Homework $4$

$1$ Long$-$Form Question $(25$pt$)$

Suppose a worker $($hereafter$,$ called type $A)$ has the preferences given by

$U_A(w,x)=ln(w)-\sqrt[\phantom{2}]{\frac{x}{25}}$

where $w$ is the wage and $x$ is the level of risk.

Derive the MRS of $x$ and