Question

Kenobi Tool Company has recently patented a new woodworking tool: a plasma-powered sabre saw. This tool cuts wood with a beam of plasma-energy, making an exact cut with a perfect finish. Given their patent, Kenobi is a monopolist seller.

Kenobi is now deciding on the final design specifications of the product. Specifically, Kenobi could product either a Heavy duty version of the tool or a Light duty version. They could sell only one of the two versions, or they could choose to offer both versions. The marginal costs (per-unit manufacturing costs) of the two versions are given in the table.

In addition, market research shows that Kenobi's customer base boils down to two distinct kinds of buyers: Professionals and Hobbyists. Compared to Hobbyists, Professionals are willing to pay more for the product and have a stronger preference for the heavy duty version. Specifically, assume that the Reservation Prices (RP) for buyers in these two segments are as in the following table.

	Heavy version	Light version
Professional's RP:	$200	$150
Hobbyist's RP:	$120	$120
Marginal cost/unit:	$100	$60

Assume that the two market segments are of equal size.(You may assume that there is exactly one Professional buyer in the marketplace, and exactly one Hobbyist buyer when doing your calculations.) Each buyer is interested in buying only one saw, and buys whichever one gives the highest (non-negative) surplus. What product line and prices should Kenobi implement? To address this, answer the following questions.

(1a.) If Kenobi were to sell only the Heavy version of the saw, what price should it charge to maximize total profit? (Hint: Do not forget to consider manufacturing costs. Answer must be justified with analysis.) (2 points)

(1b.) If Kenobi were to sell only the Light version, what price should it charge to maximize total profit? (2 points)

(1c.) If Kenobi were to offer both versions of the saw (at two different prices), what is the highest profit they could earn using this approach? (Remember that each buyer only wants one saw.) (3 points)

(1d.) Besides the above product, Kenobi Tool Company also sells a patented, plasma-based tile cutter. Based on historical sales data, Kenobi has estimated the demand curve for this product to be D(p) = 2000 - p. What is the elasticity of this demand curve at a price of p=1500? (3 points)

price discrimination is possible

Answer 1

1a) If Kenobi were to sell only the Heavy version of the saw it should charge $200 to maximize total profit. Reason- Profit=$200-$100=$100 This is the maximum profit it can yield. If suppose it charges $120 as per Hobbyist's RP,profit would have been=2x120-200=$40, , which is less than $100.

1b) If Kenobi were to sell only the light version of the saw it should charge $120 to maximize total profit. Reason- $240-$120=$120 This is the maximum profit it can yield. If suppose it charges $150 as per Professional's RP,profit would have been=150-60=$90, which is less than $120.

1c) Kenobi would charge $200 for  the Heavy version of the saw and $120 for the light version of the saw. Profit would be ($200-$100)+ (120-60)=$160

1d) Elasticity= (dq/dp)*(p/q)= -1*(1500/500)=-3

The elasticity of this demand curve at a price of p=1500 is -3.