A monopoly publishing house publishes a magazine, earning revenue from selling the
magazine, as well as by publishing advertisements. Thus R = q.p(q) + A(q), where R is
total revenue, q denotes quantity, p(q) is the inverse demand function, and A(q) is the
advertising revenue. Assume that p(q) is decreasing and A(q) is increasing in q. The cost
of production c(q) is also increasing in the quantity sold. Assume all functions are twice
differentiable in q.
(i) Derive the profit-maximising outcome.
(ii) Is the marginal revenue curve necessarily negatively sloped?
(iii) Can the monopolist fix the price of the magazine below the marginal cost of production?
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