Suppose that the downstream market for widgets is characterized by the inverse demand curve P = 100 - Q. Widget retailer is controlled by the monopolist WR Inc., which obtains its widgets from the monopoly wholesaler WW Inc. at a wholesale price of ww per widget, WW inc. obtains the widgets in turn from the monopoly manufacturer WM ltd. at a manufacturing price of wm per widget. WM Inc. incurs marginal costs of $10 per unit in making widgets. WW and WR each incur marginal costs of $5 in addition to the prices that they have to pay for widgets. What is the equilibrium widget price to consumers, P, the equilibrium wholesale price ww and the equilibrium manufacturing price wm? What is the profit earned by each firm at these prices? Show that vertical integration by any two of these firms increases profit and benefits consumers. Show that integration of all three firms is even more beneficial.

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9. Suppose that the downstream market for widgets is characterized by the inverse demand curve P = 100 - Q. Widget retailer is controlled by the monopolist WR Inc., which obtains its widgets from the monopoly wholesaler WW Inc. at a wholesale price of ww per widget, WW inc. obtains the widgets in turn from the monopoly manufacturer WM ltd. at a manufacturing price of wm per widget. WM Inc. incurs marginal costs of $10 per unit in making widgets. WW and WR each incur marginal costs of $5 in addition to the prices that they have to pay for widgets.

  1. What is the equilibrium widget price to consumers, P, the equilibrium wholesale price ww and the equilibrium manufacturing price wm? What is the profit earned by each firm at these prices?

  2. Show that vertical integration by any two of these firms increases profit and benefits consumers.

  3. Show that integration of all three firms is even more beneficial.

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