When supply rises by 50 with an increase in price of 25 elasticity of supply would be

Learning Objectives

1. Explain the concept of elasticity of supply and its calculation.
2. Explain what it means for supply to be price inelastic, unit price elastic, price elastic, perfectly price inelastic, and perfectly price elastic.
3. Explain why time is an important determinant of price elasticity of supply.
4. Apply the concept of price elasticity of supply to the labor supply curve.

The elasticity measures encountered so far in this chapter all relate to the demand side of the market. It is also useful to know how responsive quantity supplied is to a change in price.

Suppose the demand for apartments rises. There will be a shortage of apartments at the old level of apartment rents and pressure on rents to rise. All other things unchanged, the more responsive the quantity of apartments supplied is to changes in monthly rents, the lower the increase in rent required to eliminate the shortage and to bring the market back to equilibrium. Conversely, if quantity supplied is less responsive to price changes, price will have to rise more to eliminate a shortage caused by an increase in demand.

This is illustrated in Figure 3.10 “Increase in Apartment Rents Depends on How Responsive Supply Is”. Suppose the rent for a typical apartment had been R0 and the quantity Q0 when the demand curve was D1 and the supply curve was either S1 (a supply curve in which quantity supplied is less responsive to price changes) or S2 (a supply curve in which quantity supplied is more responsive to price changes). Note that with either supply curve, equilibrium price and quantity are initially the same. Now suppose that demand increases to D2, perhaps due to population growth. With supply curve S1, the price (rent in this case) will rise to R1 and the quantity of apartments will rise to Q1. If, however, the supply curve had been S2, the rent would only have to rise to R2 to bring the market back to equilibrium. In addition, the new equilibrium number of apartments would be higher at Q2. Supply curve S2 shows greater responsiveness of quantity supplied to price change than does supply curve S1.

Figure 3.10 Increase in Apartment Rents Depends on How Responsive Supply Is

The more responsive the supply of apartments is to changes in price (rent in this case), the less rents rise when the demand for apartments increases.

We measure the price elasticity of supply (eS) as the ratio of the percentage change in quantity supplied of a good or service to the percentage change in its price, all other things unchanged:

Equation 3.5

[latex]e_S = \frac{ \% \: change \: in \: quantity \: supplied}{ \% \: change \: in \: price}[/latex]

Because price and quantity supplied usually move in the same direction, the price elasticity of supply is usually positive. The larger the price elasticity of supply, the more responsive the firms that supply the good or service are to a price change.

Supply is price elastic if the price elasticity of supply is greater than 1, unit price elastic if it is equal to 1, and price inelastic if it is less than 1. A vertical supply curve, as shown in Panel (a) of Figure 3.11 “Supply Curves and Their Price Elasticities”, is perfectly inelastic; its price elasticity of supply is zero. The supply of Beatles’ songs is perfectly inelastic because the band no longer exists. A horizontal supply curve, as shown in Panel (b) of Figure 3.11 “Supply Curves and Their Price Elasticities”, is perfectly elastic; its price elasticity of supply is infinite. It means that suppliers are willing to supply any amount at a certain price.

Figure 3.11 Supply Curves and Their Price Elasticities

The supply curve in Panel (a) is perfectly inelastic. In Panel (b), the supply curve is perfectly elastic.

Time: An Important Determinant of the Elasticity of Supply

Time plays a very important role in the determination of the price elasticity of supply. Look again at the effect of rent increases on the supply of apartments. Suppose apartment rents in a city rise. If we are looking at a supply curve of apartments over a period of a few months, the rent increase is likely to induce apartment owners to rent out a relatively small number of additional apartments. With the higher rents, apartment owners may be more vigorous in reducing their vacancy rates, and, indeed, with more people looking for apartments to rent, this should be fairly easy to accomplish. Attics and basements are easy to renovate and rent out as additional units. In a short period of time, however, the supply response is likely to be fairly modest, implying that the price elasticity of supply is fairly low. A supply curve corresponding to a short period of time would look like S1 in Figure 5.10 “Increase in Apartment Rents Depends on How Responsive Supply Is”. It is during such periods that there may be calls for rent controls.

If the period of time under consideration is a few years rather than a few months, the supply curve is likely to be much more price elastic. Over time, buildings can be converted from other uses and new apartment complexes can be built. A supply curve corresponding to a longer period of time would look like S2 in Figure 5.10 “Increase in Apartment Rents Depends on How Responsive Supply Is”.

Elasticity of Labor Supply: A Special Application

The concept of price elasticity of supply can be applied to labor to show how the quantity of labor supplied responds to changes in wages or salaries. What makes this case interesting is that it has sometimes been found that the measured elasticity is negative, that is, that an increase in the wage rate is associated with a reduction in the quantity of labor supplied.

In most cases, labor supply curves have their normal upward slope: higher wages induce people to work more. For them, having the additional income from working more is preferable to having more leisure time. However, wage increases may lead some people in very highly paid jobs to cut back on the number of hours they work because their incomes are already high and they would rather have more time for leisure activities. In this case, the labor supply curve would have a negative slope. The reasons for this phenomenon are explained more fully in a later chapter.

This chapter has covered a variety of elasticity measures. All report the degree to which a dependent variable responds to a change in an independent variable. As we have seen, the degree of this response can play a critically important role in determining the outcomes of a wide range of economic events. Table 3.2 “Selected Elasticity Estimates”1 provides examples of some estimates of elasticities.

Table 3.2 Selected Elasticity Estimates

Key Takeaways

• The price elasticity of supply measures the responsiveness of quantity supplied to changes in price. It is the percentage change in quantity supplied divided by the percentage change in price. It is usually positive.
• Supply is price inelastic if the price elasticity of supply is less than 1; it is unit price elastic if the price elasticity of supply is equal to 1; and it is price elastic if the price elasticity of supply is greater than 1. A vertical supply curve is said to be perfectly inelastic. A horizontal supply curve is said to be perfectly elastic.
• The price elasticity of supply is greater when the length of time under consideration is longer because over time producers have more options for adjusting to the change in price.
• When applied to labor supply, the price elasticity of supply is usually positive but can be negative. If higher wages induce people to work more, the labor supply curve is upward sloping and the price elasticity of supply is positive. In some very high-paying professions, the labor supply curve may have a negative slope, which leads to a negative price elasticity of supply.

Try It!

In the late 1990s, it was reported on the news that the high-tech industry was worried about being able to find enough workers with computer-related expertise. Job offers for recent college graduates with degrees in computer science went with high salaries. It was also reported that more undergraduates than ever were majoring in computer science. Compare the price elasticity of supply of computer scientists at that point in time to the price elasticity of supply of computer scientists over a longer period of, say, 1999 to 2009.

Case in Point: Oil Prices Revisited

WTI Crude Oil Spot price

Recall from our discussion of the dynamics of the world oil prices earlier in Chapter 2 that in early 2016, the world price of oil fell to almost $30 per barrel. In this situation, the OPEC countries, which were losing their revenue from oil sales, faced a tough choice: cut their oil production to prop up the price, as they’ve done in the past, or maintain their output and let the price continue to fall with the purpose of driving the producers of the more costly shale oil out of the market. As we could see, OPEC decided not just to go with the latter choice, but increase their oil production substantially. What we’ve learned above about the price elasticities of demand and supply will help us better understand why OPEC made that decision.

Let’s see what would have happened had OPEC decided to cut its oil production instead of increasing it. Suppose OPEC is making its decision when the price of oil has fallen to $30 and the world pro-duction of oil is 100 million barrels per day. OPEC accounts for about 40% of the world oil production, i.e. produces 40 million barrels per day, so its total revenue from oil is $30×40 million = $1,200 million or $1.2 billion. Will OPEC be able to increase its oil revenue if it reduces its production target by, say, 5%, to boost the price?

Let’s first consider what will happen in a very short run, when other countries don’t have enough time to increase their oil production. Figure 5.13 illustrates this situation. The world market is initially in equilibrium at point E1, where the price of oil is $30 per barrel and 100 million barrels per day is supplied. In the very short run, the supply of oil is practically perfectly inelastic; that is, the supply curve is vertical.

Figure 3.12

If OPEC cuts its oil production by 5% (i.e. by 40 million × 0.05 = 2 million barrels per day), the world production will decrease from 100 million to 98 million barrels per day. That is, the OPEC’s production cut will shift the supply curve from S1 to S2, so the market will move along the demand curve (D) from the initial equilibrium, E1, to a new equilibrium, E2, where the price is higher.

We can predict what the new price of oil will be given that the short-run price elasticity of demand for oil is estimated at −0.1. Since the percentage change in quantity is −2% (using the conventional formula, %ΔQ = (98 – 100)/100 = −0.02 or −2%), we can write:

[latex]e_S = \frac{ \% \: change \: in \: quantity \: supplied}{ \% \: change \: in \: price}[/latex]

[latex]{-0.1} = \frac{ {-2{\%}} }{ \% \: change \: in \: price}[/latex]

Solving this equation for %ΔP, we get:

-0.1 x %ΔP = -2%

[latex]{{\%}{\Delta}P} = \frac{ {-2{\%}} }{ {-0.1}}[/latex]

= 20%

That is, the price rises by $30×0.2 = $6, from $30 to $36.

Since OPEC is now selling 38 million barrels of oil at $36 per barrel, its total revenue is $36×38 million = $1,368 million. This is $168 million or 14% more than the revenue OPEC received before the oil production cut. Thus, by reducing
its oil production OPEC was able to boost the price of oil, which increased its total revenue from oil sales. This should come as no surprise. As we’ve learned in this chapter, when the demand is price inelastic, raising the price increases
total revenue. And when the demand is very price inelastic (which is the case here), even small reductions in quantity can lead to substantial price hikes and total revenue gains. This, however, is only true if the competition does not influence the market quantity supplied.

And in the case of the present day’s world market for oil, that could be true in a very short run, but not in a longer run.
Let’s see how the world market for oil will respond to OPEC’s production cuts in a longer run, when other countries—including such major world oil producers as the United States and Russia—increase their production of oil in response to a higher price. As we know, both demand and supply are more price elastic in the long run than in the short run. Figure 5. 14 shows what happens if the world supply of oil is still inelastic, but no longer perfectly inelastic (say, ES = 0.2) and the demand for oil becomes less inelastic (say, ED = −0.2).

Figure 3.13

Now, when OPEC reduces its production of oil by 2 million barrels shifting the world supply curve from S1 to S2, as in Figure 3.26, other oil producers respond to the initial excess demand for oil and a higher price resulting from it by increasing their production, which partly compensates the OPEC’s reduced supply. The market moves along the supply curve S2 from point X to the new equilibrium at point E2, where the price of oil is $30.50 per barrel and the quantity is 99 million barrels per day. As you can see, because both demand and supply are now less price inelastic, the price rises only by $1.50 (5%). Will the OPEC’s total revenue from oil still increase? Note first that since other countries increase their oil production while the OPEC countries reduce theirs, the OPEC’s market share decreases from 40% to 38.4% (as OPEC is now producing 38 million barrels per day out of the total world production of 99 million barrels per day). The OPEC’s total revenue then is $30.50×38 million = $1,159 million, which is 3.4% less than its revenue before the production cut ($1,200 million). Of course, in an even longer run, when both demand and supply are even more elastic, OPEC’s oil production cuts to prop up the price will result in even greater losses of their oil revenues.

Source: Ogloblin, Constantin; Brown, John; King, John; and Levernier, William, “Microeconomics for Business” (2018). Business Administration, Management, and Economics Open Textbooks. 6.

Answer to Try It! Problem

While at a point in time the supply of people with degrees in computer science is very price inelastic, over time the elasticity should rise. That more students were majoring in computer science lends credence to this prediction. As supply becomes more price elastic, salaries in this field should rise more slowly.

1Although close to zero in all cases, the significant and positive signs of income elasticity for marijuana, alcohol, and cocaine suggest that they are normal goods, but significant and negative signs, in the case of heroin, suggest that heroin is an inferior good. Saffer and Chaloupka (cited below) suggest the effects of income for all four substances might be affected by education. [Other References listed below]

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