Simple Price Modeling in Google SpreadsheetToshi Takeuchi

You have a new product. Now, how much should you charge?

Pricing is one of the most critical decision you make in marketing.

● What if you don't have any comparable products you can use for benchmark?

● This is a question many startups face when they try to introduce an innovative product.

● You don't want to pull it out of thin air.

So what's the solution?

Price Modeling Case Study ofA Japanese mobile application

We conducted a small scale market research.

● Location: Sapporo, often used to run marketing research targeting average Japanese urban consumers.

● Approach: used a local snow festival where we could talk to a lot of people efficiently in a short amount of time (saves time and money)

● Dataset: we collected 1,000 responses

After demoing the service, we asked:

Price (Yen) Responses % Cummulative %

0 30.38% 100%

100 33.6% 69.62%

200 21.51% 36.02%

300 14.51% 14.51%

Q 1. How much are you willing to pay for a monthly subscription?

Demand Curve

This is almost a linear line!

After demoing the service, we asked (continued):

Q 2. How much are you willing to pay per use?

Price (Yen) Responses % Cumulative %

0 13.44% 100%

30 14.52% 86.56%

40 48.65% 72.04%

50 1.35% 23.39%

60 18.81% 22.04%

70 1.62% 3.23%

80 0.27% 1.61%

90 1.07% 1.34%

100 0.27% 0.27%

Demand Curve

This is non-linear :(

Why Cumulative % = Demand %

1. If you are willing to pay 100 yen, you will not say no to 90 yen. So at 90 yen we get people willing pay 90 yen + 100 yen.

2. If you are willing to pay 100 yen or 90 yen, you will not say no to 80 yen. So at 80 yen we get people willing to pay 80 - 100 yen, and so forth.

3. This give us a nice downward sloping line that represent the percentage of people willing to pay for a given price point = a demand curve.

Run linear regression on the monthly subscription demand curve

"linest" function returns all coefficients we need

Good R2!

Demand Curve: Q=0.98548-0.0029007*P

Link to the spreadsheet

Evaluating the model against the data

Looks like the survey data is biased (people may have given answers they think their interviewers wanted). Drop suspicious responses for 300.

More conservative approach

How to pick the best price: depends on what you mean by "best"

● Profit Maximization? Revenue Maximization? Market Penetration?

● If Revenue Maximization, P = 157 yen● If Profit Maximization, P=195 yen

More details in the appendix

if marginal cost MC is 75 yen (a guess).P is lower if MC is lower.

Final Stage: Decision Time

The ultimate optimal price is unknowable, but this analysis gives you some possible ranges. ● 200 yen if we go for profit maximization at

MC=75; 150 yen if MC=50● 150 yen if we go for profit maximization● If we choose 200 yen, how easy is it to drop

it to 150 in case we change our mind?● If we choose 150 yen, how easy is it to raise

it to 200 in case we change our mind?

AppendixThe Math

If Revenue Maximization is the goal...

● Demand Curve: Q=a+b*P● Total Revenue = P*Q = a*P+b*P^2● This is a parabola. The max revenue is at

the peak (vertex). ● Price at Vertex P' = -a/(2*b) = 157.14 yen at

a = 1.005366667, b = -0.003199

If Profit Maximization is the goal...

Microeconomics 101: Profit is max when marginal revenue (MR) = marginal cost (MC)● For demand curve P=a-b*Q, MR=a-2b*Q● MC unknown, but guess 75 yen/user/month● MR=MC, so a-2b*Q=75● Optimal Q' = (a-75)/(2b)● a = intercept/slope, b=1/slope● Q' = 38.27%● Optimal P' = a-b*38.27 = 194.64 yen● P' will be lower if MC is lower.

What if the demand curve is non-linear?

Non-linear demand curve with Pay Per Use model

● The curve is "kinked" - an anchoring effect?

● All we need is a rough estimate, so keep it simple by segmenting the curve into separate linear lines.

● Segment at 50-60 yen?

Do the math

● Pick two ranges 0-60 yen and 50-100 yen and run linest function.

● Looks like either you can go with either 40 or 50 yen per use.

Segment 0-60 yen Range 50-100 yen Range

Revenue Maximizing Price 39.67 Out of range (45.94)

Profit Maximizing Price 47.17 Out of range (45.94)