cross+price+elasticity


 * Cross–Price Elasticity of Demand**

By: Dan Kelsey

The Cross-Price Elasticity of Demand (CPED) utilizes the two axes of the supply and demand curves to measure the rate of response of quantity demanded of one good, due to a price change of another good (Moffatt, 2007). The formula for CPED is the percent change in quantity demanded of good X divided by the percent change in the price of good Y. The formula is defined as: CPED Qx,Py = (%ΔQx^d)/(%ΔPy )
 * Definition:**

The resulting elasticity indicates if the two products are complements or substitutes. If the products are substitutes, then an increase (decrease) in the price of Y decreases (increases) demand for X. Conversely, if an increase (decrease) in the price of Y increases (decreases) demand for X, then X and Y are complements and the CPED is less than 0. If the CPED of the two goods equals zero, then the goods are independent and no relationship exists.

The following graph demonstrates the relationship between two substitutes:




 * Everyday Example:**

CPED measures the impact of a change in price of a barrel of oil and how midwest farmers determine their allocation of crops. The recent increases in the price of gas have influenced the demand and research for alternative fuels. Since corn and soybeans are the basis of alternative fuels, their demand has increased.The increased demand for these crops mean that farmers can increase their profit per acre by planting more corn and soy beans. However, the increased planting of corn and soy beans means that less land is available for other crops. This is another example of substitutes - an increase in the price of oil results in an increase in the quantity of corn and soy beans, and the increase in the amount of corn and soybeans results in a price increase for other agricultural items (watermelon, wheat, etc) (Farris, 2007).


 * Application of CPED:**

CPED has been the subject of several research papers and is used to examine the relationships between goods in myriad of ways ranging from terrorism (Anderton & Carter, 2005) to the relationship between smoking and drinking (Bask & Melkersson, 2004). Depending on the outcome of the measure, it provides government, industry, and business with additional information that can be used in planning for the future. Following are some of the ways in which CPED has been applied.

//Government Policy:// In their study on rational choice theory and the study of terrorism, Anderton and Carter (2005) state “if the cross price elasticity is positive, then terrorism and other goods are gross substitutes, and a benevolence policy will indeed reduce terrorism; if the cross price elasticity is negative, then they are gross compliments, and a benevolence policy will instead increase terrorism.” Although their study focused on rational choice theory, they concluded by stating that “higher market wages might cause an individual to supply more time to market activities and less time to terrorism or vice versa depending on income and substitution effects” (Anderton & Carter, 2005). Based on their findings, this illustrates how CPED can be used in government policy decisions regarding international relations.

CPED can also be applied to urban planning and ensuring cities are building the appropriate infrastructure to assure people do not move out of the city. Panayides and Kern (2005) found that “technological advances in telecommunications increases city size when it increases the return to relationships more in the city than in the hinterlands.” They found that the CPED between electronic and face-to-face communications to be negative and therefore complimentary. Because face-to-face communications could be more easily done within the environs of a city, the presence of electronic communications actually increases willingness to remain in the city.

//Drinking,Smoking, and Consumer Behavior:// The following studies illustrate how the CPED can be used by business to examine consumer behavior and make the appropriate business decisions. Bask and Melkersson (2004), use the rational addiction model to examine the relationship between drinking and smoking. They found that the own price elasticities of alcohol and cigarettes were negative and the CPED between both goods was negative. Because of the negative elasticity, the goods are complements. In their examination, they found the elasticities for each item individually to be greater than their CPED. This indicates that while cigarettes and drinking are complements, they do have an effect on the other’s elasticity.

Kumar and Swaminathan (2005) examined coupon elasticity and the relationships between coupons issued by vendors, store policies, and the elapsed time between the issuance and subsequent usage of the coupon. Their findings can be used by business for ordering goods to assure proper stocking levels and manage orders with manufacturers. Likewise, manufacturers need information regarding coupon elasticity for production planning. Although this may appear to be related more to own price elasticity, store owners must not only adjust orders for additional items to be available when a coupon is released, but they must also plan for a reduction in sales of substitute goods and adjust orders accordingly.

The final example is the relationship between use of the internet and book sales (Ghose, Smith, & Telang, 2006). The authors addressed concerns of the Association of American Publishers and Author’s Guild who believed that used-product markets would significantly cannibalize new product sales. The authors of the study were able to gain access to records from Amazon.com and found “that used books are poor substitutes for new books for most of Amazon’s customers. The cross-price elasticity of new-book demand with respect to used-book prices is only 0.088.” In fact, they found that the increase in book sales less the loss in sales on the part of publishers lead to an increase of total welfare to society of 87.92 million dollars annually from the introduction of used-book markets at Amazon (Ghose et al., 2006).

//Conclusion:// The examination of the relationship between the change in price of one good and a corresponding change in the demand of another good allows all segments of government and business to prepare and better understand their markets. The increase in understanding will allow them to plan for future changes and better anticipate the outcomes.

1. Rousslang and Parker (1984) studied the CPED of U.S. imports. Why did they believe CPED was important to study as it relates to the import of goods? a. They believed it was important to understand how the prices of one country will affect demand for output from other countries. b. They believed CPED could be used to examine the effect of tariffs on imported goods. c. Understanding CPED could change policy and provide assistance to developing countries. d. A and B. e. A, B, and C above.
 * Multiple Choice Questions:**

//Answer: e – All of the above. Selective use of tariff’s on goods from developed countries can allow developing countries to have a price advantage.//

2. In a study of private cheese labels and national brands in which Kraft had an 80% market share (Huang, Jones, & Hahn, 2007), it was found Kraft may have increased their price beyond consumers’ tolerance for brand loyalty. What could this mean in terms of CPED? a. The difference in the price gap between Kraft and private labels diminished elasticities between them. b. A lowering of the price gap will increase the market share of Kraft. c. All of the above. d. None of the above.

//Correct Answer: c – All of the above. The authors found that by raising their price, Kraft was actually competing with private labels. They proposed reducing price and gaining market share through advertising.//

3. A study examined the charges for recycling versus charges for trash collection. The authors found a CPED of 1.16 between recycling and garbage collection (Isely & Lowen, 2007). The CPED indicates: a. There is no relationship between recycling pick up and trash pick up. b. Recycling and trash pick up are complements. c. Recycling and trash pick up are substitutes.

//Answer: c – Recycling and trash pick up are substitutes. As stated above, a positive CPED indicates two goods are substitutes. Although the finding of substitute goods may sound contradicting in this example, it actually represents a gain in social value because people are willing to separate items for recycling instead of placing all items in the same trash can. If all items were placed in the same trashcan, the CEPD would be < 0 and indicate they were compliments.//

4. A restaurant located in downtown Indianapolis historically has $10,000 in additional business when the Colts play a home game. Because of the new stadium, ticket prices for the games will be raised by 20%. The mayor’s economic advisor says people will still eat downtown and has calculated a revised CPED of -.75. What will be the additional revenue after the stadium is opened? a. The restaurant will have $8,000 in additional revenue. b. The restaurant will have $7,500 in additional revenue. c. The restaurant will have $8,500 in additional revenue. d. Not enough information to answer the question.

//Answer:c. The calculation is X divided by .20 which equals -.75, so X equals -.15, and the new revenue equals 10,000 - (.15 x 10,000) equals $8,500.//

5. The original price of an item is $90 and increased to $100. The demand for a related product decreased from 10,000 units to 6,500 units. What is the CPED? a. .722 b. 3.51 c. -3.15 d. 1.38

//Correct Answer: c -3.15. This is calculated as follows: ((6,500-10,000)/10,000)/((100-90)/90)= -3.15//

Anderton, C., & Carter, J. (2005). On Rational Choice Theory and the Study of Terrorism. //Defence & Peace Economics, 16//(4), 275-282.
 * References:**

Bask, M., & Melkersson, M. (2004). Rationally Addicted to Drinking and Smoking? //Applied Economics, 36//(4), 373-381.

Farris, Paul L., (2007), Personal conversation, September 18, 2007

Ghose, A., Smith, M. D., & Telang, R. (2006). Internet Exchanges for Used Books: An Empirical Analysis of Product Cannibalization and Welfare Impact. //Information Systems Research, 17//(1), 3-19.

Huang, M.-H., Jones, E., & Hahn, D. E. (2007). Determinants of Price Elasticities for Private Labels and National Brands of Cheese. //Applied Economics, 39//(5), 553-563.

Isely, P., & Lowen, A. (2007). Price and Substitution in Residential Solid Waste. //Contemporary Economic Policy, 25//(3), 433-443. Kumar, V., & Swaminathan, S. (2005). The Different Faces of Coupon Elasticity. //Journal of Retailing, 81//(1), 1-13.

Moffatt, M. (2007). //Cross-Price Elasticity of Demand//. About.com. Retrieved September 12, 2007, from the World Wide Web: http://economics.about.com/cs/micfrohelp/a/cross_price_d.htm

Panayides, A., & Kern, C. (2005). Information Technology and the Future of Cities: An Alternative Analysis. //Urban Studies, 42//(1), 163-167.

Rousslang, D., & Parker, S. (1984). Cross-Price Elasticities of U.S. Import Demand. //Review of Economics & Statistics, 66//(3), 518.