Price change to maximize profit. A business sells n products, and is considering changing the price...

Price change to maximize profit. A business sells n products, and is considering changing the price of one of the products to increase its total profits. A business analyst develops a regression model that (reasonably accurately) predicts the total profit when the product prices are changed, given by Pˆ = βT x + P , where the n-vector x denotes the fractional change in the product prices, xi = (pnew − pi)/pi. Here P is the profit with the currentiprices, Pˆ is the predicted profit with the changed prices, pi is the current (positive) price of product i, and pnew is the new price of product i.

(a) What does it mean if β3 < 0? (And yes, this can occur.)
(b) Suppose that you are given permission to change the price of one product, by up to 1%, to increase total profit. Which product would you choose, and would you increase or decrease the price? By how much?
(c) Repeat part (b) assuming you are allowed to change the price of two products, each by up to 1%.

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milcah answered 8 months ago

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