Question

Based on previous studies, you believe the linear demand function for your good is: QXd = 20,000 -10PX + 7PY + 0.5M + 250AX where PX is the price of X PY is the price of a related good Y M is the income of the buyers in the market and AX is advertising for X. The good currently sells for $25, the related good sells for $40, the company is spending $50 on advertising, and average consumer income is $25,000.

The marketing manager wants to know the own price elasticity and income elasticity for this good. Compute them. The marketing manager also wants to know how much sales will increase if she increases the advertising budget by 10%. Compute this from the information given.

Answer 1

QXd = 20,000 -10PX + 7PY + 0.5M + 250AX

Substituting values of AX;

QXd = 20,000 -10(25) + 7(40) + 0.5 (25,000)+ 250(50)

= 20,000 - 250 + 280+ 12,500 +12,500

=45,030

Price elasticity = (dQ/dP) (P/Q)

dQ/dP = - 10

Ed = - 10(25/45,030)

=0.00555

Income Elasticity = dQ/dI (I/Q)

dQ/dI = 0 .5

Ei = 0.5 (25,000/45,030)

= 0.277

Elasticity of Ads = dQ/d A *(A/Q)

dQ/dA = 250

EA = 250*(50/45,030)

= 0.277

Hence ,10 % rise in advertisement expenditure will lead to 2.77 % rise in sale. (10*.277)