Question

You are a distributor for Mainteance, repair and operation items. Volumes have declined over the past 12 months due to aggressive pricing by a new competitor. Consider the following representative product, product x, which you purchase from your major supplier. Your firm buys product X from the supplier for $45/unit, and your firm incurs a cost of $20/unit for handling and shipping to the customer. you estimate that market demand/week decreases by 2 units for every $1 increase in price. Your firm sells at $77.50 per unit (i.e. Gross Margin = 77.50 - 45 - 20 = 12.50) and at this selling price, demand is 25 units/week.

You decide to approach your supplier with a proposal for a new 12-month contract. The terms are:

1) Supplier slashes unit prices by 55.55% (selling price for the representative product drops from $45/unit to $20/unit, which you estimate to be the suppliers variable cost) and

2) your firm agrees to pay a fixed monthly fee that will slightly more than offset (by 10%) the price reduction assuming volumes remain unchanged.

As an example, the price reduction on product x based on the current volume of 25 units/week would cost the supplier 25 X (45-20) = 625//week, so the fixed fee associated with this product would be $625 plus 10%, or $687.50/week)

If the supplier agrees to your contact, you will reduce your selling price from $77.50 to $65. Answer the following questions

1) What is the projected demand per week of product X at this new selling price p=$65 (hint find the demand function)

2) What is your firms' current gross profit per week for product X?

3) What is your firms' projected gross profit per week less than the fixed fee for product x under the proposed contract?

Answer 1

1. The demand function is graphed below as per data given:

	p	q
Expected	65	50
Current	77.5	25
	78.5	23
	90	0

2. The current gross profit = no. of units sold X gross margin per unit

= 25 X 12.5 = $312.50

3. Expected gross profit is computed below:

	p	q	Total Revenue	Fixed Cost	Payment to supplier @ $20	Handling @ $ 20	Gross Profit
			TR = p X q	FC	S	H	TR -FC-S-H
Expected	65	50	3250.00	687.50	1000	1000	562.5

So, there is an increase in profits due to the new arrangement.