Question

Question 3: Pricing Multiple Product Versions (show all work)

Casey’s company produces two versions of a software program, “Advanced” and “Basic”.

There are 3 segments of customers, the Managers, Executives and Students, and the respective segment sizes are 2000, 1000 and 5000. The per-unit cost of producing the Advanced version is $20, while the per-unit cost of producing the Basic version is $10. The willingness to pay (WTP) for each version, by segment, is given as follows:

WTP (Managers) = $100 (Advanced) and $55 (Basic)

WTP (Executives) = $62 (Advanced ) and $45 (Basic)

WTP (Students) = $45 (Advanced ) and $30 (Basic)

If Casey sells only the Advanced version, what is the optimal price it should charge and the profits? (Answer: $45, Profit=$200K)

If Casey decides to sell both versions, what are the optimal prices it should charge for each version? What is the optimal profit of the company? Assume that customers will buy if consumer surplus is at least 0 and that they need at least $1 extra in consumer surplus to switch between product versions. (Answer: Basic @ $30, Advanced @ $74, Profit=$228K)

Answer 1

			Advanced	Basic
		Cost	20	10
	Segment Size
Managers	2000	Price	100	55
Executives	1000	Price	62	45
Students	5000	Price	45	30
	Segment Size	Profit from Advanced	Profit from Basic
Managers	2000	80	45
Executives	1000	42	35
Students	5000	25	20
If Price= 100, then only managers will buy and the profit will be 100-20, 80 per unit
2000*80			160000
If Price= 62, then managers and executives will buy and the profit will be 42 per unit
(2000+1000)*42			126000
If Price= 45, then everyone will buy and the profit will be 25 per unit
(2000+1000+5000)*25			200000
So Optimum Price is 25 which resukts maximim profit od 200000

(2)

If only Basic is sold
If Price= 55, then only managers will buy and the profit will be 45 per unit
2000*45			90000
If Price= 45, then managers and executives will buy and the profit will be 35 per unit
(2000+1000)*35			105000
If Price= 30, then everyone will buy and the profit will be 20 per unit
(2000+1000+5000)*20			160000
So Optimum Price is 30 which resuLts maximim profit of 160000
	Advanced Price	Profit	Basix Price	Profit
	100	160000	55	90000
	62	126000	45	105000
	45	200000	30	160000
So, to change product version from basic to advanced, the price of advance should be basix price + cost of advanced- 1(to change the choce)
Segment that will buy	Advanced Price	Profit	Basix Price	Profit
2000	74	108000	55	90000
2000	64	88000
3000	49	87000	45	105000
8000	45	200000	30	160000
From the above table, it is clear that $64 and $49 is not desirable for advanced version as it will give less profit than basic
So, if advanced price is 45, then profit will be 200000 and everyone will buy advanced
If Advanced Price is 74, then managers will buy advaned and remaining all will buy basic
SO Profit=(74-20)*2000+(6000*(30-10)			228000
Which is optimum price foe the company