What happens to the elasticity of demand as we move down to the right along a straight line demand curve?

What happens to the price elasticity of demand when we travel along the demand curve? The answer depends on the nature of the demand curve itself. On a linear demand curve, such as the one in Figure 5.2, elasticity becomes smaller (in absolute value) as we travel downward and to the right.

Figure 5.2 Price Elasticities of Demand for a Linear Demand Curve

The price elasticity of demand varies between different pairs of points along a linear demand curve. The lower the price and the greater the quantity demanded, the lower the absolute value of the price elasticity of demand.

Figure 5.2 shows the same demand curve we saw in Figure 5.1. We have already calculated the priceelasticity of demand between points A and B; it equals −3.00. Notice, however, that when we use thesame method to compute the price elasticity of demand between other sets of points, our answer varies.For each of the pairs of points shown, the changes in price and quantity demanded are the same (a$0.10 decrease in price and 20,000 additional rides per day, respectively). But at the high prices and lowquantities on the upper part of the demand curve, the percentage change in quantity is relatively large,whereas the percentage change in price is relatively small. The absolute value of the price elasticity of demand is thus relatively large. As we move down the demand curve, equal changes in quantity represent smaller and smaller percentage changes, whereas equal changes in price represent larger and larger percentage changes, and the absolute value of the elasticity measure declines. Between points C and D,for example, the price elasticity of demand is −1.00, and between points E and F the price elasticity of demand is −0.33.

On a linear demand curve, the price elasticity of demand varies depending on the interval over which we are measuring it. For any linear demand curve, the absolute value of the price elasticity of demand will fall as we move down and to the right along the curve.

The Price Elasticity of Demand and Changes in Total Revenue

Suppose the public transit authority is considering raising fares. Will its total revenues go up or down? Total revenue is the price per unit times the number of units sold. In this case, it is the fare timesthe number of riders. The transit authority will certainly want to know whether a price increase willcause its total revenue to rise or fall. In fact, determining the impact of a price change on total revenueis crucial to the analysis of many problems in economics.

We will do two quick calculations before generalizing the principle involved. Given the demandcurve shown in Figure 5.2, we see that at a price of $0.80, the transit authority will sell 40,000 rides per day. Total revenue would be $32,000 per day ($0.80 times 40,000). If the price were lowered by $0.10 to $0.70, quantity demanded would increase to 60,000 rides and total revenue would increase to $42,000($0.70 times 60,000). The reduction in fare increases total revenue. However, if the initial price hadbeen $0.30 and the transit authority reduced it by $0.10 to $0.20, total revenue would decrease from$42,000 ($0.30 times 140,000) to $32,000 ($0.20 times 160,000). So it appears that the impact of a pricechange on total revenue depends on the initial price and, by implication, the original elasticity. Wegeneralize this point in the remainder of this section.

The problem in assessing the impact of a price change on total revenue of a good or service is thata change in price always changes the quantity demanded in the opposite direction. An increase in price reduces the quantity demanded, and a reduction in price increases the quantity demanded. The question is how much. Because total revenue is found by multiplying the price per unit times the quantity demanded, it is not clear whether a change in price will cause total revenue to rise or fall.

We have already made this point in the context of the transit authority. Consider the following three examples of price increases for gasoline, pizza, and diet cola.

Suppose that 1,000 gallons of gasoline per day are demanded at a price of $4.00 per gallon. Totalrevenue for gasoline thus equals $4,000 per day (=1,000 gallons per day times $4.00 per gallon). If an increase in the price of gasoline to $4.25 reduces the quantity demanded to 950 gallons per day, totalrevenue rises to $4,037.50 per day (=950 gallons per day times $4.25 per gallon). Even though people consume less gasoline at $4.25 than at $4.00, total revenue rises because the higher price more than makes up for the drop in consumption.

Next consider pizza. Suppose 1,000 pizzas per week are demanded at a price of $9 per pizza. Totalrevenue for pizza equals $9,000 per week (=1,000 pizzas per week times $9 per pizza). If an increase in the price of pizza to $10 per pizza reduces quantity demanded to 900 pizzas per week, total revenue willstill be $9,000 per week (=900 pizzas per week times $10 per pizza). Again, when price goes up, consumers buy less, but this time there is no change in total revenue.

Now consider diet cola. Suppose 1,000 cans of diet cola per day are demanded at a price of $0.50 per can. Total revenue for diet cola equals $500 per day (=1,000 cans per day times $0.50 per can). If an increase in the price of diet cola to $0.55 per can reduces quantity demanded to 880 cans per month, total revenue for diet cola falls to $484 per day (=880 cans per day times $0.55 per can). As in the case of gasoline, people will buy less diet cola when the price rises from $0.50 to $0.55, but in this example total revenue drops. In our first example, an increase in price increased total revenue. In the second, a price increase left total revenue unchanged. In the third example, the price rise reduced total revenue. Is there a way to predict how a price change will affect total revenue? There is; the effect depends on the price elasticity of demand.

The price elasticity of a product describes how sensitive suppliers and buyers are to changes in price. It doesn't change in relation to supply and demand, but it defines the slope of each curve.

A product with high price elasticity of demand will see demand fall sharply when prices rise. For the product with high elasticity of demand, the downward-sloping demand curve appears flatter, and for every change in price, there is a large change to the quantity demanded. A demand curve for a product with low elasticity appears to be steeper, because the quantity demanded doesn't change much, even if prices do. Products with low price elasticity are described as being inelastic.

Products with high price elasticity are generally non-staple goods. For example, the demand for teeth-whitening kits may be highly dependent on price and thus fairly elastic. The demand for toothpaste, on the other hand, might be relatively inelastic regardless of whether the price changes. A key factor affecting demand elasticity includes the availability of substitute goods, or goods that are very close to the product in question.

The amount of time available to ponder different options and the type of good also matter; a consumer might drive around shopping for the best deal on items that consistently take large portions of a budget, such as groceries, while ignoring price differentials for small and relatively infrequent purchases, such as shoe polish.

Similarly, a product with high price elasticity of supply has a flatter, upward-sloping curve. A product with a low elasticity of supply has a steeper curve. Price elasticity of supply can be calculated by dividing the percentage change in supply by the percentage change in price. The same factors that affect the elasticity of demand affect supply elasticity, namely the availability of substitute inputs and the time needed to make changes to production. (For related reading, see "How Does Price Elasticity Affect Supply?")

ANSWER

The price elasticity of demand will decrease down the demand curve. When moving from left to right, down the demand curve, the price elasticity of demand changes from being elastic to inelastic.

Explanation

Price elasticity of demand varies between different pairs of points down along a linear demand curve; it diminishes in absolute value down the curve. This is because, as the consumer moves down the curve, equal changes in quantity demanded represent smaller and smaller percentage changes, yet equal changes in price will represent larger and larger percentage changes. As a result, the absute value of the price elasticity of demand falls.

Thus, at the upper portion of the demand curve (leftwards), demand is price elastic. This is because the higher the price and the lower the quantity demanded, the larger the absolute value of the price elasticity of demand since the percentage change in quantity demanded exceeds the percentage change in price. On the middle portion of the demand curve, elasticity becomes unitary. On the lower portion of the curve (rightwards), price is lower and quantity demanded larger and the absolute value of demand elasticity is relatively smaller (inelastic) for the percentage change in quantity demanded is smaller than the percentage in price.