Lindsay evaluates opportunities using the following value function under prospect theory:

v$($w$)=$ w$1/2$ when w $>0$

$=-4(-$w$)1/2$ when w $<0$

Part a$.$

Is Lindsay loss$-$averse? Explain.

Part b$.$

Assume that Lindsay weights values by probabilities, instead of using a prospect theory weighting function. Which of the following prospects would be preferred?

P$1(0\mathrm{.}40,8,000,-200)$

P$2(0\mathrm{.}50,12,000,-800)$

P$3(0\mathrm{.}50,2,500,-100)$