The demand for Wanderlust Travel Services (X) is estimated to be Q x = 22,000 -

Question

The demand for Wanderlust Travel Services (X) is estimated to be Qx = 22,000 - 2.5Px + 4Py - 1M + 1.5Ax, where Ax represents the amount of advertising spent on X and the other variables have their usual interpretations. Suppose the price of good X is $450, good Y sells for $40, the company utilizes 3,000 units of advertising, and consumer income is $20,000.

a. Calculate the own price elasticity of demand at these values of prices, income, and advertising.
b. Is demand elastic, inelastic, or unitary elastic?

c. Calculate income elasticity of demand. Is this good normal or inferior good?

d. If consumer income is expected to increase by 4% next year, by how much the price needs to change in order to maintain the same number of customers?

e. Calculate cross price elasticity. Are goods X and Y complements or substitutes?

f. Assume that you are thinking about changing the price of good X. Rewrite the demand function for good x in terms of Q and Px (you just have to evaluate your demand function at Py, M, and Ax, so it looks like Q = a-bPx)

g. Find a total revenue function and find the quantity that maximizes total revenue. At this quantity, is demand elastic, inelastic, or unit elastic? Please make sure to show all calculations supporting your answer.

*** Answer shoud definitely include last 3 question, though the best answer would include all ***

Explanation / Answer

a) own price elasticity of demand is given by ((dQ/Q)/(dPx/Px))*100 now evaluating this at given values gives out elasticity=-20% or -0.2

b)INELASTIC

elasticity of 0.2(modulus) signifies that there is not much change in demand for a given change in price so the demand is inelastic

c)income elasticity of demand is given by ((dQx/Qx)/(dM/M)) calculated at given values gives out elasticity= (-3.61) which is negative signifies that the demand for good decreases if the income increases which is for INFERIOR goods.

d)320

In the case of this good if income increases then demand decreases so in order to maintain the demand at same level we have to decrease the price of this good, if income increases by 4% then price should be decreased by $320(can be obtained by just equating 2.5*x=800(change in demand due to income change))

e)cross price elasticity is ((dQx/Qx)/(dPy/Py))=0.029

positive signifies that demand of X increases given an increase in price of Y, meaning X and Y are SUBSTITUTES.

f)Q=6660-2.5Px

if we need to change the price of X then we have to keep all other factors constant and find the function depending only on price of X

g)total revenue function is given T.R=Px*Qx=6660Px-2.5*(Px)^2 (denote this function by R)

for maximizing revenue (dR/dPx)=0 => Px=1332 and Qx=6660-(2.5*1332)="3330"

at this quantity demand elasticity is -0.33 which means it is INELASTIC

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