Intuition behind risk premium In Lecture 20 of MIT's Microeconomics course, a situation is proposed where a 50/50 bet will either result in losing \$100 or gaining \$125 with a starting wealth of \$100. It is stated that a person would be willing to insure themselves for \$43.75 (the difference between \$100 and \$56.25). What is the intuition behind this?

Thanks in advance!
The name for the amount $56.25 is certainty equivalent.

The expected utility for the individual from taking the bet is calculated as follows:
$$E[U]=\frac12U(100+125)+\frac12U(100-100)=75$$
Suppose the individual can pay an amount of money $x$ so that she can avoid taking the bet (which leads to expected utility $75$). What's the maximum amount of money $x$ she's willing to pay? Well, she would pay up to a point where she's indifferent between taking and not taking the bet.

If she takes the bet, expected utility is $75$. If she pays, her utility is $U(100-x)$. We want her to be indifferent, so that $U(100-x)=75$. Reading off from the blue curve in your graph (the curve describing $U$), we see that 
$$U(56.25)=75$$
which means $100-x=56.25$, or $x=43.75$. 

So we can interpret 43.75 as the maximum amount of money that an individual is willing to pay in order to avoid the (risky) bet.