Risk Averse, Risk Loving, Concave, Convex?

[Katie]

I noticed on the lecture slides that for the "utility functions," a risk averse individual has a concave function, and a risk loving individual a convex. However a few slides later, there are graphs with Cb on the x axis and Cg on the y axis, and on these, risk aversion is a convex function, and risk loving is a concave function. What is going on here? If asked a conceptual question on a test, how would you explain this discrepancy?

[Lindsay Appell]

Hi Katie!

The discrepancy here is because of the difference between utility curves and indifference curves. Utility curves show the relationship between consumption and utility; indifference curves, on the other hand, show the relationship between consumption in the good state and consumption in the bad state at a fixed level of utility. 

For a risk averse person, the utility curve is concave. This shows that as consumption increases, utility increases, but it increases at a slower and slower rate (the slope is decreasing). Intuitively, I think of this as saying that risk averse people are not as motivated by large payments. Risk averse people's indifference curves, however, are convex. This shows that when choosing between consumption in the good state and consumption in the bad state, risk averse people prefer averages to extremes (because averages carry less risk). 

For a risk loving person, the utility curve is convex. This shows that as consumption increases, utility increases, but it increases at a faster and faster rate (the slope is increasing). Intuitively, this is saying that risk loving people are very motivated by large payments. Risk loving people's indifference curves are concave. This shows that when choosing between consumption in the good state and consumption in the bad state, risk averse people prefer extremes to averages (because extremes carry more risk). 

Let me know if I can clarify anything further!

-Lindsay