## What is the midpoint method for calculating price elasticity of demand?

1. What is the midpoint method for calculating price elasticity of demand? How else can the price elasticity of demand be calculated? What is the advantage of the midpoint formula?

2. What are the key determinants of the price elasticity of demand for a product? What determinant is the most important?

3. In 2003, when music downloading first took off, Universal Music slashed the average price of a CD from $21 to $15. The company expected the price cut to boost the quantity of CDs sold by 30 per cent, other things remaining the same. What was Universal Music’s estimate of the price elasticity of demand for CDs? If you were making the pricing decision at Universal Music, what would be your pricing decision? Explain your decision.

4. In May 2009, iTunes raised the price of 33 songs from 99¢ per download to $1.29 per download. In the week following the price rise, the quantity of downloads of these 33 songs fell 35 per cent. Taking this into account calculate the price elasticity of demand for these 33 songs.

5. A 5 per cent fall in the price of chocolate sauce increases the quantity of chocolate sauce demanded by 10 per cent; and with no change in the price of ice cream, the quantity of ice cream demanded increases by 15 per cent. Calculate the price elasticity of demand for chocolate sauce. Calculate the cross elasticity of demand for ice cream with respect to the price of chocolate sauce. Are ice cream and chocolate sauce substitutes or complements? Why?

1. The midpoint method is a common method to calculate the elasticity especially the price elasticity of demand, price elasticity of supply, income elasticity of demand, and cross elasticity of demand (Gordon, Goldfarb and Li 2013). The midpoint method for calculating price elasticity of demand in order to analyse the changes in demand due to the change in the price of the product is as follows:

Price elasticity of demand= {(Q2 - Q1) / [(Q2 + Q1) / 2]} / {(P2 - P1) / [(P2 + P1) / 2]}

Here, Q1 and P1 is the initial quantity and price level respectively while Q2 and P2 are the final quantity and price level after the changes.

Price elasticity of a product can be further calculated using the percentage method. The price elasticity is measured by its coefficient Ep. it measures the percentage change in the quantity of a commodity demanded that results due to the percentage change in the price. Thus, the formula for calculating price elasticity ad per the percentage method is:

## What are the key determinants of the price elasticity of demand for a product?

Ep= percentage change in the quantity demanded / percentage change in the price

= (δq / δp) * (p / q)

If the value of Ep is greater than 1 then the demand is said to be elastic, while the demand is inelastic is the value is Ep is lesser than 1.

The advantage of using the midpoint formula is that the midpoint method avoids the problem of obtaining a different answer while computing the price elasticity between any two points on the demand curve. Moreover, Thimmapuram and Kim (2013) mentioned that unlike the usual formula, the midpoint formula does not depend on the value that is taken as the old value or the new value. The midpoint method allows to obtain a better approximations and thus is useful in calculating the price elasticity for demand.

2. The price elasticity of demand for a product is determined by on or a combination of a number of key factors. The factors are as follows:

Availability of substitute goods: The elasticity of a particular good becomes high, when there is more substitutes of the product available in the market. Consumers are able to switch from one good to the other even when there is a small price change for a good (Walras 2013). On the other hand, the demand for the goods become inelastic when there is no close substitute.

Proportion of the consumer’s budget: When a good consume a greater portion in the budget of the consumer, the elasticity of the good increases. A relative increase in the price level of the good will induce the consumers to look for substitute and thus affect the demand of such good.

Degree of necessity: The more a good is necessary, the lower will be the elasticity. Consumers will buy the goods that are necessary despite the changes in the goods. While, in case of luxury goods consumers reduce the demand, when the price of the product increases (Sneddon 2013).

Duration of price change: in case of non-durable goods, the elasticity becomes higher in the long run than in the short run. In the short run, consumers are unable to find substitutes due to the change in the price (Ataman et al. 2016). However, it is possible in the long run and thus consumers are able to adjust their behaviour.

Brand loyalty: Loyalty of the customers towards a certain brand, overrides the sensitivity to price changes and thus the demand for the good becomes inelastic in nature.

## Case Study: Universal Music Pricing Decision

The availability of the substitute and the degree of necessity of a product are the main determinants of the price elasticity of demand for a product. However, the other factors apart from availability of the substitute and the degree of necessity are important in determining the price elasticity of the products in the market.

3. The price of the CD decreased from $21 to $15. Thus, percentage change in the price = (7 / 21) * 100 = 0.33 * 100 = 33%.

Expected increase in the quantity = 30%

Therefore, the price elasticity for the CDs are = % change in the quantity of CD / percentage change in the price of the CD

PED = 30% 33% = 0.90

In this case, the demand for the CDs is inelastic. Considering other factors ceteris paribus, the reduction in the price leads to decrease in the revenue earnings of Universal Music. Moreover, the close substitute for CD is downloading the music, thus the quantity demanded for the downloaded music increases substantially (Saada 2013). On the other hand, the price for the downloaded music falls as the consumers increase the access to internet and other download sites. The demand for the Universal Music’s CDs fall as the price level of the substitutes that is downloaded music falls. It can be thus inferred that the decision regarding reducing the price level was due to the decrease in the demand for the CDs.

4. During 2009 the price of song for downloading increased from 99¢ to $1.29.

As 1 dollar = 100 cents, $1.29 = 1.29*100 = 129¢

Now, the figures can be put in the following way:

When P1 = 99¢, Q1 = 33.

After increase in price of each song, the new price and quantity are

P2 = 129¢ and Q2 = 33 * (1 – 35 / 100) = 33 * 0.65 = 21.45 ~ 21

Therefore, price elasticity of demand for 33 songs is calculated as follows:

Ep = (dq / q*100) / (dp / p*100) = dq/dp* p/q = (Q2-Q1) / (P2-P1) * p/q = (21-33) / (129-99) * 99/33 = - 12/30 * 99/33 = - 1.2

The calculated price elasticity of demand shows that the Ep is negative as per the nature of it. Absolute value of the price elasticity of 33 songs is greater than one. Hence, it can be said that price elasticity of those songs are price elastic. It indicates that as quantity demanded for those songs decreases with the increase in price. Willingness of people for purchasing those songs decreases. The price elasticity of demand signifies that the proportional change in quantity demanded is more than proportional change in price of the downloaded songs (Phlips 2014).

5. Price elasticity of demand is given by percentage change in quantity demanded in response to the percentage change in the price of the product. = Ep

Ep = = 2. This can be written in another language. Chocolate sauce can be assumed as a normal good. Hence, there is a negative relation between quantity demanded and the price of chocolate sauce. As 5 percent fall in price of chocolate sauce induces quantity demanded to rise 10 percent, 1 percent fall in sauce causes quantity demanded to rise 10 / 5 = 2 percent. Therefore, it can be stated that demand price elasticity is 2 for chocolate sauce.

Cross price elasticity of demand is described as change in quantity demanded of a product in response to the change in price of the related product (Rios, McConnell and Brue 2013). Related product may be complementary or substitute. Here, chocolate sauce is the complementary product of the ice cream as the fall in price of chocolate sauce leads to the rise in the quantity demanded for ice cream.

Cross price elasticity = = = 3

References

Ataman, B., Pauwels, K., Srinivasan, S. and Vanhuele, M., 2016. Advertising’s Long-Term Impact on Brand Price Elasticity Across Brands and Categories. Available at SSRN.

Foxall, G.R., Yan, J., Oliveira-Castro, J.M. and Wells, V.K., 2013. Brand-related and situational influences on demand elasticity. Journal of Business Research, 66(1), pp.73-81.

Gordon, B.R., Goldfarb, A. and Li, Y., 2013. Does price elasticity vary with economic growth? A cross-category analysis. Journal of Marketing Research, 50(1), pp.4-23.

Hildenbrand, W., 2014. Market demand: Theory and empirical evidence. Princeton University Press.

Phlips, L., 2014. Applied Consumption Analysis: Advanced Textbooks in Economics (Vol. 5). Elsevier.

Rios, M.C., McConnell, C.R. and Brue, S.L., 2013. Economics: Principles, problems, and policies. McGraw-Hill.

Saada, A.S., 2013. Elasticity: theory and applications (Vol. 16). Elsevier.

Sneddon, I.N., 2013, October. Crack problems in the theory of elasticity. In Developments in Theoretical and Applied Mechanics: Proceedings of the Third Southeastern Conference on Theoretical and Applied Mechanics (p. 73). Elsevier.

Thimmapuram, P.R. and Kim, J., 2013. Consumers' price elasticity of demand modeling with economic effects on electricity markets using an agent-based model. IEEE Transactions on Smart Grid, 4(1), pp.390-397.

Walras, L., 2013. Elements of pure economics. Routledge.

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