Suppose that an economist has been able to gather data on the relationship between demand and price for a particular product. After analyzing scatter plots and using economic theory, the economist decides to estimate an equation of the form Q = aPb, where Q is quantity demanded and P is price. An appropriate regression analysis is then performed, and the estimated parameters turn out to be a = 1000 and b = -1.3. Now consider two scenarios:
(1) The price increases from $10 to $12.50;
(2) The price increases from $20 to $25.
a. Do you predict the percentage decrease in demand to be the same in scenario 1 as in scenario 2? Why or why not?
b. What is the predicted percentage decrease in demand in scenario 1? What about scenario 2?
Be as exact as possible.