    Page Links Price elas. of demand       · Definition       · Determinants       · Excel Workbook Price elas. of supply Income elas. of demand Elas. and price controls

# Tutorial 4: Elasticity

In Tutorials 2 and 3 we saw that a decrease in the price of a good or service leads to an increase in the quantity of it demanded. But this "law of demand" reveals nothing of the size of the buyer's response to a price change. Similarly, although we also saw that price and the quantity supplied are directly related, we do not know the size of the seller's response to a price change. Finally, although we saw that an increase in income will increase the demand for normal goods, we have not discussed how to measure the size of the increase in demand.

In economics, the term elasticity is used to describe a measure of how responsive one variable is to a change in another. Specifically, elasticity measures the percentage change in the dependent variable in response to a one percent change in the independent variable. In the syntax of mathematics: In this tutorial we discover how to measure the size of the impact on quantity of a change in price and income, and explore the implications of price controls given differences in responsiveness.

## Price elasticity of demand Price elasticity of demand (Epd) measures how responsive the quantity demanded is to a change in product price. Similarly, wage elasticity of demand measures how responsive the the quantity of labor demanded is to a change in the wage rate. Mathematically:  The term ( ), measures the slope of the demand curve, and the term (P/Q) measures the price (P) and quantity (Q) values for a point on that demand curve. If we write the equation for demand as Q(P) = a + b*P, then

Epd = b*(P/Q) where b < 0.

Similarly, if we write the equation for demand in inverse form, P(Q) = (a/b) + (1/b)*Q, then

Epd = (1/b)*(P/Q) where b < 0.

These latter forms of the equation for price elasticity of demand are refered to as the point-slope formula. Because b < 0 (do you know why?), Epd < 0 as well. Many times, however, the minus sign is dropped for convenience.

## Determinants of price elasticity of demand So far we have learned two ways to calculate price elasticity of demand:

1. using numerical data, as the ratio of the percentage changes in Q and P;
2. using the known equation for demand (or inverse demand), as the product of the slope coefficient and the ratio of the price and quantity values for a point on that demand curve.

But what if we have neither the numerical data nor an equation describing demand? One can still get a feeling for how responsive buyers will be to a price change by remembering the four determinants of buyer responsiveness:

1. Proportion of income spent;
2. Availability of good substitutes;
3. Necessity (or luxury);
4. Time.

The greater the proportion of household income spent on an item, the more responsive buyers will be to a change in its price. Most durable goods, such as houses, cars, appliances, etc., are quite expensive (as a portion of household income). A 10% increase in the payments on a house is likely to leave buyers with a good deal less cash each month and, hence, demand will be rather price elastic. A 10% increase in the price of pop is likely to be nearly ignored by buyers, hence demand will be rather price inelastic.

The greater the avilability of substitutes for the good or service whose price has just increased, the greater the response of buyers. This is because if buyers can easily purchase a similar item (whose price has not risen) then they will. Soft drinks, cereals, clothing, etc., have many close substitutes. Thus demand tends to be rather price elastic for these goods. For services such as medical care, fewer substitutes are available, hence demand tends to be rather price inelastic.

Consumtion of goods and services that are considered a luxury can be easily reduced if the price rises. Hence demand tends to be more elastic for fur coats, luxury cars, extensive vacations, etc. Goods considered a necessity are so important that buyers tend to respond little to a price change. They do respond however, although demand tends to be price inelastic for such goods.

The amount of time one has to respond to a price change affects the size of that response. For most goods, in the short run, buyers tend to purchase nearly the same quantity as before a price change. So in the short run, demand tends to be price inelastic. But given time, buyers can alter their consumption behavior and look for hard to find substitutes. So in the long run, demand tends to be price elastic. Take an increase in the price of gasoline for example. If you do not learn about the price increase until you pull up to the pump (and you believe gas prices have increased at all gas stations) you will likely top off your tank as usual. But given time, you can find ways to drive your car shorter distances, buy a car that gets better gas mileage, or even move so that you live closer to where you work. So in the long run, you will be much more responsive to a price increase than you can be in the short run.

But this time response is not true for a class of goods known as durable goods (houses, automobiles, household appliances, TV's, computers, or capital equipment purchased by firms). Take cars for example. In the short run, buyers tend to be very responsive to an increase in the price of a new car. When the family car is only a few years old it is easy to postpone the purchase of a new one. But in the long run, as cars wear out, buyers become less responsive to the price increase. In fact, short run price elasticity of demand for new cars has been estimated to be -1.2 one year after a price change, but -0.42 ten years after that price change1.

 Now it's time to "do the thing". Click on the following link to download the Price Elasticity Workbook. Work through General Questions 1 - 6 and Excel Question 10 to improve your understanding of price elasticity of demand. Return here when you have finished. Need help downloading the Excel file?

Now we take a close look at price elasticity of supply...

1 Pindyck and Rubinfeld, Microeconomics, 4th edition, 1998, Table 2.2, p. 40.

 Copyright © 1996-2002 Mark S. Walbert, Illinois State University. Original graphics © FTSS. URL: http://www.ilstu.edu/~mswalber/ECO240/ Revised: 19-Aug-2002