steps of answering are needed

QUESTION 1 [15 Points] a) [10 Points] Suppose that a risk averse individual faces the uncertain situation {$W, $W - $1; 1 - p, p}. Prove (with explanations) that this individual will purchase a "full insurance policy" given that insurance companies sell "actuarially fair" insurance plans. To earn credit, you must derive your answer by stating salient assumptions and showing & explaining all essential steps/ calculations. b) [5 Points] Repeat part (a) for (i) a risk loving agent and (ii) a risk neutral agent. Do these agents fully insure themselves? Why or why not? To earn credit, you must derive and explain your answer by stating salient assumptions and showing & explaining all essential steps/ calculations