Maggie’s private marginal benefit for cigars is PMBM(x) = 100 − x, where x the number of cigars. Rui’s marginal external cost is MECR(x) = x/2. Cigars cost Maggie PMC =$20 (a) Calculate and graph Maggie’s net private marginal benefit and Rui’s marginal external cost functions. Find the socially optimal number of cigars, x∗, Maggie would be allowed to smoke. Find the Pigouvian tax, t∗, which would generate the social optimum and show this on your graph.

(b) How many cigars, xNL, would Maggie smoke if she were allowed to smoke as many as she pleased if she is not liable (NL) for costs to Rui? Find the dead-weight-loss, DW LNL at xNL. If, instead, Maggie were liable (L) for damages to Rui, how many cigars, xL, would Rui allow to be smoked and what is the dead-weight-loss of this, DW LL? Show these on your graph.

(c) Suppose that transactions costs, T C, are less than min[DW LL, DW LNL]. Which rule, liable or not liable, causes less social costs for society? Explain. Which rule would Rui and Maggie each prefer? Explain. Hint: Let PL and PNL be the payment made to get the one with property rights to trade.

(d) Suppose that transactions costs, T C, are greater than max[DW LL, DW LNL]. Which rule, liable or not liable, causes less social costs for society? Explain.

(e) Suppose that min[DW LL, DW LNL] < T C < max[DW LL, DW LNL]. Which rule, liable or not liable, causes less social costs for society? Explain.