Analysis and WTP with Conditional Pricing

Question

Hello,

I've conducted a CBC Analysis and implemented a conditional pricing table. I had different prices "low", "middle" and "high" for the "private label" and "brand", so overall 6 different prices shown to the respondents.

Now, I did a Logit and HB estimation and chose to change the attribute coding for price to linear coding and took the average prices for each attribute level (low, middle, high) as value.
I know that I must take into account, that the "brand" was, on average, shown with a higher price. So, since I got a negative brand utility, I can say that the private label was preferred and the respondent was, on average, not willing to pay the higher price for the brand. Am I correct?

Additionally, I want to calculate the Willingness-to-pay for my attributes. I took the simplest way and calculated:  -1*(attribute coefficient/price coefficient) (I know that there are better (more correct) ways to calculate WTP, but for my purposes, this way is sufficient). When I do that for the brand coefficient, I get a negative WTP for brand (since the brand utility is negative too).

Since the brand product was on average 0.13$ more expensive than the private lable, should I add that amount to my WTP?
So, for example, my average WTP for brand is -0.05$. I would normally say that the average respondent would only buy the brand if it's 0.05$ cheaper than the private label. But since the brand is 0.13$ more expensive, can I take that into account and say the "adjusted" WTP for the brand product is: -0.05$ + 0.13$ = 0.08$ ?

Thank you very much for your help!

Answer 1

You shouldn't be using the brand coefficient in the numerator so much as the difference between the brand's utility and the private label utility.   You use the coefficient itself when you have an attribute that you've modeled with a linear function.  Same goes for price - you want that expressed in utility per $, so that when you divide the difference in brand utilities by the utility/$ your answer is expressed in $.

Comments

Thank you for your answer.

So if i have brand utility of -0.15 and private label utility of 0.15, I take the difference which is 0.30 and divide it by the price utility (-5.25), which is linear coded, to get a WTP in $.
When I do that I get a negative $ value for the brand (-0.057$). So how do I account for the higher brand price (on average 0.13$ higher), which was shown to the respondent with the conditional pricing?

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You mentioned that you also tried more correct ways of getting WTP, and I would certainly recommend one of those (the share-based price equalization method) instead of this naive algebraic calculation.  

If you are going to do this naive algebraic calculation, I recommend doing it at the respondent level and then taking the median of the respondent level WTPs as your WTP estimate.

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Thank you Keith!
I'll try both and see how it works.