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HW11

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Econ 300
Assignment 11

  1. ''No cartel in history has every succeed for very long. There is just too much opportunity to cheat.'' What does it mean for a cartel member to cheat? What would a member of, say, the OPEC cartel actually do if it were to cheat? Why would this undermine the cartel? Why don't member of the DeBeers cartel cheat (at least not very much)?

  2. A carrot monopolist can prodce at constant average and marginal costs of $ AC=MC=5.$ The firm faces a weekly market demand curve for carrots given by

    $\displaystyle Q=53-P.$    

    1. Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolist's profits.

    2. Suppose that a second firm enters the carrot market. Let $ q_{A}$ be the output of firm $ A$ and $ q_{B}$ the output of firm $ B.$ Market demand is now given by

      $\displaystyle q_{A}+q_{B}=53-P.$    

      On the assumption that firm $ B$ has the same costs as firm $ A$ , calculate the profits of firm $ A$ and $ B$ as functions of $ q_{A}$ and $ q_{B}$ .

    3. Suppose (as in the Cournot model) that each of these two firms chooses its level of output so as to maximize profits on the assumption that the other's output is fixed. Calculate each firm's reaction function (which expresses desired output of one firm as a function of the other's output.)

    4. On the assumption in part $ c$ , what is the only level for $ q_{A}$ and $ q_{B}$ with which both firm will be satisfied (what $ q_{A},q_{B}$ combination satisfies both reaction functions)?

    5. With $ q_{A}$ and $ q_{B}$ at the equilibrium level specified in $ d$ , what will be the market price of carrots, the profits for each firm, and the total profits earned?

  3. In the 1845 Alcoa case, Judge Learned hand was faced with deciding whether Alcoa had a monopoly in aluminum production. A crucial issue concerned the distribution between ''primary'' aluminum production (P) and ''secondary'' (recycled) production (S). Three different market share-measures were used to evaluate Alcoa's position:
    $\displaystyle I$ $\displaystyle =$ $\displaystyle \frac{P_{A}}{P}$  
    $\displaystyle II$ $\displaystyle =$ $\displaystyle \frac{P_{A}}{P+S}$  
    $\displaystyle III$ $\displaystyle =$ $\displaystyle \frac{P_{A}-F}{P+S}$  

    where $ P_{A}$ =Alcoa's primary production (Alcoa was not significantly engaged in recycling) and $ F$ = the amount of Alcoa's primary production that it used for its own fabricated products.

    1. Which of these definitions seems to provide the best approximation for the market in aluminum production?

    2. How would you answer $ a$ if you were an Alcoa attorney? How would you answer if your were a government attorney?

    3. The figures showed the following results for each of the three market-share measures:
      $\displaystyle I$ $\displaystyle =$ $\displaystyle 0.9$  
      $\displaystyle II$ $\displaystyle =$ $\displaystyle 0.64$  
      $\displaystyle III$ $\displaystyle =$ $\displaystyle 0.33$  

      If you were Judge Hand, how would you rule on the charge that Alcoa had a monopoly? How did the judge actually rule?

  4. Minnesota. They are the only sellers of pumpkins at the market, where the demand function for pumpkins is $ Y=3,200-1,600P.$ The total number of pumpkins old at the market is $ Y=Y_{c}+Y_{s}$ , where $ Y_{c}$ is the number that Carl sells and $ Y_{s}$ is the number that Simon sells. The cost of producing pumpkins for either farm is $ \$0.50$ per pumpkin no matter how many pumpkins he produces. Assume that Carl and Simon are Cournot competitiors.

    1. Calculate and graph each of their reaction functions.

    2. How many pumpkins will each grow?

    3. How much profit does each farmer make?

  5. Suppose that the pumpkin market in Lake Witchisit is as we described it in the last problem except for one detail. Every spring, the snow thaws off of Carl's pumpkin field a week before it thaws off of Simon's. Therefore, Carl can plan his pumpkins one week earlier than Simon can. Now Simon lives just down the road from Carl, and he can tell by looking at Carl's fields how many pumpkins Carl planted and how many Carl will harvest in the fall. (Suppose also that Carl will sell every pumpkin that he produces). Therefore, Simon sees how many pumpkins Carl is actually going to sell this year. Simon has this information before he makes his own decision about how many to plant.

    1. How many pumpkins will each grow?

    2. Show your above result graphically.

    3. How much profits would each make?

    4. If he wanted to, it would be possible for Carl to delay his planting until the same time that Simon planted so that neither of them would know the other's plans for this year when he planted. Would it be in Carl's interest to do this?

    5. Suppose that Carl and Simon sign a marketing agreement. They decide to determine their total output jointly and to each produce the same number of pumpkins. To maximize their joint profits, how many pumpkins should they produce in toto? How much does each one of them produce? How much profit do each of them make?

  6. Firms $ A$ and $ B$ are the only producers of a homogeneous good. The demand for the market is $ P(Y_{A}+Y_{B})=100-8(Y_{A}+Y_{B}).$

    1. Suppose that the two firm are identical and that the cost function of each is $ C(y)=4y$ . Calculate the market equilibrium if both firms are Cournot duopolists.

    2. Suppose that Firm A is the leader. Calculate the Stackelberg market equilbrium.

  7. The inverse market demand curve for bean sprouts is given by $ % P(Y)=100-2Y$ and the total cost function for any firm in the industry is given by $ TC(y)=4y.$

    1. If the bean sprout industry were perfectly competitive, the industry output would be ______ and the industry price would be _______.

    2. Suppose that two Cournot firms operated in the market. Calulate how much each firm would produce, the market price, and total output.

    3. For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graph.

    4. If the two firms decided to collude, industry output would be _____ and the market price would be _____.

    5. Suppose one of the firms acts as a Stackleberg leader and the other firm behaves as a follower. The leader will produce ______ and the follower will produce ________. This implies an industry output of ______ and price of __________.


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Next: About this document ...
Jenn Thacher 2008-08-25
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