Question

4) Given the following demand function: Q = 50P-1.310.9 40.2 Where: Q: monthly quantity demanded A: Advertising exp. (S000 US) : price in I: Disposable income (SUS) a) What is the price elasticity of demand (use calculus)? b) Will an increase in price increase or decrease the amount spent on this product? c) What is the income elasticity of demand?

Answer 1

Q = 50 p^-1.3 I^0. 9 A^0. 2 price elasticity of demand, e_a = partial differential Q/partial differential P times p/Q partial differential Q/partial differential P = 50 (-1. 3) p^-1. 3 -1 I^0. 9 A_0. 2 = -65 p^-2.3 I^0. 9 A_0. 2 e_alpha = -65 p^-2. 3 I^0. 9 A^0. 2 times p/50 p^-1. 3 I^0. 9 A^0. 2 = -65/50 = -1. 3 e_alpha > 1, it implies that consumers are respond to changes in price. Increase in price will decrease the amount spent the good. Income elasticity, e_I = partial differential Q/partial differential I times I/Q partial differential Q/partial differential I = 50 times 0. 9 times p^-1. 3 I^0. 9 - 1 A^0. 2 = 45 p^-1. 3 I^-0. 1 A^0. 2 e_I = 45 p^-1. 3 I^-0. 1 A^0. 2 times I/m50 p^-1.3 I^