Question

1. Based on previous studies, you believe the linear demand function for your good is:

                                Q_X^d = 20,000 -10P_X + 7P_Y + 0.5M + 250A_X

                where P_Xis the price of X

                                P_Y is the price of a related good Y

                                M is the income of the buyers in the market

                                and A_X 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.

2. 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

1) Demand function for good X is given by Q_X^d = 20,000 -10P_X + 7P_Y + 0.5M + 250A_X

We are also given that Px is 25, Py is 40, M is 25000 and Ax is 50. Given this, we find that the quantity

demanded

at these values is arrived at Qxd = 20000 - 10*25 + 7*40 + 0.5*25000 + 250*50 = 45030 units

Now find the own price elasticity = ed = own price coefficient x Px/Qx = -10 x 25 / 45030 = -0.0055. Since its

absolute value is less than 1, the demand is inelastic.

Income elasticity = Income coefficient x M/Qx = 0.5 x 25000/45030 = 0.277. Since the value is positive, good X

is a normal good

2) Advertising elasticity = Advertising coefficient x Ax/Qx = 250 x 50/45030 = 0.277

If advertising budget is increased by 10%, sales will increase by 10% x 0.277 = 2.77%.