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) Correct option is B = 7.56%

As per the estimated coefficients, a 1% reduction in the deal rate will lead to a 0.756%  increase in sales. This tells a 10% reduction in deal rate leads to a 7.56% increase in sales.

Alternatively, a 1 unit reduction in the deal rate will lead to a 0.756 unit increase in sales. This means a 100% reduction in deal rate leads to a 75.6 % increase in sales. Dividing this throughout with 10 gives a 10% reduction in deal rate leading to a 7.56% increase in sales.

2) Correct option is C= 30%

As per the estimated coefficients, 1 unit of advertisement leads to a 0.242 unit increase in sales. This means advertisement leads to a 24.2% increase in sales.

From above, a 1% price reduction leads to a 0.756% increase in sales. For a 24.2% increase in sales, price should be reduced by 24.2%/0.756% which is equal to 32.01 %. This is closest to 30%.