Question

A barber charges $12 per haircut and works Saturday through Thursday. He can perform up to 20 haircuts a day. He currently performs an average of 12 haircuts per day during the weekdays (Monday through Thursday). On Saturdays and Sundays, he does 20 haircuts per day and turns 10 potential customers away each day. These customers all go to the competition. The barber is considering raising his prices on weekends. He estimates that for every $1 he raises his price, he will lose an additional 10% of his customer base (including his turnaways). He estimates that 20% of his remaining weekend customers would move to a weekday in order to save $1, 40% would move to a weekday in order to save $2, and 60% would move to a weekday in order to save $3. Assuming he needs to price in increments of $1, should he charge a differential weekend price? If so, what should the weekend price be? (Assume he continues to charge $12 on weekdays.) How much revenue (if any) would he gain from his policy?

Solve using Excel

Answer 1

Number of customers on weekdays = 12

Number of weekdays = 4 (Friday not included as per question)

Hence total number of customers in weekdays = 12 * 4 = 48

Number of customers on weekends = 20

Number of weekends days = 2

Hence total number of customers in weekdays = 20 * 2 = 40

Hence total customer base = 88

The revenues for each of the barber's strategies is calculated in excel as follow:

Please note the notations for clear understanding.

Current Price (in $)	Pricing increase(in $)	Updated price(in $)	Customers base lost due to hike in price (in %)	Current customer base		Customer base lost		Estimates of customer transfer	Transferred customers from weekends to weekdays	Updated customer base		Revenue generated per week(in $)
				Weekdays	Weekends	Weekdays	Weekends			Weekdays	Weekends
C	P	UP = C + P	P	W	WD	Wl = W * P	WlD = WD * P	E	T = E*WlD	UW = W + T -Wl	UWD = WD - WlD	R = (UW + UWD)* UP
12	1	13	10.00%	48	40	5	4	20.00%	8	51	36	1131
12	2	14	20.00%	48	40	10	8	40.00%	13	51	32	1162
12	3	15	30.00%	48	40	15	12	60.00%	17	50	28	1170

Note: An "IF" formula is used to ensure that the barber can operate in his capacity of 20 every day or 80 for weekdays and 40 for weekends.

The values of the number of employees transferred and the additional number of employees added is rounded up to make a meaningful sense out of it.

It is made sure that the number of potential customers that are lost every weekend i.e. 10 customers per weekend is also taken care of.

For more understanding go through the formulas behind the cells shown below:

Initiallly for 88 customers base the revnue generated was 88 * 12 = $1056

Now to compare with the other policies as follows we have:

Pricing increase(in $)	Revenue generated per week(in $)	Increase in revenue(in $)
1	1131	75
2	1162	106
3	1170	114