Standard error of binomial variables derived from continuous variables

Question

I'm currently working on a project measuring willingness to pay (WTP) for a particular product. The data we are collecting are continuous variables denominated in the local currency. One thing we are interested in is the "demand curve" for this product, expressed as the fraction of respondents willing to pay a particular price.

In order to represent the demand curve, we will create a series of binary variables, say wtpX, where wtpX is 0 if X is greater than the respondent's willingness to pay and wtpX is 1 if X is less than the respondent's willingness to pay.

I have two related questions:

1. The data we collect contains much more information than simply whether a respondent is willing to buy at price X or not. When we compute the confidence intervals for the proportion of the population willing to pay a particular price, can we take this into account in order to reduce standard errors?
2. We will be constructing a number of the wtpX variables, but these variables are clearly not independent. Should I take this into account when computing standard errors?

Answer 1

If these are correlated identically distributed binary variables then p can still be estimated by # willing to pay /total but if they are negatively correlated the variance will be less than p(1-p)/n. But if they are positively correlated they will have highly variance. But why would these successive variables have the same p? Also I think Peter's question indicates that there may other ways and possible better ways to approach this problem.