A large firm has two divisions: an upstream division that is a monopoly supplier of an input whose only market is the downstream division that produces the final output. To produce one unit of the final output, the downstream division requires one unit of the input. If the inverse demand for the final output is P = 1,000 − 80Q, would the company’s value be maximized by paying upstream and downstream divisional managers a percentage of their divisional profits?

E3

Continuing from the previous questions where you are a manager of a firm is the exclusive manufacturer of a unique pair of rainbow shorts with demand and cost functions that are Q=100−2P; C=40+2Q2.   Now assume that the firm incurs a one-time cost of $10 for a zoning violation.  What is the price that the manager should now charge to maximize profits? (Just give the number, no need to include "$")

A dominant or price setting firm and several smaller price takers serve a market where total market demand is Qd = 700 – 3P and the combined supply from all the smaller firms is Qs = - 20 + 2P. State the dominant firm’s marginal revenue function (MRf), and use it to determine its profit maximizing quantity and the price (P) it will set for the market if MC = $56.

A market consists of a dominant firm and a number of fringe firms. The followings are the information about these firms. Total market demand: QALL=300 – (2.5) P The competitive fringe supply function (total): QF=2P-12 The dominant firms marginal cost function: MC = 12 + (1⁄2) QD.  a) What is the equilibrium price set by the dominant firm?  b) How much will the competitive fringe supply to the market at the price found in question (a)?        Show the answers graphically.

Topside Tiles, which produces roofing tiles, is a local monopoly. Its inverse demand function is p=140-2Q, and its constant marginal cost is 10. The owner has delegated the decision of how much output to produce to the plant manager. The manager's income, Y, is 5% of revenue: Y=0.05R. Show that a manager who wishes to maximize income, Y, will choose an output that exceeds the profit-maximizing level. Is there a conflict of interest between the owner and manager? Is this situation an agency problem? (Hint: This problem can be solved using a graph, by using calculus, or by using the rule that the MR curve has twice the slope of the demand curve.) The output that maximizes profit is (Enter your response rounded to one decimal place.) units.

"Tiffany" is a retailer monopolist who makes a unique product called the "diamond ring" that requires exactly one diamond as input, which is sold by a wholesaler monopolist, the "Diamond Corporation". Diamond Corporation faces a marginal cost of £60 per unit of input (this is also the firm's average cost). Assume that "Tiffany" faces the following inverse demand curve for diamond rings: Pt 320 – Qt where Pt is the price of red diamond rings in pounds per unit and Qt is the quantity of diamond rings offered for sale by "Tiffany". Similarly, Diamond Corporation charges a price, Pa, for the inputs in £ per unit and Qa is the quantity of inputs sold by Diamond Corporation. a) Derive the profit-maximising price and output for both firms, assuming that the two monopolists act as independent profit-maximising companies. Calculate profits of each firm. Use a clear diagram to illustrate your answers to explain your calculations. b) Now assume that the two firms merge. Calculate the post-merger…

Suppose that there are two types of firms in a perfectly competitive market. Firms of type A have costs given by CA(q) = 30q2 + 10q. Firms of type B have costs given by CB(q) = 50q2 + 10. ( dCA dq = 60q + 10 and dCB dq = 100q). There are 60 firms of type A and 100 firms of type B. Derive the individual firm supply functions for each type of firm and What is the range of prices in which some firms produce but others do not? Are there prices at which no firms produce Why?