Constructing risk preference

The next step to my Possible Topic#2 (although the preliminary result was not too encouraging) is to construct individual risk preference coefficients.

A respondent was asked this question:

You have an equal chance of receiving either Rp1.6 million per month or Rp400 thousand per month, depending on how lucky you are. Option 1 guarantees you an income of Rp800 thousand per month. Which option will you choose?

If he chooses (2), the riskier option, then we assume that he prefers (2) to (1). That means U(2) > U(1).

We assume a constant relative risk aversion (CRRA) utility function (following Binswanger 1980, Holt and Laury 2002, Kimball, Sahm and Shaphiro 2009, Cameron and Shah 2009, and many more):

W^(1-r)/ 1-r

where r is the Arrow-Pratt coefficient of relative risk aversion defined as:

- WU''(C) / U'(C)

Hence, for the above gamble, we can write the individual's preference as:

0.5(1600^(1-r)/ 1-r) + 0.5(400^(1-r)/ 1-r) - (800^(1-r)/ 1-r) > 0

Solving the inequality, we get r < 1.

Now, let's say the individual chose the safer option for the follow-up question:

You have an equal chance of receiving either Rp1.6 million per month or Rp200 thousand per month, depending on how lucky you are. Option 1 guarantees you an income of Rp800 thousand per month. Which option will you choose?

The solution is r > 0.3058. So, for this individual, we conclude that his risk aversion lies between 0.3058 and 1, or 0.3058 < r < 1. Higher r implies a greater risk aversion, while lower or negative value of r implies a more risk-loving behavior.