Question

We consider data on weekly sales for coffee. Data has n = 18 weeks of coffee sales in Q units, the deal rate (D = 1 for usual price, = 1.05 in weeks with 5% price reduction, and = 1.15 in weeks with 15% price reduction), and advertisement (A = 1 with advertisement, = 0 otherwise)

Model = log(Q) = B0 + B1D + B2A + u

estimate by OLS -> log(Q) = 0.701 (0.415) + 0.756D (0.091) + 0.242A (0.110)

Standard error is in brackets

1. Based on the estimated coefficients, a 10% price reduction is associated with a A)75.6% B)7.56% C)0.756% increase in sales

2. Based on the estimated coefficients, the efect of advertisement is approx the same as a A)5% B)15% C)30% D)45% price reduction

Answer 1

1).

Consider the given problem here the estimated regression model is given below.

=> Log(Q) = 0.701 + 0.756*D + 0.242*A, where “Q=weekly sales for coffee”. For usual price “D=1”, if the price reduced by 10% implied “D=1.1”, => change of “D” is “0.1”, => the relative change of sales is “0.756*0.1 = 0.0756”. So, the percentage change in sales is “0.0756*100 = 7.56%”. The correct answer is “B”.

2).

Here “A=1” with advertisement and “=0” otherwise. The change of “A” is “1”, => the relative change in sales is “0.242”. Now, let’s assume price reduced by 30%, => the relative change in sales is “0.756*0.3 = 0.2268”. So, approximately the effect of advertisement is equivalent to the 30% reduction in price. So, the correct answer is “C”.