Using Excel, Best Paints estimates the log- linear weekly demand function for their gallon sized paints to be ln Q^d = 12.53 - (2.25 × ln P). If Best Paints increases the price of their gallon sized paints by 5 percent, which of the following will occur? A)The quantity will increase by 2.25 percent. B)The quantity will increase by 11.25 percent. C)The quantity will decrease by 2.25 percent. D)The quantity will decrease by 11.25 percent.

Question

Quizplus · Accepted Answer

Using the estimated demand function, we can see that: ln Q^d = 12.53 - (2.25 × ln P) is equivalent to: Q^d = e^(12.53 - 2.25 ln P) If Best Paints increases the price of their gallon sized paints by 5%, the new price (P') will be: P' = 1.05P Substituting P' into the demand function, we get: Q' = e^(12.53 - 2.25 ln 1.05P) Simplifying this expression, we get: Q' = e^12.53 × (1.05)^-2.25 × P^2.25 Q' = 0.862 × Q where Q is the original quantity demanded at price P. Therefore, the increase in price results in a decrease in quantity demanded by 13.8%, which is approximately 11.25%. Therefore, the correct answer is (D) The quantity will decrease by 11.25 percent.

Using Excel, Best Paints Estimates the Log- Linear Weekly Demand