In Example 7.1, one demand function is linear and the other is called a constant elasticity demand function. Using data tables, show that the price elasticity in the linear demand function is not...

In Example 7.1, one demand function is linear and the other is called a constant elasticity demand function. Using data tables, show that the price elasticity in the linear demand function is not constant in price, and show that the price elasticity is constant in the constant elasticity demand function.

EXAMPLE 7.1 PRICING DECISIONS AT MADISON

The Madison Company manufactures and retails a certain product. The company wants to determine the price that maximizes its profit from this product. The unit cost of producing and marketing the product is $50. Madison will certainly charge at least $50 for the product to ensure that it makes some profit. However, there is a very competitive market for this product, so that Madison’s demand falls sharply when it increases its price. How should the company proceed?4

Objective To use a demand function in a nonlinear model to find the price that maximizes the company’s profit.

WHERE DO THE NUMBERS COME FROM?

Cost accountants should be able to supply the unit cost. Historical data on demands and prices of the product are needed to estimate the demand function, as discussed next.