Question

A3 Own Price Elasticity Question 1: The demand for Wanderlust Travel Services (good X) is estimated to be Qx = 22000-2.5Px + 4PY-1 M 1 .5Ax. Where Qx is the quantity of good X, Px is the price of good X, Py is the price of good Y, M is consumer income, and Ax is the amount of advertising spent on X. Suppose the price of good X is $450, the price of good Y is $40, the company uses 3,000 units of advertising, and consumer income is $20,000. a. Calculate the own price elasticity of demand at these values of prices, advertising, and income. b. Is demand elastic, inelastic, or unit elastic? c. How will your answers to parts a and b change if the price of Y increases to $50? Answer to Question:

Answer 1

Answer : By putting all given values in Qx we get,

Qx = 22000 - (2.5 * 450) + (4 * 40) - (1 * 20000) + (1.5 * 3000)

=> Qx = 22000 - 1125 + 160 - 20000 + 4500

=> Qx = 5535

a) Own price elasticity of demand (Ed) = ( $\partial$Qx / $\partial$Px) * (Px / Qx)

=> Ed = - 2.5 * (450 / 5535)

=> Ed = - 0.203

Therefore, the own price elasticity of demand is - 0.203 .

b) As here Ed = - 0.203 < 1, hence the demand is inelastic.

c) Now, if Py = $50 then,

Qx = 22000 - (2.5 * 450) + (4 * 50) - (1 * 20000) + (1.5 * 3000)

=> Qx = 22000 - 1125 + 200 - 20000 + 4500

=> Qx = 5575

Now,

Ed =  - 2.5 * (450 / 5575)

=> Ed = - 0.202

Therefore, here the own price elasticity of demand is - 0.202.

As here Ed = - 0.202 < 1, hence the demand is inelastic.

Thus, the answer of (a) changes when Py is $50 where the answer of (b) remains unchanged.