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## The midpoint formula 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 formula is used in calculating the arc elasticity. It gives the elasticity of one variable with respect to another variable between two points situated in the demand curve. The formula for price elasticity of demand is ((Q2-Q1) / ((Q2+Q1) / 2)) / ((P2-P1) / ((P2+P1) / 2)).

Figure 1: Two points on the demand curve for calculating mid point arc elasticity.

Source: As created by the author.

In the figure above, P1 and Q1 are the initial level of price and quantity in the demand curve. Similarly, P2 and Q2 are the next level of price and quantity, which comes due to the change in price and commodity. According to Nelson (2013), the midpoint elasticity is calculated from these two points. It is calculated by dividing the variable by the midpoint value.

The other ways of calculating the price elasticity of demand are:

• Total expenditure Method
• Revenue Method
• Point Elasticity of Demand
• Proportionate method

## Advantages of the midpoint formula over other methods

According to Mankiw (2013), the advantage of using the midpoint formula is that wherever the two points on the demand curve might be, that does not affect the value of the price elasticity of a product’s demand. The points can be situated at any places of the demand curve, but the value will remain unaffected. According to Baumol and Blinder (2015), instead of taking the starting points in the curve, it is calculated by dividing the variable by the midpoint values. This makes the mid-point elasticity method more reliable than the other methods.

2. The key determinants of the price elasticity of demand for a product are as follows:

1. The type of the commodity determines the price elasticity. A necessary good does not show the same price elasticity value as a luxury good.
2. As stated by Wang (2016), the substitute goods available for a commodity determine the price elasticity of a good. If the good can be easily substituted by other goods, then price elasticity will be closer to one. If the available substitutes are less numbered, the price elasticity will be closer to zero, as the good cannot be replaced by other commodities during an increase in price.
3. The duration of the change of price also plays a key determining role for the price elasticity of demand for the good. In the case of a long time of increased price, the consumers will prefer using the substitute goods.
4. Importance of a commodity to the consumers is a key determinant of the price elasticity of demand for a product. As stated by Varian (2014), a necessary good is always more important to a consumer than a luxury good.
5. Consumers’ level of income also determines the price elasticity of demand. If a consumer have low income level, then an increase in price will affect his demand pattern and he will shift to a substitute good. On the other hand, if the consumer’s income is high, he will be less affected by the change in price.
6. Brand loyalty of the consumers also plays an important role here. A loyal consumer will stick to the good, even when a change in price occurs.

3. The quantity demanded has been changed by 30 percent or 3/10. The price has been changed by \$21 - \$15 = \$6. Hence, the percent change in price is (15-21) / [1/2 (15 + 21)] = 1/3. Now the price elasticity of demand is Ed.

Ed = {(Q1-Q2) / [1/2 (Q1+Q2)]} / {(P1-P2) / [1/2 (P1 + P2)]}. Here, Q1 is the initial quantity with P1 being the initial price. Q2 is the new level of quantity and P2 is the new level of price.

Now putting the respective values, Ed becomes Ed = (3/10) / (1/3) = 9 / 10 = 0.9. Here the Ed is less than 1. Hence, the demand is inelastic.

This shows the change in price has no effect on the demand of CDs of Universal Music. According to Toutkoushian and Paulsen (2016), this can be caused by Veblen effect or brand loyalty. Hence, the price decision can be in the favour of the company, where the company can increase the price, but due to the inelastic demand curve, the demand for the CDs of Universal Music remains the same. This way, the increased price level will only mean more revenue.

4. iTunes increased the price of 33 songs in the May of 2009. The price increased from 99¢ per download to \$1.29 per download. Hence, the change in the price level of per download of 33 songs is as follows (\$1.29-\$0.99) = \$ 0.3. This means, the total change in the level of price was (33*0.3) = \$9.9. Therefore, the percentage change in the level of price per download was Pd = (P1-P2) / [1/2 (P1 + P2)]. Here, P1 and P2 are the initial and changed level of price. Pd = (\$0.99-\$1.29) / [(1/2)*(\$0.99 + \$1.29)], or 0.2632. The percentage change in quantity demanded for all 33 songs are given by 35% = 35/100 = 0.35. Hence, the price elasticity of demand Ed for the songs is = {(Q1-Q2) / [1/2 (Q1+Q2)]} / {(P1-P2) / [1/2 (P1 + P2)]}. Putting the values in Ed, the elasticity can derived as, 0.35/0.2632 = 1.3.

## Determinants of Price Elasticity of Demand

As stated by Gordon, Goldfarb and Li (2013), here, the price elasticity of demand is greater than 1. This means the demand for the 33 songs are elastic. Hence, an increase in the price level will result in decrease in the quantity demanded and vice versa. According to Cavalli and Naimzada (2015), this follows the basic law of demand, which states that an increase in the price will cause a decrease in the quantity demanded of a good, assuming all other things remaining constant.

5. Given that, 5 per cent fall in the price of chocolate sauce increases the quantity of chocolate sauce demanded by 10 per cent. Hence, own price elasticity for chocolate sauce is as given below:

Price Elasticity of demand is given by =

= 10% / 5% = 2.

The price elasticity for demand of chocolate sauce is 2, which is greater than 1, i.e. Ed > 1. Hence, it is elastic. As stated by Thimmapuram and Kim (2013), now any decrease in the price level will increase the demand, and an increase in the price level of the good will decrease the demand for chocolate sauce.

The cross price elasticity of a product is as given by:

= 15% / 5% = 3

Therefore, the cross price elasticity for ice cream is 3, which is greater than 1. Hence, the ice cream is elastic with respect to the price of chocolate sauce. According to Rios, McConnell and Brue (2013), that means a fall in the price of the chocolate sauce will increase the demand for the ice cream, and vice versa. This only makes ice cream and chocolate sauce complements. The reason behind this scenario is chocolate sauce is used with ice cream. It improves the taste of the ice cream. Hence, makes it a complementary product for ice cream.

References:

Baumol, W.J. and Blinder, A.S., 2015. Microeconomics: Principles and policy. Cengage Learning.

Cavalli, F. and Naimzada, A., 2015. Effect of price elasticity of demand in monopolies with gradient adjustment. Chaos, Solitons & Fractals, 76, pp.47-55.

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.

Mankiw, N.G., 2013. Elasticity and its Application

Nelson, J.P., 2013. Meta-analysis of alcohol price and income elasticities–with corrections for publication bias. Health economics review, 3(1), pp.1-10.

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

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.

Toutkoushian, R.K. and Paulsen, M.B., 2016. Demand and Supply in Higher Education. In Economics of Higher Education (pp. 149-198). Springer Netherlands.

Varian, H.R., 2014. Intermediate Microeconomics: A Modern Approach: Ninth International Student Edition. WW Norton & Company Thirlwall, A.P., 2014. The balance of payments constraint as an explanation of the international growth rate differences. PSL Quarterly Review, 32(128).

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