Chapter AA, Problem 4P

To determine

Concept Introduction:

Price Electricity of demand: The price elasticity of demand is the measure of the change in the quantity sold or demanded of a product or service in relation to its price change. It is represented in percentage terms.

Profit-maximizing price: It is a process that an entity employs to find out the best output and price level in order to maximize its profit. Profit-maximizing price is the price at which the profit is maximized at a given quantity of output and where the marginal revenue is equal to the marginal cost.

(1)

The selling price at which the postal service of St. Vincent makes more money.

Explanation of Solution

The postal service of St. Vincent makes more money selling the souvenir sheets for $7.00 each. Calculations are given below:

	$7.00 Price	$8.00 Price
(A) No of sheets sold	100,000	85,000
(B) Selling price per sheet	$7.00	$8.00
(C) Variable cost per sheet	$0.80	$0.80
Total Sales (A) x (B)	$700,000	$680,000
Less : Variable cost (A) x (C)	$80,000	$68,000
Contribution margin	$620,000	$612,000
Less: fixed cost	$675	$675
Net Income	$1,515	$1,805.40

To determine

(2)

To compute:

The price elasticity of demand for the souvenir sheets.

Explanation of Solution

Price elasticity of demand for the souvenir sheets is -1.19 and is computed as below.

$Priceelasticityofdemand=\%ChangeinQuantityDemanded÷\%Changeinprice$

$\begin{array}{l}\begin{array}{l}A)\%Changeinquantitydemanded\\ =\left(100,000-85,000\right)/\left(\left(100,000+85,000\right)/2\right)\end{array}\hfill \\ =15,000/92,500\hfill \\ =16.22\%\hfill \\ \begin{array}{l}B)\%Changeinprice\\ =\left(\$7.00-\$8.00\right)/\left(\left(\$7.00+\$8.00\right)/2\right)\end{array}\hfill \\ =\$-1.00/\$7.50\hfill \\ =-13.67\%\hfill \\ \hfill \\ Priceelasticityofdemand=16.22\%/-13.67\% =-1.19\hfill \end{array}$

To determine

(3)

To compute:

The profit-maximizing price for souvenir sheets.

Explanation of Solution

Profit-maximizing price for souvenir sheets is $5.01 per souvenir sheet. Calculations are given below.

Price elasticity of demand = −1.19

Variable cost per unit = $0.80

$\begin{array}{l}Profit-maximizingprice=\left\{Priceelasticityofdemand/\left(1+Priceelasticityofdemand\right)\right\}\times variablecostperunit\hfill \\ =\left\{1.19/\left(1+\left(-1.19\right)\right)\right\}\times 0.80\hfill \\ =\$5.01 \hfill \\ Profit-maximizingpriceis\$\mathrm{5.01.}\hfill \end{array}$

To determine

(4)

To compute:

The profit-maximizing price for souvenir sheets if the variable cost is $1.00

Explanation of Solution

The postal service of St. Vincent should charge $6.26 per sheet if the variable cost is $1.00 per sheet.

$\begin{array}{l}Profit-maximizingprice=\left\{Priceelasticityofdemand/\left(1+Priceelasticityofdemand\right)\right\}\times variablecostperunit\hfill \\ =\left\{1.19/\left(1+\left(-1.19\right)\right)\right\}\times 1.10\hfill \\ =\$6.26\hfill \end{array}$