# How to Interpret Marginal Willingness To Pay (MWTP)

Generally, marginal willingness to pay (MWTP) is the indicative amount of money your customers are willing to pay for a particular feature of your product (i.e., how much your customers are ready to pay for an upgrade from feature A to feature B, in addition to the price they are already paying now). The word ‘marginal’ refers to the fact that MWTP is always relative to a baseline, which is your baseline product (with various baseline features specified). Conjoint studies are well-suited to the calculation of MWTP.

Conjoint.ly offers a straightforward way to estimate MWTP, which can be useful in situations where you want to get a directional estimate and your study does not include competitor brands, SKUs, or pricing tiers. This output is available for Generic Conjoint experiments.

It is very important that you treat MWTP as an indicative amount. The appropriate interpretation is for an estimate of MWTP of $11.30 is “The median person values an upgrade from 500MG to 1GB as much as they value a price drop by$11.30”. But you should not interpret it as:

• Half of 500MB consumers will switch to 1GB if 1GB is priced $11.30 more than 500MB. • Everyone will choose to 1GB rather than 500MB if the price difference between the two is less than$11.30.
• I can safely price a subsciption tier with 1GB at $11.30 more than the one with 500MB. One should also avoid adding up MWTPs across different attributes. Finally, when MWTP is greater than the price of the product as a whole, it simply means consumers tend to value a feature more than any reasonable amount of price change. ## Requirements for MWTP In order for this feature work, a few conditions need to be met: • There must be a price attribute in your study. • None of the values of price should be zero (because zero is a special price). • If there are more than two price levels, they should have approximately equal gaps between them. • Prices should be either all positive or all negative. • The relationship between price and preference must be linear (i.e. preference for lower price must be higher, or vice versa) as shown below: There are many potential reasons why price-preference relationship is counter-intuitive (i.e. non-linear, or even linear but positive), including: • Small sample size: If the number of survey respondents is below the recommended number, this will likely affect the results. • Price-quality inference: Certain groups of respondents prefer higher prices, resulting in a non-linear relationship between price and preference. ## Formula Mathematically, MWTP is defined as marginal rate of substitution of a feature upgrade for price: $$\textrm{MWTP}_{i→j} = -V_{i→j} / V_p$$ where: • MWTPi→j is the standard marginal willingness to pay of feature j relative to feature i, • Vi→j is the preference for upgrade to feature j (from baseline feature i), • Vp is the preference for price (which is usually negative). A negative value of MWTP means that the feature is less preferred by the customer than the baseline. Therefore customers need to have a reduction in price to compensate for the downgrade to the inferior feature. We recommend calculating this value for each respondent separately and then taking the median MWTP across respondents. ## Calculations steps Consider that you obtain the following individual-level estimates for the HB model: Respondent Opt-in coefficinet Coefficient for price (per $1) Coefficient for level A of attribute 1 Coefficient for level B of attribute 1 Coefficient for level C of attribute 1 Coefficient for level D of attribute 2 Coefficient for level E of attribute 2
1 -0.4 -3.0 0 1.0 0.4 0 -2.0
2 5.0 4.0 0 2.0 0.1 0 -1.1
3 1.0 5.0 0 -0.2 0.3 0 -0.2

Let’s say we want to calculate MWTP of level B relative to level C. In this case we need to calculate preference for the upgrade, and then the MWTP:

Respondent Price B C Preference for the upgrade from B to C MWTPB→C
1 -3.0 1.0 0.4 -0.6 = 0.4 - 1.0 -0.2 = - -0.6 / -3.0
2 4.0 2.0 0.1 -1.9 = 0.1 - 2.0 0.5 = - -1.9 / 4
3 5.0 -0.2 0.3 0.5 = 0.3 - -0.2 -0.1 = -0.5 / 5
Median 4.0 1.0 0.3 -0.6 -0.1

Thus, in this example MWTPB→C is -$0.1 for the median respondent, but across the three respondents it varies from -0.2 to 0.5. ## Market Value of Attribute Improvement (MVAI) Another way to calculate marginal willingness to pay is Market Value of Attribute Improvement (MVAI). This concept was developed in 2002 by Elie Ofek and V. “Seenu” Srinivasan. It is defined as: • the amount of money by which you can increase the price of your product, • upgrading from one feature to another feature, • but anchoring share of customers' preference for your product constant. Let’s use an example of mobile phone plans. We will consider three attributes (mobile data, international minutes and SMS), each with a different number of levels (in addition to the price attribute, which is required for MWTP to work). First, we need to consider the various offerings that are present on the market. The table below presents a hypothetical set of competitors. Brand Monthly fee Mobile data inclusion International calls inclusion SMS inclusion Share of preference Telstra$49.00 500MB 0 min 300 messages 30%
Vodafone $39.00 10GB 90 min Unlimited text 20% Optus$45.00 Unlimited 300 min Unlimited text 25%
None of the above 25%
Total 100%

In order to find MVAI for Telstra’s mobile data upgrade from 500MB to 1GB, we need to:

• Tweak the price of Telstra’s offering (i.e. increase it),
• Upgrade from 500MB to 1GB,
• But anchor the preference share for Telstra’s offering at 30%:
Brand Monthly fee Mobile data inclusion International calls inclusion SMS inclusion Share of preference
Telstra $53.00 () 1GB () 0 min 300 messages 30% () Vodafone$39.00 10GB 90 min Unlimited text 21%
Optus $45.00 Unlimited 300 min Unlimited text 25% None of the above 24% Total 100% Thus, in this example MVAI of 1GB relative to 500MB for Telstra is $4 = $53 -$49. As seen in this example, finding MVAI requires changing a single feature, trying different price values, keeping share of preference constant.

Importantly, MVAI is not necessarily how much a particular feature is worth to the current buyers of the brand, but rather how much is it worth to the whole market (because the brand may lose some current customers but gain others who might be more willing to pay for the feature).

## MWTP for Brand-Specific Conjoint experiments

At Conjoint.ly, we do not recommend calculating MWTP for Brand-Specific Conjoint because it will lack statistical robustness, and often managerial usefulness. Instead, we suggest using preference share simulations to understand what price you would need to put for your product to take share from competitors.

However, if you have a sufficiently large sample size (say, 50% more than the sample size recommended by the system) and you must get MWTP, then you are able to follow the .