# How to calculate CRRA bounds from Holt and Laury (2002) type lottery?

Lottery is between:

Option A: a certain choice of £5

Option B: £10 with probability 0.1 and £1 with probability 0.9

The probability of receiving £10 increases in each subsequent choice.

How do I calculate the CRRA bounds of this, using $$U(x) = \frac{x^{(1-r)}}{1-r}$$?

Let me rewrite your Option B as follows: £10 with probability $$p$$ and £1 with probability $$1-p$$ where $$p\in[0,1]$$ varies across the items in the list of options.
Let $$\bar p$$ be the point where the subject's choice switches. For example, subject chooses Option A for all $$p<\bar p$$ and Option B for all $$p>\bar p$$. Then we can use the indifference condition $$$$U(5)=\bar pU(10)+(1-\bar p)U(1)$$$$ to infer the risk aversion parameter $$r$$.
In experiments where $$p$$ is discretized, we can take $$p_0,p_1$$ as the values that are immediately before and after the switching point in choice list. For example, subject chooses Option A for all $$p\le p_0$$ and Option B for all $$p>p_1$$. Then the bounds on the risk aversion parameter can be inferred from the following inequalities: $$$$U(5)\ge p_0U(10)+(1-p_0)U(1) \quad\text{and}\quad U(5)\le p_1U(10)+(1-p_1)U(1).$$$$
• +1 NB To infer $r$, we also need to know your initial level of wealth. – user17900 Jan 2 at 12:19