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 $0.85 each. St. Vincent has been selling these souvenir sheets for $10.00 each and ordinarily sells about 55,000 units. To test the market, the postal service recently priced a new souvenir sheet at $11.00 and sales dropped to 45,000 units.

Required:

1a. Calculate the contribution margin for sale price of $10.00 each or $11.00 each?

	$10.00 Price	$11.00 Price
Unit sales
Sales
Cost of Good Sold
Contribution Margin

1b.Does the postal service of St. Vincent make more money selling souvenir sheets for $10.00 each or $11.00 each?

	$10.00
	$11.00

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.)

Price elasticity of demand

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

Profit- Maximizing price

Answer 1

1a) Contribution margin is the differnce between sales and variable cost of the goods sold. It is the portion of sales (left after covering variable cost) which can be used to cover fixed costs.It shows that higher the contribution margin higher will be the profits of the company.

The contribution margin is $5,03,250 and $4,56,750 when sales is of 55,000 units and 45,000 units respectively.

1b) The postal service of of St. Vincent make more money by selling at price of $10 because contribution margin is higher than selling at price of $11.

2) Price elasticity of demand measures the change in quantity demanded of a product due to change in price of product. The formula to calculate  price elasticity of demand is as follows:

Price elasticity of demand (e_d) = In(1+% change in quantity sold) / In(1+% change in price)

% change in price = [($11-$10) / $10 ]*100

% change in price = 10%

% change in quantity sold =[ (45,000 - 55,000) / 55,000] * 100

% change in quantity sold = -18.18%

Therefore, price elasticity of demand is as follows:

Price elasticity of demand (e_d) = In(1-18.18%) / In(1+10%)

Price elasticity of demand (e_d) = ln(0.8182)/ln(1.10)

Price elasticity of demand (e_d) = -0.0871 / 0.0414

Price elasticity of demand (e_d) = - 2.10

Therefore, the price elasticity of demand for the souvenir sheets is -2.10.

3) The profit-maximising price is calculated by marking up the variable cost. The variable cost is $0.85. The formula is as shown below

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

Profit-maximizing markup on variable cost = -1 / 1 + e_d

Profit-maximizing markup on variable cost = -1 / 1+ (-2.10)

Profit-maximizing markup on variable cost = -1 / -1.10

Profit-maximizing markup on variable cost = 0.91

Now, the profit-maximizing price will be calculated by using below formula:

Profit-maximizing price = (1 + Profit-maximizing markup) * Variable cost

Profit-maximizing price = ( 1 + 0.91) * $0.85

Profit-maximizing price = $1.6235

Therefore, the profit-maximizing price for souvenir sheets is $1.6235