, whether we measure the steak in pounds or ounces.

Where to find price elasticity of demand simply as the ratio of the percentage of change in quantity demanded to the percentage change in price.

Percentage changes should always carry the sign (plus or minus) of the change. Positive changes or increases, take a (+). Negative changes, or decreases, take a (-). The law of demand implies that price elasticity of demand is nearly always are negative number: Price increases (+) will lead to decreases in quantity demanded (-) , and vice versa. Thus, the numerator and denominator should have opposite signs, resulting in a negative ratio.

Types of Elasticity Table 1 gives the hypothetical responses of demanders to a 10 percent price increase in four markets. Insulin is absolutely necessary to an insulin-dependent diabetic, and the quantity demanded is unlikely to respond to an increase in price. When the quantity demanded does not respond at all to a price change, the percentage of change in quantity demanded is zero, and the elasticity is zero. In this case, we say that the demand for the product is perfectly inelastic. Figure 11(a) illustrates the perfectly inelastic demand for insulin. Because quantity demanded does not change at all when price changes, the demand curve is simply a vertical line.

Unlike insulin, basic telephone service is generally considered a necessity, but not an absolute necessity. If a 10 percent increase in telephone rates results in a 1 percent decline in the quantity of service demanded, demand elasticity is (-1/10) = -0.1.

When the percentage change in quantity demanded is smaller in absolute size than the percentage change in price, as is the case with telephone service, then elasticity is less than 1 in absolute size. When a product has an elasticity between 0 and -1, we say that demand is inelastic. The demand for basic telephone service is inelastic at -0.1 stated simply, inelastic demand means that there is some responsiveness of demand, but not a great deal, to a change in price.

A warning: you must be very careful about signs. Because it is generally understood that demand elasticities are negative (demand curves have a negative slope), they are often reported and discussed without the negative sign. For example, a technical paper might report that the demand for housing "appears to be inelastic with respect to price, or less than 1 (.6)." What the writer means is that the estimated elasticity is -0.6, which is between 0 and -1. Its absolute value is less than 1.

Returning to table one, we see that a 10 percent increase in beef prices drives down the quantity of beef demanded by 10 percent. Demand elasticity is thus (-10 divided by 10) = -1. When the percentage change in quantity of product demanded is the same as the percentage change in price in absolute value, we say that demand for the product has unitary elasticity. The elasticity is minus one (-1). As Table 1 shows, the demand for beef has unitary elasticity.

When the percentage decrease in quantity demanded is larger than the percentage increase in price and absolute size, we say that demand is elastic. The demand for bananas, for example, is likely to be quite elastic because there are many substitutes for bananas, other fruits, for instance. If a 10 percent increase in the price of bananas leads to a 30 percent decrease in the quantity of bananas demanded, the price elasticity of demand for bananas is (-30/10) equals -3. When the absolute value of elasticity exceeds one, demand is elastic.

Finally, if a small increase in the price of a product causes the quantity demanded to drop Immediately to zero, demand for that product is said to be perfectly elastic. Suppose, for example, that you produce a product that can be sold only at a predetermined, fixed price. If you charged even one penny more, no one would buy your product because people would simply buy from another producer who had not raised the price. This is very close to reality for farmers, who cannot charge more than the current market price for their crops.

A perfect elastic demand curve is Illustrated in Figure 11(b). Because the quantity demanded drops to zero above a certain price, the demand curve for such a good is a horizontal line. 

*MAIN SOURCE: CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 84-87*

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