[35 marks] Question 8: A damages rule S and B contract for S to take B on a whitewater rafting trip. 1 B and S negotiate a price p Rt. 2 S and B simultaneously choose care levels s [0, 1] and b (0,1), respectively. 3 Nature chooses whether B suffers an accident. The probability of an accident is T. 4 If there is no accident, then B doesn't incur any harm and S doesn't have to pay any penalty. But if there is an accident, B incurs harm of H(s,b) and S has to pay damages of d(s,b) to B. B's total expected costs are b+ [H(s,b) - ds, b)and S's are s+nd(s,b). Assume that H is decreasing in both s and b. (a) Write down an expression for expected total social costs, TSC(s,b). (b) Derive expressions for the expected marginal social costs of s and b. (c) Let st(b) be the efficient response of S (assumed to be single-valued), st(b) := arg min TSC(s,b). Consider the following damages rule: d= H(s,b) - H(s+(6),b). Write down expressions for expected total private costs for S and B, TPCs(s,b) and TPCB(s; b) if this damages rule applies. Derive expressions for the expected marginal private costs of s and b under this rule. (d) Imagine that s and bare complements in reducing expected total social costs. What assumption(s) on the harm function would give us this complementarity. Illustrate efficient responses and best responses in (s, b) space assuming complementarity. [35 marks] Question 8: A damages rule S and B contract for S to take B on a whitewater rafting trip. 1 B and S negotiate a price p Rt. 2 S and B simultaneously choose care levels s [0, 1] and b (0,1), respectively. 3 Nature chooses whether B suffers an accident. The probability of an accident is T. 4 If there is no accident, then B doesn't incur any harm and S doesn't have to pay any penalty. But if there is an accident, B incurs harm of H(s,b) and S has to pay damages of d(s,b) to B. B's total expected costs are b+ [H(s,b) - ds, b)and S's are s+nd(s,b). Assume that H is decreasing in both s and b. (a) Write down an expression for expected total social costs, TSC(s,b). (b) Derive expressions for the expected marginal social costs of s and b. (c) Let st(b) be the efficient response of S (assumed to be single-valued), st(b) := arg min TSC(s,b). Consider the following damages rule: d= H(s,b) - H(s+(6),b). Write down expressions for expected total private costs for S and B, TPCs(s,b) and TPCB(s; b) if this damages rule applies. Derive expressions for the expected marginal private costs of s and b under this rule. (d) Imagine that s and bare complements in reducing expected total social costs. What assumption(s) on the harm function would give us this complementarity. Illustrate efficient responses and best responses in (s, b) space assuming complementarity