Draw on example 10.1 to show that for y=30, partial coverage (denoted by c) induces a higher level of welfare than full coverage.
Determine the second-best optimal level of partial coverage. Which incentive condition must this level satisfy? Show that for y=25, partial coverage does not induce a higher care level. Determine the cutoff wealth level ŷ for which partial coverage enhances welfare for ŷ

Data from example 10.1

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Let the firm be risk neutral with p(a)=min {1/a,1}, and assume that y>1. Under full solvency, the firm solves -p'(a)D=1, which in this case corresponds to (1/a)D=1 and a = a = D.5. Under this specification, expected profit as defined by (10.8) reduces to V-2D However, when bankruptcy is possible, the decision corresponds to (10.16), so that 1/a(v-a)=(1-1/a). Solving for a results in al(y)=0.5 and expected profit, as defined by (10.15), reduces to y-20.5+1. To determine the firm's optimal choice, we equate the expected profit levels under the solvency and non- solvency cases, and compute the level of wealth that endogenously defines the transition point between the two. In doing so, we obtain 3-D+D0.5 +0.25 as the wealth level corresponding to the transition point, which is greater than =a*+D=D0.5+D. On the other hand, a(y)=0.5