# Ec201 essay

CAS EC 201. Intermediate Microeconomic Evaluation. Downside set eight (due on Wednesday December 9, 2020) 1. On this train we look at a duopoly market. Agency one produces amount y1 and agency two produces amount y2. The market inverse demand operate is p(y) = 300 − 20y. Agency one’s value operate is C1(y1) = 40y1 and agency two’s value operate is C2(y2) = 245 + 20y2. 1.1 Assuming corporations compete `a la Cournot, discover the equilibrium amount of output for every agency. Discover the equilibrium market worth and the revenue earned by every agency. 1.2 Agency two has a decrease marginal value than agency one, however there may be the fixed 245 that seems in agency two’s value operate. Suppose this displays the truth that agency two has a brand new know-how that requires paying a licensing payment for a patent (the fastened value) which then permits agency two to provide at a decrease marginal value. Therefore, even in the long term, agency two can't keep away from paying the fee 245 if it will produce. Suppose agency one will get to decide on its amount first, and after seeing this amount agency two will get to decide on its amount. What amount maximizes one’s income, and what revenue does one earn? What revenue does agency two earn on this case? (Trace: it is a Stackberg mannequin and you need to resolve it ranging from the second step, working backward.) 2. Assume now that the market demand operate is p(y) = A − y, for some A ≥ zero and each corporations’ value operate is C(y) = y 2 . Plot the best-reply operate in a graph with y1 on the horizontal axis and y2 on the vertical axis. Discover the Cournot-Nash equilibrium portions. three. Suppose a monopolist produces Soma which is used as an enter by two industries producing two totally different items (say Amos and Mosa). In flip, these two corporations are monopolists of their respective industries. Assume that each corporations convert one unit of Soma into one unit of output. The demand for Amos has a relentless elasticity of demand of −three/2, and for Mosa the elasticity of demand is −2. That's, the inverse demand operate for Amos is p AMOS(y) = y −2/three and the inverse demand operate for Mosa is p MOSA(y) = y −half . Lastly, assume that the monopolist’s fixed marginal value of manufacturing is \$1. Suppose the monopolist is ready to cost totally different costs for the identical good (Soma) to the 2 corporations, an instance of third-degree worth discrimination. We wish to decide the worth it's going to cost to every of them. three.1 Write the revenue of the producer of Amos as a operate of the amount of Amos produced and the worth charged by the producer of Soma, p SOMA. (Trace: the value operate of this agency is C(y AMOS) = p SOMAy AMOS. Why?) Discover the profitmaximizing amount for this agency. You could have simply derived the demand operate of the producer of Amos for Soma. Why? 1 three.2 Utilizing the demand you derived within the earlier step, compute the optimum amount the producer of Soma ought to promote to the producer of Amos and the optimum worth it ought to cost. three.three Repeate the earlier steps for the producer of Mosa. Which of the 2 corporations is charged a lower cost? Why? four. From 1988 by means of 2005, over 46,000 intentions to merge have been filed with the US Federal Commerce Fee and Division of Justice in accordance with the HartScottRodino Act. In reviewing a merger between two corporations in the identical trade anti-trust authorities should commerce off the prices of monopoly energy with the advantages of effectivity features, normally decrease prices, which may be handed by means of to customers. To look at this trade-off formally, suppose two corporations face a requirement operate p(y) = 1 − y. four.1 Pre-merger, every of two corporations has fixed marginal value c of manufacturing, and the two corporations compete `a la Cournot. Compute the Cournot-Nash equilibrium of the trade and the equilibrium worth. four.2 By merging, the corporations may cut back their marginal prices of manufacturing. Postmerger, the merged agency can have a relentless marginal value of αc, the place α < 1. The merged agency will act like a monopolist. What's the profit-maximizing amount for the merged agency? What's the profit-maximizing worth? four.three When does the merger enhance client surplus? (For what values of α?) 2
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