The demand function has a constant elasticity

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In a monopolized industry, the demand function has a constant elasticity: q = D(p) = p−ε where ε > 1 is the elasticity of demand. Marginal cost is constant and equal to c. (i) Show that a social planner (or a competitive industry) would yield a total welfare of Wc = c1−ε/(ε − 1). (ii) Compute the welfare loss, WL, under monopoly. (iii) Show that the ratio WL/Wc (relative dead-weight loss) increases with ε, that WL is nonmonotonic in ε, and that the fraction Πm/Wc of potential consumer surplus that can be captured by the monopolist increases with ε. Discuss the result. (Note that the “size” of the market changes with ε.)

Reference no: EM131240789

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