4 Given the following demand function Q 50P1310 9A02 Where

4) Given the following demand function: Q = 50P-1.310 9A0.2 Where: P: price in US $ I: Disposable income (SUS) Q: monthly quantity demanded A: Advertising exp. (S000 US) a) What is the price elasticity of demand (use calculus)? b) Wil an increase in price increase or decrease the amount spent on this product? c) What is the income elasticity of demand?

Solution

a). Price elasticity of demand = dQ/dP = -1.3(50)P^-2.3 I^0.9 A^0.2 = - 65P^-2.3 I^0.9 A^0.2

b). Yes, an increase in price will decrease the amount spent on this product. This is because, price and quantity are negatively correlated, and a change in price reduces the quantity demanded in more than proportion.

c). Income elasticity of demand = 0.9(50) P^-1.3 I^-0.1 A ^0.2