Question

1.       A study of demand for coffee from Sarah’s Coffee, LLC resulted in the following regression equation:

                                                                                       (.005)    ( .047)     (.078)

where Q is the number of bags of coffee sold monthly, P is the price for a bad of Sarah’s coffee, Y is per capita income of the surrounding area, and P^P is the price of pastry at Sarah’s coffee shop. The p-value for each coefficient is shown in parenthesis. The R² = 0.46. Answer the following:

a)      Interpret the coefficient on coffee price P. What happens to the demand for coffee if coffee prices increase by $0.50?

b)     Interpret the coefficient on pastry price P^P. What happens to the demand for coffee if pastry prices increase by $2.00?

c)      Are pastries a substitute or complement to coffee? How do you know? Is coffee and normal or inferior good? How do you know?

d)     Which explanatory variables have real effects (statistically significant) on coffee demand? How do you know?

Answer 1

Since the equation is missing, I will guide you on solving the question and then you can relate with the equation.

a. The coefficient on the coffee price P depicts that when price of coffee rises by $1, the quantity demanded of coffee will fall by the coefficient of P mentioned in the equation. If coffee prices increases by $0.50, then demand for coffee will fall by Coefficient / 0.50 units of coffee.

b. The coefficient of the pastry will show the amount by which quantity demanded of pastry will change when price of pastry changes by 1 unit. The demand for coffee will change or decrease by - Coefficient of pastry * $2 when the price of pastry changes by 2 units.

c. Since the coefficient of the price of pastry is negative thus, pastry is a complement to coffee, thus. increase in price of pastry reduces the demand for coffee. If the coefficient of the Y or per capita income is positive then coffee is a normal good and if it is negative, then coffee is an inferior good.

d. The coefficients with a lower p value and high t values are significant. The coefficient with p value equal to 0.005 is statistically significant.