Abstract
In this paper I provide bounds on the marginal rate of substitution between losing $x and winning $y, starting from wealth level $w, for a risk averse individual that rejects a small stake gamble for a range of initial wealth levels. I then prove a theorem that can be used to identify the kinds of large stakes that would be rejected by any such individual. The theorems allow us to understand how much risk aversion is embedded in anyone’s rejections of certain small stakes gambles and provide tighter connections between the results in Rabin (2000) and the received theory of decision making under risk.
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