Question

The postal service of St. Vincent, an island in the West Indies, obtains a significant portion of its revenues from sales of special souvenir sheets to stamp collectors. The souvenir sheets usually contain several high-value St. Vincent stamps depicting a common theme, such as the life of Princess Diana. The souvenir sheets are designed and printed for the postal service by Imperial Printing, a stamp agency service company in the United Kingdom. The souvenir sheets cost the postal service $0.75 each. St. Vincent has been selling these souvenir sheets for $8.00 each and ordinarily sells about 53,000 units. To test the market, the postal service recently priced a new souvenir sheet at $9.00 and sales dropped to 43,000 units.

Required:

1a. Calculate the contribution margin for sale price of $8.00 each or $9.00 each?

1b.Does the postal service of St. Vincent make more money selling souvenir sheets for $8.00 each or $9.00 each?

	$8.00
	$9.00

2. Estimate the price elasticity of demand for the souvenir sheets. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 4 decimal places.)

3. Estimate the profit-maximizing price for souvenir sheets. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Ans.

Contribution margin:-

Contribution margin is sales revenue minus the variable expenses. Contribution margin per unit of selling price per unit minus variable expenses per unit. The total contribution margin generated by an entity represents the total earnings available to pay fixed expenses and to generate a profit.

Ans. 1 a & b

	$8 Price	$9 Price
Unit sales	53,000	43,000
Sales	424,000	387,000
Less:- Cost of goods sold @ $0.75 per unit	39,750	32,250
Contribution margin	384,250	354,750

Hence, the postal service of St. Vincent make more profit selling souvenir sheet for $8 each.

Ans. 2

The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.

			Change	Change in %
Percentage change in quantity	53,000	43,000	-10,000	-20.8333%
Percentage change in price	$8	$9	$1	11.7647%
Price elasticity of demand				-1.7708

Working Notes:-

Price elasticity of demand=Percentage change in quantity/Percentage change in price.

Price elasticity of demand=[(Q2 - Q1)/(Q2 + Q1)/2] / [(P2 - P1)/(P2 + P1)/2]

Price elasticity of demand=[(43,000 - 53,000)/[(43,000 + 53,000)/2] / [($9 - $8)/[($9 + $8)/2]

Price elasticity of demand=-20.8333%/11.7647%=-1.7708

Therefore, price elasticity of demand is -1.7708.

Ans. 3

Calculation profit-maximizing price for souvenir sheets as follows:

The price elasticity of demand is 1.7708 and variable cost per unit is $0.75.

Profit maximizing price=(1 + Profit maximizing markup on variable cost) x variable cost per unit

Profit maximizing price=(1 + 1.30) x $0.75

Profit maximizing price=2.30 x $0.75

Profit maximizing price=$1.73

Working Notes:-

Profit maximizing markup on variable cost=-1/(1 + Price elasticity of demand)

Profit maximizing markup on variable cost=-1/(1- 1.7708)

Profit maximizing markup on variable cost=1.30

Hence, profit maximizing price is $1.73.