FIGURE 3–2
Hypothetical Demand Curve Showing Total Revenue 
When P=1 and Q=50

FIGURE 3–3
Hypothetical Demand Curve Showing Total Revenue 
If price is raised to $2

Percent change in Quantity:  (50 – 40)/50 = 20%
Percent change in Price:  (2 – 1)/1 = 100%
Price Elasticity of Demand: (20% / 100%) = 0.2  Þ Demand is inelastic.

  

FIGURE 3–4
Hypothetical Demand Curve, Illustrating that
Demand is still inelastic if price is raised $3

Is demand still inelastic if price is raised to 3? Yes. Total revenue can be increased from 80 to 90 [P*Q = $3*30] by raising price, thus demand is still inelastic at P = 2 and Q = 40.  The two rectangles above show how much total revenue is increased by getting a dollar more for each of the 30 units sold, compared to the $20 of lost revenue from losing 10 units of sales at $2. 

FIGURE 3–5
Hypothetical Demand Curve illustrating that Deman becomes more elastic as price is raised along a straight line demand curve

Percent change in price is now 33.3%. Percent change in Q now 33.3%. Total revenue falls from 90 to 80. A monopolist would never charge a price under $3, never sell more than 30 units, and thus would never operate on the inelastic portion of the demand curve.

We have seen that the basic formula for calculating the price elasticity of demand from percentage change in price and percentage change in quantity can also be used to calculate either percentage change in price or percentage change in quantity, if you have the other two variables.  Now we move to a second type of demand elasticity.  
   

Cross-Price Elasticity of Demand 

Often there is no exactly identical domestic product corresponding to an imported product.  Hence a different tool must be used to relate changes in the market for the imported good, as a result of actual or proposed trade policy changes, to adjustments in the related domestic markets.  The cross-price elasticity of demand  (cross elasticity, for short) relates the percentage change in quantity demanded for a product with the percentage change in the price of another product.

The cross-price elasticity can be positive or negative, depending on whether we observe a change in the price of a substitute or a complement.  Substitutes are goods or services that can be used in place of one another (substituted), such as bread, rice, or pasta, coffee or tea, brand names or generic substitutes, etc.  Using the conjunction “or” between them indicates that you use one or the other, and that a fall in the price of one good would encourage more people to use that good, and reduce demand for the substitute.  For instance, trade policies that raise the price of rice in Japan have caused the younger generation to consume much more bread and pasta than their parents and grandparents.  Thus the cross-price elasticity between bread and rice is positive, and the goods are substitutes.

Complements are goods that are usually consumed in combination or in conjunction with each other, such as peanut butter and jelly, bacon and eggs, autos and gas, cereal and milk, new homes, furniture, and appliances, etc.  The conjunction “and” is used to indicate that consumption of the two goods should increase or decrease together.  This leads to a negative cross-price elasticity, since a rise in the price of milk will lead to a fall in the consumption of cereal, since the cost of consuming “cereal and milk” has risen, even though the price of cereal remains the same. 

Note that unrelated goods can act like substitutes through the impact of price changes on total disposable income.  For instance, we may observe negative cross-price elasticity between pizzas and gasoline, since a rise in the price of gas leaves less disposable income to use for things like pizza.   
   

Income Elasticity of Demand 

As disposable (after tax) income rises, demand for most goods increases.  The percentage change in demand for a good divided by the percentage change in income is the income elasticity of demand.  Goods and services with income elasticities above one are called income elastic.  Examples of these goods on which people spend a large portion of any increase in income include air travel, restaurant meals, movies, and other entertainment.  Goods and services with income elasticities between zero and one are called income inelastic.  Food (excluding restaurant meals), especially in high income countries like the US, clothing, alcoholic beverages, and newspapers are examples of goods for which a rise in income generates little additional consumption.   

Some goods and services are actually consumed less as income rises.  These inferior goods have negative income elasticities, and include things like bus rides and low-end brands of everyday goods.  After you make your first million, you are probably done purchasing these goods, except for bouts of nostalgia for your university days!  

Elasticity of Supply 

Another useful concept for trade policy analysis is the income elasticity of demand . 

As disposable (after tax) income rises, demand for most goods increases. Goods for which demand falls as income rises are called inferior goods . These inferior goods have negative income elasticities, and include things like bus rides and low-end brands of everyday goods.

Goods and services with income elasticities between zero and one (demand increases, but by a smaller percentage than the increase in income) are called normal goods .  Food (excluding restaurant meals), especially in high income countries like the US , clothing, alcoholic beverages, and newspapers are examples of goods for which a rise in income generates little additional consumption.

Goods and services with income elasticities above one are called superior or luxury goods .  Examples of these goods on which people spend a large portion of any increase in income include air travel, restaurant meals, movies, and other entertainment. 

For most countries the income elasticity of demand for imports is higher than one because, as we discussed earlier, when people feel wealthier they are more inclined to buy more expensive foreign goods that might be more attractive, or just different. The income elasticity tends to vary with the stage of a country’s development. The richer the country, the higher is its tendency to buy foreign goods and services when its income rises. For countries at the bottom of the development ladder, the income elasticity might be less than one because growth might be associated with an increased capacity to produce goods at home. Also, domestic consumers use their added income to consume more basic needs such as food, clothing, and shelter, which in most poor countries are primarily produced domestically.  Some typical income elasticities are found in Table 3–3.

Table 3 – 3 Some Income Elasticities of Demand in the United States

Source: H.S. Houthakker and Lester D. Taylor, Consumer Demand in the United States, (Cabridge, Mass: Harvard U. Press, 1970), reprinted in Joseph Stigliz, Prinicples of Microeconomics, (New York: W. W. Norton & Co., 1993).  Note again that in 1993, the best available study was dated 1970!

Note that a large fraction of an increase in income goes to discretionary purchases or “luxuries,” while “necessities” like dishes, furniture, water, and clothing show only a modest increase in demand.  With a more detailed breakdown, we might see that French wines and champagnes, Cuban cigars, and Asian teak tables show a higher income elasticity within those broad categories. 
  

Elasticities in the Long Run 

The price elasticity of supply  (hereafter just ‘elasticity of supply’) measures the percentage change in production in response to a given percentage change in price. 

This supply elasticity can vary from zero (perfectly inelastic supply) to infinity (perfectly elastic supply).  A few examples of perfectly inelastic supply do exist.  Rembrandt will not be doing any more paintings, and there are probably no more hidden away in European attics to be discovered.  Perfectly inelasticity is also a useful approximation for some supplies in the very short run, especially for produce, where the amount you harvest is closely related to the area you plant.[1]  At the other extreme, supply can be nearly perfectly elastic, even in the short run, up to some capacity constraint, for things like phone calls, internet access, and water. 

In general, supply is more elastic the longer the time horizon under consideration.  In the short run, existing workers can be asked to work more overtime, which may raise your cost significantly (subject to local labor laws regarding allowable overtime amounts and compensation).  In the long run, more employees can be trained and more machinery installed to produce additional output at a lower cost.  Hence a permanent price increase may yield little additional supply right away, but over time the supply increase will be greater and the price increase smaller than it was initially. Thus the supply elasticity is greater in the long run.  For example, NAFTA gave Mexican producers greater access to the US market in important areas like garments, textiles, and sugar.  Mexico responded with an increase in exports to the US , but there was even greater growth in new investment in these areas, creating more capacity and even larger export increases in later years. 

In general terms, the long run is a period of time over which all costs are variable. In contrast, the short term is a period of time over which some costs are fixed. Returning to the oil shock analogy from page 24 , increased oil exploration led to major discoveries in Alaska and the North Atlantic . More was invested in the development of alternative energy sources such as wind, solar, and atomic energy.  All these factors combined to increase the supply of alternatives to OPEC oil over time, raising the elasticity of supply in the broader “energy sector” in the long run. 
  

Some Cautions When Using Elasticities 

Estimated elasticities are only “correct” for a specific context.  If you try to apply them outside that context, your calculations may be poor estimates of the actual changes. The list below may be helpful.

Problem 1: Old elasticity estimates. 

Danger: Changes in tastes, new products, etc. may have changed elasticities, making them incorrect.

Solution: Develop familiarity with data sources to find the most current estimates possible.  Use sensitivity analysis  to present a reasonable range of estimates.

Problem 2: Large price changes. 

Danger: Elasticity estimates are based on historical ranges of variation, and are generally valid only for small changes around a certain point on the demand curve.  As we saw earlier, elasticities may change substantially for movements along a demand curve, thus estimates of changes in quantity demanded (price) derived using large (greater than 33%) price (quantity) changes may be unacceptably incorrect.

Solution: There is no generally valid solution. In some cases you will overstate the actual change; in others you will understate it. For instance, a material such as aluminum has many potential uses, and is widely used if it is cheap.  As its price rises, people will use plastic wrap instead of aluminum foil, but airplane manufactures will continue to use aluminum, because of its desirable weight to strength ratio, even when the price rises substantially.[3] Hence one might use a smaller PED for large price increases and a larger one for large price decreases. But other products have the opposite characteristics.

Thus understanding the particular product and market is necessary. Use sensitivity analysis to present a reasonable range of estimates, understanding that the honest approach is to expand the range of sensitivity analysis to reflect this additional source of uncertainty.

Problem 3: Cannot find an estimated elasticity for the particular product or service you need to analyze.

Danger:  Use of a broader or narrower category can greatly change the appropriate elasticity, making your estimates incorrect.

Problem 4: Need long-run estimates but have only short-run, or vice versa. 

Danger: Long-run and short-run elasticities can be very different, as shown in Table 3–2. 

Problem 5: Trying to estimate your own elasticities from historical data. 

Danger:  To do this correctly, you must hold constant all other potential factors affecting supply and demand, such as income, prices of other goods, production costs, etc.

Solution: Unless you have excellent econometric skills, you are better off presenting a plausible, round-number estimate, with sensitivity analysis.  Remember that a shift in the supply curve means a movement along the demand curve, and vice versa. 

Problem 6: Using estimates from advanced industrial countries for developing countries

Danger: The chances of the exact elasticities you need being available for Thailand or Namibia are very          low, hence you will be tempted to use more readily available elasticities for industrial countries in Europe or North America.

Solution: More hard work! Step one is to search for specific information on the relevant sector and country. Step two could be to look at the same sector in “similar” countries (determining the degree of similarity is another potential problem). Using elasticities from industrial countries should be the last resort, and one should think carefully about how the market situation in the developing country you are studying suggests modifications of the elasticities.
 

Finding Elasticity Estimates

Typically, government agencies do not regularly compute such estimates.  Often the only way to find elasticity estimates for detailed industrial categories is to survey economic research. Fortunately, you needn’t always conduct the survey yourself, if you are working on a “hot” issue area.  Computable or applied general equilibrium modelers are the leading users of such data, so if a reasonably unbiased empirical model of this issue exists, the authors have undoubtedly done such a survey already, and should make that information available to you.[5]  The Journal of Economic Literature is one source of reviews of such models. 

Regional journals, such as the North American Journal of Trade and Finance, Asian Economic Journal, etc., are good sources for trade-related elasticities germane to current or proposed trade agreements.  Finally, collections of papers from conferences devoted to either CGE modeling in general or topic areas in particular can be excellent sources of elasticity data, or at least good starting points for your search.  

Several recent books and articles are devoted to international demand elasticities:

The Demand for Imports and Exports in the World Economy, W.C. Sawyer and R.L. Sprinkle, Ashgate Publishing 1999.

“Long-Run Industry-Level Estimates of US Armington Elasticities,” by M. Gallaway, C. McDaniel, and S. Rivera, USITC working Paper #2000-09a, (October 2000), (available on-line at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=249027.

Footnotes

[1] Even then, more intensive cultivation methods can be used to increase yields if prices are rising, while some output could be withheld from the market and stored if prices fall below expectations.

[2] For a detailed discussion of sensitivity analysis and examples of its use, see the corresponding section in Chapter 9.

[3] Stiglitz, Principles of Microeconomics, New Your: W.W. Norton, 1993 p.112.

[4] Ibid.

[5] Some current leaders in data-intensive CGE modeling are Alan Deardorff and Robert Stern (and many of their formers students at the University of Michigan, now spread around the world), Jaime De Melo (and other current and former World Bank researchers), Joseph Fracois (and other current and former researchers at the US ITC), Lawrence Goulder (and other former students of John Shoven at Stanford University), Thomas Hertel (GTAP – Purdue University, Department of Agricultural Economics), Sherman Robinson (and others he has trained at UC Berkeley, the USDA, and IFPRI), John Whalley (and his students from Western Ontario), and B. Hockman.
  

top