A monopolist’s marginal cost of supplying a good to consumers is ˜c = c + t (where t is a unit commodity tax). Let pm(˜c) denote the corresponding monopoly price.
(i) Compute dpm/dc˜ for the following demand functions: p = q−1/ε,p = α − βqδ,p = a − b ln q.
(ii) Sumner (1981) uses an ingenious approach to estimate the elasticity of demand—and thus the degree of monopoly power—in the American cigarette industry. He notes that in the United States, commodity taxes—and therefore the generalized cost ˜c—vary across states. Although data on c are hard to obtain, data on t are readily available. Sumner uses varying levels of taxation across states to estimate the elasticity of demand. Bulow and Pfleiderer (1983) argue that the method has limited applicability. What do you think?