# Research Design: Indifference curves and budget lines

I have a basic Idea on how to construct indifference curves such that we must use two goods and then ask for pairs of bundles which are preference indifferent.

When doing applied research on estimating a consumers demand for a given bundle of goods, (which is probably done by survey as far as I'm concerned) what are the main questions we are seeking to answer in order that the data will work out nicely when using such a framework? How should such questions be worded on a survey?

In order to derive a preference indifference curve between different quantities of two goods, one possible questioning protocol would consist in:

1. First choosing any arbitrary combination of quantities for the bundle of goods (e.g. 20 units of A and 5 units of B);

2. Then choosing any arbitrary quantity of one of the goods (e.g. 15 units of good A);

3. Asking the consumer whether he (or she) is willing to exchange the first bundle of goods (20 of A and 5 of B) by a bundle of goods comprising 15 units of A (or any other quantity as specified in the previous paragraph) and 10 units of B (or any other quantity provided that is greater than 5);

4. If the consumer chooses the first bundle then the previous question should be asked again provided that that the previous 10 units of B be replaced by a greater quantity (e.g. 15 units of B); otherwise, if the consumer chooses the second bundle then the question of the previous paragraph should be asked again provided that that the previous 10 units of B be replaced by a smaller quantity (e.g. 8 units of B);

5. When the consumer considers that he (or she) is indifferent between two bundles, it means that the two bundles are indifferent and therefore the corresponding points should lie over the same indifference curve.

6. Following the previous procedure for a significant set of other combinations of quantities (bundles) would allow to draw the corresponding indifference curve(s).

One of the main approaches in the literature is based on offering a consumer a choice between sets of bundles and then using a revealed preference theory framework to infer what kind of utility and demand functions (if any) are consistent with the observed choice behavior.

For example, suppose that we one data observe a consumer able to buy any of bundles $\{A,B,C,D,\ldots\}$. From this set, he chooses $A$. Applying the Generalized Axiom of Revealed Preference, we can place some restrictions on the preferences that could generate this choice. For example, in the below figure the choice of $A$ from the set $\{A,B,C,D,E,F\}$ is consistent with the blue and green preferences, but not the red or orange ones.

Note that this approach works with observational as well as survey data. It has the advantage that much work has been done to understand exactly what can and cannot be inferred from a set of observed data—culminating in Afriat's theorem. A fairly neat introduction to this literature was written by the inimitable Hal Varian: "Revealed Preference".