Question

As you know we are the only gourmet nut producer in the south. We are known not only for the quality of our nuts, but also for our unique seasonings.Right now we are charging a price of $5 per bag for all of our nuts, no matter which brand is more popular. This includes our cinnamon-cayenne roasted almonds, maple-chipotle roasted pecans, and honey-mesquite roasted cashews. However, we feel that our generic approach to pricing is un-optimal and outdated given the difference in demand for each nut. Our sales analytics team has supplied us with the following estimates of demand for our different nuts: (Almonds-A, Pecans-P, and Cashews-C)QA = 1,200 – 150PAQP = 3,000 – 100PPQC = 2,400 – 200PCThe sales department has also informed us that our costs are constant across the different nuts at $2 per bag. Please review our current pricing strategy and let us know if we have anyway of customizing prices across the different nuts. Ultimately we are after ways of increasing our profits, so that is objective number one.

Answer 1

QA - Quantity of Almonds, PA- Price of Almonds

Q P - Quantity of Pecans, PP- Price of Pecans

QC - Quantity of Cashews, PC- Price of Cashews

Using the above notations, I am summarising the outcomes here -

	Almonds	Pecans	Cashew
Demand Function	QA = 1,200 – 150 PA	Q P = 3,000 – 100 PP	QC = 2,400 – 200 PC
Revenue Function Q x P	QA x PA = 1,200 PA– 150(PA) 2	Q P X PP = 3,000 PP– 100(PP) 2	QC X PC = 2,400 PC – 200 (PC)2
Costs	$2	$2	$2
Profit Function	1,200 PA – 150(PA) 2 - 2	3,000 PP – 100(PP) 2 - 2	2,400 PC – 200 (PC)2- 2
Differentiating Profit function w.r.t Price and setting the equation = 0	1200-300 PA=0	3000 - 200 PP =0	2400-400 PC=0
Profit Maximising Price Obtained	$4	$15	$6
Price Charged now	$5	$5	$5

Comparing the last two rows I have based the pricing strategy on the gourmet producer's objective of Profit maximisation.

Price of Almonds should be brought down by $1 to arrive at $4.

Price of Pecans be increased by $10 to arrive at $15.

Price of Cashews be increased by $1 to arrive at $6.

Therefore based on the analysis above customisation of prices of different nuts should be done accordingly.