Elasticity of demand: concepts and economic applications

Economics Problem

Coca-Cola in dispensers located on a golf course sells for $1.25 a can, and golfers buy

1,000 cans. Assume the course raises the price to $1.26 (assume a penny raise is possible) and sales fall to 992 cans.

Using the midpoint formula, what is the price elasticity of demand for Coke at these prices?

Assume the demand for Coke is a linear line. Would the elasticity of demand be elastic or inelastic at 75 cents a can?

At $2.00 a can?

It would be far too narrow and incorrect to think of the concept of price elasticity as something which is connected solely to a mathematical formula. Pricing is a strategy which is an aspect of marketing which should not be based on guesswork as it is something which communicate the value of a product. "Price elasticity is the measurement of how quantity demanded of a good will be affected by changes in its price. In other words, it's a way to figure out the responsiveness of consumers to fluctuations in price" (Guo, 2012). Essentially, price elasticity helps to determine the demand of a good when changes are made to its price.

Price Elasticity of Demand = (% Change in Quantity Demanded)/(% Change in Price)

As the result of the fact that the amount of something generally minimizes with the price, the price elasticity coefficient is negative 99% of the time. Generally, when the price elasticity of a given item is less than one, it's seen as something which is inelastic: "That means a one unit increase in price resulted in a less than one unit decrease in demand. On the other hand, if the coefficient is more than 1, the good is elastic. That means a unit increase in price will cause an even greater drop in demand" (Guo, 2012).

a. Price

elasticity of demand = [(992-1000) / { (992+1000)/2 } ] / [1.26-1.25)/

{ (1.26+1.25)/2 }

(-8/1992) / (0.1/2.51) = -0.10

Thus, based on the following principles, one can conclude that the good is inelastic.

b. As the demand for coke is a linear line.

Slope of line= (1.26 -1.25) / (992-1000) = -0.00125

Select equation of demand

Price -- 1.25 = -0.00125 (qty -- 1000)

Price = -0.00125 *qty +2.5

So, at 75 cents, demand = ( 0.75 -2.5) / ( -0.00125) = 1400

Price elasticity of demand = [(1400-1000)/{ (1400+1000)/2 } ] / [0.75-1.25) / { (0.75+1.25)/2 } ]

= (400/2400) / (-0.5/2.00) = -0.66

At 75 cents one can conclude that the demand for coke is inelastic.

c. As the demand for coke is a linear line.

Consider: Slope of line= (1.26 -1.25) / (992-1000) = -0.00125

Equation of demand as follows:

Price -- 1.25 = -0.00125 (qty -- 1000)

Price (approximately) = -0.00125 *qty +2.5

So, at $2 cents, demand = ( 2 -2.5) / ( -0.00125) = 400

Price elasticity of demand = [(400-1000)/{ (400+1000)/2 } ] / [2-1.25) / { (2+1.25)/2 } ]

= (-600/1400) / (0.75/3.25) = -1.04

At even $2 per can the math engaged in demonstrates that at such an increased price, the demand for coke is elastic.