Question

The price elasticity of demand for the output of a firm is -2 and the price elasticity of demand for the output of the entire industry is -0.5.

a. Calculate the Rothschild Index for this industry.

b. Suppose that a firm and industry prices increases by 5 percent. What is the relative impact on firm and industry sales?

Answer 1

Given that:

The price elasticity of demand for the output of a firm (ef) is -2.

And, the price elasticity of demand for the output of the entire industry (eI) is -0.5.

1. The Rothschild Index for this industry would be:

1. Price elasticity of demand is always negative as it shows the inverse relationship between he price of any product to its quantity demanded by the consumers. Therefore, while interpreting the price elasticity of demand, one can ignore the minus sign.

Hence, the price elasticity of demand for the output of a firm is – 2 that is greater than 1 (ignore minus sign), which implies that the demand in elastic. On the other hand, the price elasticity of demand for the output of the entire industry is -0.5 that is smaller than 1 (ignore minus sign), which implies that the demand in inelastic.

As a result, 5% increase in price of both, the firm and the industry, will lead to relatively larger decrease in the quantity demand of the product of the firm, and a relatively smaller decease in the quantity demanded of the product of the entire industry. Hence, there will be relatively larger impact on the firm’s sales than the entire industry’s sales.