Suppose a worker has a choice between taking two jobs. Job $1$ yields an income $I=100$

with probability $0\mathrm{.}25$ and an income $I=9$ with probability $0\mathrm{.}75.$ Job $2$ yields an income $I=$

$25$ with certainty, i$.$e$.$ probability $1.$ Our worker of interest has the following utility function:

$U(x)=\sqrt[\phantom{2}]{x}.$

a$.$ Is the worker risk averse, risk neutral, or risk loving? Explain.

b$.$ Calculate the expected utility for each job. Does the worker take the first or

second job?

c$.$ Plot your work from part $($b$)$ on a graph.

d$.$ Find the risk premium. Identify the risk premium on your graph from part $($c$).$