Exercise $11\mathrm{.}7$

Tennis Products, Inc., produces three models of high$-$quality tennis rackets. The following table contains recent information on the sales, costs, and profitability of the three models:

Model

Average Quantity Sold

Current Price

Total Revenue

Variable Cost Per Unit

Contribution Margin Per Unit

Contribution Margin$*$

$($Units$/$Month$)$

$($$$)$

$($$$)$

$($$$)$

$($$$)$

$($$$)$

A $30,00030900,00015\mathrm{.}0015450,000$

B $10,00035350,00018\mathrm{.}0017170,000$

C $20,00045900,00020\mathrm{.}0025500,000$

Total $$2,150,000$ $$1,120,000$

$*$Contribution to fixed costs and profits.

The company is considering lowering the price of Model A to $$27$ in an effort to increase the number of units sold. Based on the results of price changes that have been instituted in the past, Tennis Products$$ chief economist estimates the arc price elasticity of demand to be $-2\mathrm{.}5.$ Furthermore, she estimates the arc cross elasticity of demand between Model A and Model B to be approximately $0\mathrm{.}5$ and between Model A and Model C to be approximately $0\mathrm{.}2.$ Variable costs per unit are not expected to change over the anticipated changes in volume.

The proposal to cut the price of Model A to $$27$ would the total revenue from Model A from $$900,000$ to

$

$.$ The contribution margin of Model A would $.$

Now consider the entire line of tennis rackets. The price cut would the total revenue from $$2,150,000$ to

$

and the contribution margin from $$1,120,000$ to

$

$.$ Based on this analysis, the firm lower the price of Model A$.$