Unit 4 - Elasticity


An understanding of demand and supply gives us the fundamentals of how markets operate - the determination of prices and output in the product market for example. However, responses of output to a change in the price of the good are not uniform across goods.

In analyzing the consumer's demand curve for a good, we have shown that as the price of the good rises, our quantity demand for that good decreases. How much, if at all, our quantity demanded of a good falls when the good's price rises, depends on the nature of the good. There are some goods that we are reluctant or unable to sacrifice consumption when the price rises. Other goods have an abundance of equivalent or nearly equal substitutes that we gracefully shift our consumption towards when the price of the good rises. The responsiveness of quantity demanded to a change in a good's price is known as the elasticity of demand. In this section we will explore the concept of elasticity as it relates to the demand and supply curves, to incomes and to the prices of related goods.

The Price Elasticity of Demand

We begin our discussion of elasticity with the price elasticity of demand. The price elasticity of demand measures the responsiveness of the quantity demand of a good when the price of that same good changes. We calculate the elasticity of demand by measuring the percentage change in the quantity demand over the percentage change in price of that good (% change in Qd / % change in price). In general, if the quantity demanded of a good is very responsive to a change in the good's price, the good is considered to be elastic. In simpler terms, this implies if we raise the price of an elastic good, there is a significant reduction in the consumption of that good, and vise versa for a price decrease (1).

(1) Be sure to recognize that when we speak of the price elasticity of demand for a good, we are referring to the change in the quantity demand of the good when the price of the same good changes. Later we will look at the cross-price elasticity of demand which examines the change in the demand for a good when the price of another good changes.

In contrast to a product where the quantity demanded of the good is very responsive to a change in the product's price, is an inelastic good. Goods that are inelastic, show little response in the quantity demanded to a change in price. Inelastic goods tend to be necessities and those that have few available substitutes in the short-run. An increase in the price of an inelastic good offers little opportunity for substitution in consumption, resulting in a minimal change in the quantity demanded. For price decreases, there is little additional consumption of inelastic goods. This yields the logical conclusion that producers will have no incentive to drop prices for inelastic goods unless market conditions dictate they do so.

So far we have discussed some general relationships between elasticity and the response in the quantity demand when there is a change in the price of a product. Now let us be more explicit:

Let us take a graphical look at several demand curves. We begin with a relatively elastic demand curve as shown in Figure 4-1. This graph shows the demand curve for a good with a number of close substitutes in consumption such as soft drinks or colas.
To calculate the price elasticity of demand we examine the response when the price of a six-pack of sodas goes from $2 to $2.20, a 10% increase in price. In this case, the quantity demanded falls from 1,000 to 850, a 15% decrease in the quantity demanded. Calculating the price elasticity of demand (% change in quantity demanded / % change in price = 15%/10%) yields a price elasticity of 1.5 (2). The price elasticity of demand of 1.5 calculated here, implies that for every 1% change in the price of sodas, quantity demand changes by 1.5% - clearly a relatively elastic good.

(2) For simplicity, we use absolute values when calculating price elasticity's.

Figure 4-2 follows with an relatively inelastic demand curve for a good such as gasoline. There are few substitutes for purchasing gasoline, especially in the short-run. In this case the price of a gallon of gas rises from $1 a gallon to $1.10, a 10% increase. The quantity demand falls very little - from 20 gallons to 19, a 5% decrease. The resulting elasticity calculation is 0.5 (% change in quantity demanded / % change in price = 5%/10%, in absolute terms). With a price elasticity of 0.5, for every 1% increase (decrease) in the price of gasoline, the quantity demanded of gasoline decreases (increases) by one-half as much.



In the graphs above, we show the two extremes of the price elasticity of demand. The left graph shows a perfectly elastic demand curve, which characterizes goods with perfect substitutes such as agricultural commodities. If a typical producer facing a perfectly elastic demand curve tries to raise the price of the good, demand falls to zero.

We will revisit this type of demand curve later in the course when we discuss an industry structure known as perfect competition. The graph on the right (Figure 4-4), shows a perfectly inelastic demand curve that is vertical. Goods that have perfectly inelastic demand have no substitutes and are considered an absolute necessity such as insulin used by diabetics and a few other life-sustaining health care products. If the price of a perfect inelastic good is increased, there is no effect on the quantity demanded. While perfectly elastic and inelastic goods represent some goods, the majority of consumer goods have a downward sloping demand curve, characterized by an elasticity somewhere between the two extremes.

We now turn our attention to optimal producer behavior given the elasticity of demand for their product. In other words, given the price elasticity of demand facing the firm in the relevant range of production, how would a change in the price of the good affect a firm's revenues? Remember, if a firm raises prices they reduce sales (for a typical downward sloping demand curve) and the firm increases sales when there is a reduction in prices.

A firm's revenues equals the total sales of a good sold times the price charged.

TR = P x Q:
Total Revenue = Price x Quantity

Assume that a firm faces a price elastic demand in the relevant range of good pricing. If the firm lowers price quantity demanded will increase. The effect on total revenue is a factor of the two parts:

In summary, a price elastic demand implies the percentage change in quantity demanded (output) exceeds the percentage change in price. Thus the firm that lowers prices under these circumstances will have a net gain in total revenues due to the increase in revenues resulting from greater sales exceeding the reduction in revenues coming from a lower price per unit of output sold to consumers.

Since firms facing an elastic demand can increase total revenue when they cut prices, the opposite condition exists when they try to raise prices. With many substitutes in consumption available, a price increase leads to a significant decline in consumption - the percentage change in quantity demanded (output) exceeds the percentage change in price. Producers that raise prices when facing an elastic demand will find that total revenues decrease as the gain from charging higher prices is more than offset by a desertion of consumers to cheaper substitutes, with sales and output falling.

To understand the changes in revenue which occur when the firm prices in the inelastic portion of the demand curve, we reverse our reasoning from the elastic circumstances discussed above. When price elasticity is inelastic, the percentage change in quantity demanded (output) is less than the percentage change in price. As a result, the change in revenues due to the response in the quantity demanded is less than the change in revenues as a consequence of the price change. We conclude that a firm pricing in the inelastic range of the demand curve will have a net increase in total revenues when they raise the price of the good they produce to the consumer. For the most part, the consumer will have little opportunity to significantly reduce consumption and must pay the higher price. The opposite holds true when the firm pricing in the inelastic portion of the demand curve reduces price - total revenues decline.

For an example of the change in revenue with different values of the elasticity consider a firm that raises it price by 1%.

Assume:

P0 = $100, Q0 = 1,000 units and TR = $100,000  (P0 x Q0)

Also assume that the price elasticity of demand is equal to 0.5. With a 1% increase in price we have.

P1 = $101, Q1 = 995 units and TR = $100,495  (P1 x Q1)

If the elasticity is equal to 0.5, then a 1% increase in price will lead to a 0.5% decrease in quantity demanded. In this example, we can see if the good has an inelastic demand, total revenue will increase in response to a price rise.

Let us modify our example to show what happens when price is increased by 1%, but the good is elastic. For example, assume the price elasticity of demand is equal to 2.0.

Assume:

P0 = $100, Q0 = 1,000 units and TR = $100,000  (P0 x Q0)

Also assume that the price elasticity of demand is equal to 0.5. With a 1% increase in price we have.

P1 = $101, Q1 = 980 units and TR = $98,980  (P1 x Q1)

If the elasticity equals 2.0, then a 1% increase in price will lead to a 2% decrease in quantity demanded. In this example, we can see if the good has an elastic demand, total revenue will decrease in response to a price rise.


Summary of Price Elasticity of Demand

Elasticity Description Change in Quantity Demanded with a 1% Increase in Price Change in Revenue with an Increase in Price Change in Quantity Demanded with a 1% Decrease in Price Change in Revenue with a Decrease in Price
Zero Perfectly inelastic - vertical demand curve Zero Increased by 1% Zero Decreased by 1%
Between 0 and 1 Inelastic Decreased by less than 1% Increased Increased by less than 1% Decreased
1 Unitary elasticity Decreased by 1% No change Increased by 1% No change
Greater than 1 Elastic Decreased by more than 1% Decreased Increased by more than 1% Increased
Infinite Perfectly elastic - horizontal demand curve Decreased to zero Decreased to zero No change Increased by 1%

Elasticity Over Time

OPEC was formed during the 1950s by emerging oil producing nations located throughout the world. Until the 1970s, oil prices remained fairly steady at around $3 to $4 a barrel. As a result of the oil embargoes of 1973 and 1979, oil prices surged to over $35 a barrel, and were soon expected to top $60 a barrel. Instead, by the mid-1980s, prices per barrel had collapsed to well below $20. It was during the 1970s when the combination of an inelastic good (oil or gasoline) coupled with soaring prices had the most dramatic economic effects.

Gasoline is typical of a good that is inelastic in the short-run. When an automobile and energy dependent country such as the United States was hit by soaring gasoline prices during the 1970s, consumers had little short-run choice but to pay higher prices for gas required to run their mostly gas-guzzling cars. The OPEC nations were not the only beneficiaries of escalating oil prices. U.S. oil producers in Texas, Louisiana, Alaska and other states as well as gasoline and petroleum distributors also enjoyed soaring profits. In fact, due to rising pump prices, major U.S. gasoline retail firms were required to pay a windfall profits tax.

However, over time the price elasticity of demand for gasoline increased and consumption became more responsive to increases in prices. Substitutes develop such as fuel-efficient automobiles and improved public transportation. As a response to the oil shocks of the 1970s, Ford rolled out the legendary Pinto and Chevrolet the memorable Vega; both more fuel-efficient than the typical Ford or General Motors car produced during that period. Needless to say, given consumer choices, consumption of foreign imports, especially fuel-efficient cars from Japan soared.

Along with reducing gasoline consumption, conservation and alternative fuels and sources of petroleum helped to alleviate the dependency on OPEC oil sources. Natural gas, coal, solar and other alternative fuels were increasingly substituted for oil by consumers, industry and electric utilities. The Iran-Iraq war lead to widespread cheating by OPEC members who exceeded their predetermined quotas and quickly adjusted spending to higher cash flows of income. Eventually, gasoline prices fell as oil production increased during the 1980s. Although the major gasoline companies were reluctant to lower the prices of an inelastic good such as gasoline, an increase in market supplies led to this outcome in the United States.

The conclusion we can draw from the wild 1970s, characterized by escalating energy prices, lower thermostats, disco music and clothing that was often of dubious taste, is that over time, elasticity increases. Even for goods that are very price inelastic such as gasoline and some health care products, substitutes and alternatives in consumption develop when prices increase. There may be little opportunity for consumer response in the short-run, but in the long- run he or she will often find it easier to reduce consumption of a good when its price increases by a significant amount. This idea will be developed later in this course when we study market behavior of firms. As OPEC has learned, while rapid price increases can lead to a blizzard of short-term profits, such behavior can result in a long-run demise. For this reason, OPEC and other firms that look to the long run have a market incentive not to gouge the consumer. As the price of oil rose during the 1970s, so did the cost-effectiveness of alternative fuels sources (e.g. ethanol and other food-based gasoline mixtures) that could displace oil as an energy course. Likewise, a firm that is earning excessive profits attracts competitors like dogs to a bone yard.

An excellent example of a firm showing short-run pricing restraint to ensure long-run profitability is Intel, which has most likely supplied the processor (CPU) in the computer that you are currently working on. Intel almost monopolizes the computer processor market, supplying the CPU in roughly 85% of all personal computers sold over the past decade. In the short-run, Intel could easily increase CPU prices and company profits. But this would come at the expense of long-run market share and profits. To discourage competition and ensure that PC manufacturers continue to ship the majority of their units with Intel processors, Intel continuously innovates and reduces prices for its processors. For competitors such as Cyrix and AMD, gaining inroads into Intel's market share is extremely difficult given the price, quality and name competition that Intel generates.

The Price Elasticity of Supply

Using similar concepts we discussed when examining the elasticity of demand, we now turn our attention to the price elasticity of supply. Like the demand curve, elasticity changes as we move along the supply curve. We can find supply curves for goods such as housing, which are relatively vertical (inelastic), representing little response in output to changes in prices in the short-run. Other goods, such as fast-food hamburgers, have supply curves that are relatively elastic and flatter in shape. For goods with an elastic supply, production responds quickly to changes in prices.

Many goods will have supply curves that have regions that are both very elastic and inelastic. A manufactured good such as steel or automobiles will have ranges of supply which illustrate regions where output can be rapidly expanded with little or no change in price, and parts of the same supply curve where there is little response in output, but a significant change in price. This concept is explained best using a short-run supply curve, where the firm has fixed inputs such as total productive capacity (factory, machinery, etc.), and variable inputs such as labor.

The changing elasticity along the supply curve is shown quite dramatically in Figure 4-5. At low levels of output, the supply curve is very elastic (the flat portion). The elastic portion of the supply curve represents excess productive capacity including underutilized machinery and other capital used in production.
As the firm expands output in the elastic range of the supply curve, there is little or no increase in production costs, as the idled capacity is increasingly utilized. Constant production costs imply there is little need or incentive for the firm to raise the market price of the good. In this case, the firm can easily expand output with little or no increase in the market price of the good produced.

As the firm continues to move along its supply curve, increasing output, soon all of the excess productive capacity or slack, is absorbed. All capital used in producing the good is fully utilized and the only way to further increase output is to add extra shifts of workers and overtime. The likely result is higher production costs per unit of output as wages and capital maintenance costs rise. Increased production costs are passed on to the consumer in the form of higher market prices for the final good. This is shown by the portion of the manufacturer's supply curve that is nearly vertical - incremental increases in output lead to a significant response in price.

Income Elasticity

Thus far, we have dealt with the effect of a change in the price of a good on the same good's quantity demanded or supplied. Now we turn our attention to the impact on the demand for a good when consumer incomes change, holding prices constant. The business cycle describes alternating periods of economic growth, when incomes generally increase, and contraction (recession) which lead to a decrease in consumer incomes. A firm needs to understand income elasticity to see how changes in the macroeconomy translates into the demand for the good or service produced by the firm. Our consumption of some goods, such as luxuries, is very sensitive to changes in economic growth and consumer incomes. In contrast, necessities such as food and housing tend to be less affected by economic swings and the corresponding changes in consumer incomes.

There are three possibilities for a good's income elasticity:

  1. A good is income elastic if the income elasticity of demand is greater than 1. This implies that for a 1% change in income, demand for the good changes by more than 1%.
  2. A good is income inelastic if the income elasticity of demand is greater than 0 but less than 1. This implies that for a 1% change in income, demand for the good changes by less than 1%.
  3. A good is considered inferior if the associated income elasticity of demand is a negative number. In this case, if income increases, consumers actually buy less of the good.

The first two categories above, income elastic and income inelastic, both correspond to a normal good, where the income elasticity of demand is greater than zero. A normal good is one that we buy more of when our income increases. If the income elasticity of demand exceeds a value of 1.0, the good is often considered a luxury such as a computer, cellular telephone or many types of entertainment. A necessity is a good that we buy more of when our income increases, such as health care or gasoline, but our consumption is not substantially affected. Finally, consider inferior goods characterized by consumption that actually decreases with improvements in income. For many consumers, inferior goods include items such as canned macaroni and cheese, high fat meats, cheap seats at the ball game, and many others.

Cross-price Elasticity

The final type of elasticity we will consider in this section is known as the cross-price elasticity and measures the responsiveness of our consumption of one good when the price of another good changes. The cross-price elasticity of two goods, say good A and good B, measures the percentage change in the quantity demanded of good A, when the price of good B changes by 1%. Cross-price elasticity's are given two categories: complements and substitutes.

Cross-price elasticity is important for producers to recognize. Demand for goods in industries such as autos are significantly impacted by changes in price of complements and substitutes, most noticeably gasoline and the prices of cars produced by a competing firm. Individual firms will carefully judge the impact of competitor pricing and the responsiveness of consumers to those price changes. Goods with a higher degree of substitution will have a greater positive value for their cross-price elasticity. Likewise, goods that show a more complementary relationship have an increasing negative value for their cross-price elasticity.

Take the example of the airline industry and consider goods that are close substitutes. For example one good is the price of seat on American Airlines, the other good is the demand for seat on United Airlines, each on an identical flight route - say Boston to Washington DC. In the case of the airline industry, the cross-price elasticity of demand for airline tickets is very high, and firms respond immediately to fare changes. If one airline such as American initiates a fare war, competitors such as United quickly follow in reducing prices to prevent a loss of market share. Since there is a high cross-price elasticity, if American lowers its fare from Boston to Washington DC, and United keeps its fares constant, consumers quickly shift consumption towards the lower priced American tickets. The resulting decrease in the demand for United Airlines tickets is large (3).

(3) In this example the cross-price elasticity takes on a positive value, indicating American and United tickets are substitutes. If American lowers its fare the coefficient is negative since the fare decreases and since United holds its fare constant, demand for United tickets falls as well, resulting in a
negative coefficient also. Dividing a negative decrease in demand by a negative drop in price results in the negative coefficients canceling out and a positive coefficient for the result.

Elasticity of Demand and Taxation

Taxes are levied by governments at the time of sale for some goods. The effect of the tax causes the consumer to pay a higher price for the good than the price the producer receives for the same good, the difference in the price paid and the price received is the amount of the tax. In this section, will first look at how a tax that is imposed at the point-of-sale impacts our analysis and then relate the incidence, or burden of taxation to the elasticity of demand for the good. Typical taxes we will examine in this section include excise taxes such as cigarette and gasoline. As you will see, governments prefer to tax goods with a relatively inelastic demand, since there will be little decrease in demand by consumers when the good's price increases.

Let us begin our analysis with the general effect of an excise tax. We begin with an initial, pre- tax equilibrium at Po and Qo. As mentioned, the effect of the tax is to drive a wedge between what the consumer pays for the good (Pc) and what the producer receives (Pp). The graphical consequences as shown in Figure 4-6, where the supply curve shifts inward by the amount of the tax. As the graph shows, due to the tax the price paid by consumers exceeds the price received by producers, the difference being the amount of the tax.


The above graph shows that a tax drives a wedge between the consumer's price paid and the price received by the producer. Now we turn our attention to the effect on consumption, which depends on the relative elasticity of demand. In Figure 4-7 we look at a 50 cent tax on cigarettes, imposed at the point-of-sale.
Since the demand for cigarettes is relatively inelastic, the associated demand curve has a steep slope. Beginning with the original equilibrium price for cigarettes prior to the tax, we see that the tax drives the supply curve for cigarettes upward by the amount of the tax. Since the demand curve for cigarettes is relatively inelastic, consumers end up absorbing the majority of the tax incidence, by paying the majority of the tax - the difference between the price paid by consumers after the tax (Pc) and the price paid before the tax (Po). Using the same analysis, the amount of the tax burden imposed on producers is measured by the difference between the price received by producers (Pp) and the pre-tax price received by cigarette manufacturers (Po).

Note in Figure 4-7 the effect on the demand for cigarettes due to the tax - the drop in demand is small, since cigarettes are a relatively inelastic good. Smokers are most likely to pay the tax with little reduction in their consumption of cigarettes. To measure the area of tax paid by the consumer, we take the differences in prices paid after (Pc) and before (P0) the tax, times the new level of consumption, Q1. The producers allocation to the tax is measured by the differences in prices received after (Pp) and before (P0) the tax, times the new level of consumption, Q1. The amount of tax received by the government equal the consumers plus the producers shares of the price wedge caused by the tax times the new level of consumption, Q1.

To complete our story, there is also what is known as a deadweight loss due to taxation, illustrated by the decrease in output from Qo to Q1. The deadweight loss is the reduction in economic activity, or output, due to the tax. Specifically, the deadweight loss is the shaded triangular area bounded by the original point of price and output equilibrium before the tax (Po, Qo) and the new prices paid by the consumer (Pc) and received (Pp) by the producer.

In contrast to a good with an inelastic price elasticity of demand, we compare tax incidence for a good which has a relatively price elastic demand such as satellite dishes used for receiving television stations. In areas with a developed coaxial cable infrastructure, the majority of the United States for example, demand for satellite dishes is fairly elastic, since the consumer has the alternative of relatively low priced cable hookup. We would expect any increase in the price of the dish to reduce demand significantly. Similarly, a reduction in the price of a dish, especially the smaller dish (Direct TV, etc.), leads to gains in demand.

For a similar story, consider the VCR (video cassette recorder). Introduced in the early 1980s, the original VCR's were very expensive, costing close to a $1,000 for a machine that would be considered ancient in comparison to today's cheapest models. As a consequence of the high price, demand was low. As prices fell continuously during the 1980s, demand soared, making the VCR as common as the television in people's homes. Over the next few years, as the price of small satellite dishes fall, we can expect the cable companies that only recently monopolized the cable market, to experience intense competition, as dish sales experience tremendous growth.

Figure 4-8 illustrates a relatively elastic demand curve and the impact of a tax imposed on satellite dishes at the time of sale (holding the price elasticity of supply constant from the previous graph). As you already understand, the tax causes the supply curve for satellite dishes to shift leftward, creating a gap between the price paid by consumers for the dish and the price received by producers for the same item.
To measure the area of tax paid by the consumer, we take the differences in prices paid after (Pc) and before (Po) the tax, times the new level of consumption, Q1. The producers allocation to the tax is measured by the differences in prices received after (Pp) and before (Po) the tax, times the new level of consumption, Q1. The amount of tax received by the government equal the consumers plus the producers shares of the price wedge caused by the tax times the new level of consumption, Q1. The deadweight loss is the shaded triangular area bounded by the original point of price and output equilibrium before the tax (Po, Qo) and the new prices paid by the consumer and received by the producer. Since demand for satellite dishes is relatively elastic, you will notice that the majority of the tax is absorbed by the producer and a smaller portion by the consumer.

For our analysis we can make several conclusions about the incidence of taxation and the elasticity of demand for the good being taxed:

The last point made above is an important one. Point-of-sale taxes such as excise taxes on cigarettes, gasoline and alcohol are considered regressive. A regressive tax places a greater burden on consumers as their income declines, since a greater percentage of their disposable income is spent on these goods. This is not to say that as our incomes fall, we smoke, drink and drive more, but that a greater portion of our income is absorbed on the consumption of these goods in comparison to a wealthy individual who may consume equal quantities of these goods. As a consumer's income increases their tax burden for these goods falls as they spend a smaller share of their disposable income for the consumption of these goods. In conclusion, while taxes on luxury items such as yachts, jewelry, and extravagant automobiles do not raise substantial sums of money, the tax system takes on a greater aura of fairness. (4).

(4) We will not explicitly cover the incidence of taxation for different price elasticity's of supply, holding the elasticity of the demand curve constant. If you are interested, use a similar graphical analysis to find the following conclusion: As the relative price elasticity of the supply curve falls (becomes more inelastic), the producer's tax burden increases relative to the consumer's.

Copyright 2002, Jay Kaplan
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