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##### Consider the market for a good with an inverse demand curve given by p(q) = 100? 1/3q

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**Question**

Consider the market for a good with an inverse demand curve given by;p(q) = 100? 1/3q;The market is served by a quantity-setting monopolist retailer. The retailer faces the cost function;cr(q) = q(10 + w);where w is the wholesale price charged to the retailer by the manufacturer of the good. Note that the 10;in the cost function above does not go to the manufacturer, only the w (you can think of this as a per-unit;fee charged by an exogenous shipping company who transports the goods between the manufacturing plant;and the retailer). The manufacturer is also a monopoly and sells the good exclusively to the retailer. The;manufacturer sets the wholesale price, and faces the cost function;cm(q) = 18q.;(a) Derive the wholesale demand curve faced by the manufacturer, as a function of w.;(b) Calculate the equilibrium w, q, and p.;(c) Calculate manufacturer profit, retailer profit, and deadweight loss. Hint ? this is tricky to graph, so you;need to be very careful here.;(d) Calculate the equilibrium q and p if the retailer and manufacturer merge into a single, vertically integrated;firm.;(e) Calculate total profit and deadweight loss in the merged case. How does this compare to (c)?

Paper#18229 | Written in 18-Jul-2015

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