# None-option in CVA with conditional pricing

Hi everyone,

I would like to conduct a CVA (instead of a CBC) with single rating tasks given the fact that my sample size is severly limited (N=17). I only have to attributes: (i) quantity and (ii) price, with four levels each. More specifically:

Attribute 1 (quantity):
------------------------------
0x (none-option)
1x
2x
3x

Attribute 2 (price):
------------------------------
-100% (none-option)
-30% (low)
0% (mid)
+30% (high)

I would like to know respondents' WTP for differing quantities of the good, keeping in mind that respondents can also pick zero quantities, for which, of course, they pay nothing (=none-option).
Now I wonder how to implement this design in the "most efficient" way (whatever this means). For example, I thought of four levels for the attribute "quantity" (0x, 1x, 2x, 3x), but only three levels for the attribute "price" (-30%, 0%, +30%) and to use conditional pricing. In the conditional pricing settings, I then set the price for "0x" always to zero, independent of the price attribute. However, in the market simulator and its conditional pricing table, I have to set an ascending or descending order for the different price levels of "0x". Is it appropriate to only use marginal increments, such as "0.01\$", "0.02\$", and "0.03\$" for "0x", while for all other quantity <> price combinations, I have realistic values, for example, "7\$", "10\$", and "13\$"?

How would you proceed with my setting?

Nico,

If the (a) quantity only goes with the \$0 and (b) you use 3 price points like \$8, \$10 and \$13, then you really have just nine possible combinations to show against the none, right?  You could choose to collect this even with 9 simple fixed questions, right, and then just analyze it using our HB/Reg software?  Fiddling with CVA to show this none alternative seems like more work than it's worth in this case.
answered Feb 16 by Platinum (111,275 points)
Hello Keith,
Thanks for the quick response. In case of unconditional pricing, you are right with your suggestion, I will keep that in mind. However, I am not yet sure whether conditional pricing is better in order to avoid unrealistic price-quantity combinations. How can I implement the none-option in this case? Like I said, I thought of four levels for the attribute "quantity" (0x, 1x, 2x, 3x), but only three levels for the attribute "price" (-30%, 0%, +30%).  In the conditional pricing settings, I then set the price for "0x" always to zero, independent of the price attribute. However, in the market simulator and its conditional pricing table, I have to set an ascending or descending order for the different price levels of "0x", i.e., I cannot use (\$0, \$0, \$0) for (-30%, 0%, +30%). Is it appropriate to use, for example, "0.01\$", "0.02\$", and "0.03\$" for "0x", while for all other quantity <> price combinations, I have realistic values, for example, "7\$" (-30%), "10\$" (0%), and "13\$" (+30%)?
Nico,

I think that should work.
Hi Keith,

Unfortunately, I still have some problems with the market simulator: As written, my alternatives consist of the two attributes "quantity" and "price".

Attribute 1 (quantity):
------------------------------
0x
1x
5x
10x

Attribute 2 (price): Conditional pricing
------------------------------
-30% (low)
0% (mid)
+30% (high)

Thus, the displayed prices are:
\$0 (0x, -30%)
\$0 (0x, 0%)
\$0 (0x, +30%)

\$4.20 (1x, -30%)
\$6 (1x, 0%)
\$7.80 (1x, +30%)

\$21.00 (5x, -30%)
\$30.00 (5x, 0%)
\$39.00 (5x, +30%)

\$42.00 (10x, -30%)
\$60.00 (10x, 0%)
\$78.00 (10x, +30%)

Now I have created test data using the tab "Generate data...". I analyzed the data using OLS and logit transformation. Now I would like to use the results in the market simulator. For this, I have defined the price attribute in the “Attribute Info” tab and set the quantity and price as continuous. If I now specify and simulate products, everything works fine, provided there is no product with quantity “0x”. As soon as a add a product with quantity “0x”, I get the following error message: “Error: An element with the same key has already been added.”

In the “Attribute Info” tab, the quantity “0x” level has a label and value of 0. If I change the value from 0 to, for example, 1, everything works fine again. I suppose that somehow the market simulator knows quantity "0x" to be a none-option, even though I set the market simulator not to include a none-option if available. What am I doing wrong?