Suppose that the demand function of Firm A is given by Q = f(P ).Furthermore we know that the elasticity of demand is −4 when P = 14. Suppose that the demandfunction of Firm B is given by Q = 6 f(P ) (note that this is 6 times the demand of Firm A forevery price level). What is the elasticity of demand for Firm B equal to when P = 14.
Question
Suppose that the demand function of Firm A is given by Q = f(P ).Furthermore we know that the elasticity of demand is −4 when P = 14. Suppose that the demandfunction of Firm B is given by Q = 6 f(P ) (note that this is 6 times the demand of Firm A forevery price level). What is the elasticity of demand for Firm B equal to when P = 14.
Solution
The elasticity of demand for Firm B at P = 14 would also be -4. This is because the elasticity of demand is a measure of the responsiveness of quantity demanded to a change in price, and it is not affected by a simple scaling of the demand function. In other words, multiplying the demand function by a constant (in this case, 6) does not change the percentage change in quantity demanded for a given percentage change in price, which is what the elasticity measures. Therefore, the elasticity of demand for Firm B at P = 14 is the same as that for Firm A, which is -4.
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