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Economics 454 Assignment
创建日期：2024-07-20 17:23:45
所属分类：经济Economics
标签： Economics 454
Assignment

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Economics 454  Assignment 2

This assignment can be done, either with one or two other students; you can also do it by yourself. It is up to you to find someone to work with.

This assignment can be done, either with one or two other students; you can also do it by yourself. It is up to you to find someone to work with. You can only be a member of one group. All group members will receive the same grade, so please talk about all answers. Please make sure that you both put in an equal amount of eflort: don’t put someone’s name on your assignment if s/he did not contribute sußciently to the group eflort. The due date of this assignment is March 26 in class. Assume that the equilibrium concept is Nash, wherever relevant. Fixed costs are zero unless otherwise specified.

1.Consider a market of homogeneous products in which firms compete on quantity.

Demand in this market is givenby

q(p) = 72 − 6p. (1)

There are both an incumbent firm M and a potential entrant E which can both produce the good at marginal costs 6. Prior to entry, E must incur an entry cost equal to Ce ≥ 0.

(a)Supposethat Ce = ∞. What are the equilibrium price, quantity for each firm, and profit for each firm?

(b)Supposethat Ce = 0. What are the equilibrium price, quantity for each firm, and profit for each firm?

(c)Whatis the maximum value of Ce for which E does not make a loss if it enters?

(d)What is the maximum value of Cefor which it is optimal from a welfare perspective (i.e. total surplus) for E to enter? (At the maximum value it is also optimal for E not to )

2.Suppose that there are an incumbent M and a potential entrant E,

each capable of producing a homogeneous good.  To  produce the good takes capital at a cost of 24 per produced unit of output and labor at a cost of 6  per unit of output. Demand is 36 − p. The game consists of threestages:

stage 1: M chooses how many units Km of capital to build at a cost of 24 per unit.

stage 2: E chooses whether or not to enter. If E enters then it incurs a cost equal to Ce ≥ 0.

stage 3: If E did not enter then M is a monopolist and chooses how many units qm to produce. If E did enter then E and M choose simultaneously and independently how many units to produce (qe, qm respectively). In either case, E and M have to build suflcient capacity to meet production.

Example 1 Suppose that M chooses to build Km = 10 units in stage 1, E enters, and E,M each produce 25 units in stage 3. Then M pays 10×24 = 240 in stage one and must build an additional 15 units in stage 3 for which it must pay 15 × 24 = 360. M must further pay 6 × 25 = 150 for labor. Since the equilibrium price is 90 − 25 − 25 = 40,

M’s profit is 40 × 25 − 240 − 360 − 150 = 250. Now E. E must pay Ce to enter plus 25 × (6 + 24) = 750 in

costs. Its profit is then 40 × 25 − 750 = 250.

Ignore the numbers in the example from here on.

(a)Supposethat E decided to stay  How much profit would M make?

(b)Suppose that M chooses Kmto be less than or equal to the Cournot equilibrium value of qm and E enters. Determine the equilibrium profits of E,M.

(c)What would be the largest value of Cefor which E would not lose money if it entered?

(d)Suppose that M chooses Kmto be equal to the Stackelberg equilibrium value of qm and E enters. Determine the equilibrium profits of E,M.

(e)Whatwould be the largest value of Ce for which E would not lose money if it entered in this case?

(f)Nowsuppose that M chooses Km so large that it will not be using all of it in stage 3 and E Determine the equilibrium profits of E,M.

(g)Whatwould be the largest value of Ce for which E would not lose money if it entered in this case?

(h)Draw four graphs to the same scale, one each for the cases Ce= 100, 200, 300, 500. In each graph, draw πe, πm as a function of Km assuming M,E make optimal choices in stages 2 and 3: use red for πe and blue for πm.  Please be precise:  don’t just sketch.  This question will take some time and will yield  a lot of points.

(i)Please comment on what is happening and why in each

3.Suppose that there is a single producer of a good and a single retailer.

The producer’s marginal cost is 14  and the retailer’s marginal cost is the wholesale price w plus a unit retail cost equal to 4. The producer  choosesthe wholesale price and the retailer the retail  The demand function is 26 − p.

(a)Writedown the retailer’s profit function as a function of the retail price p and the wholesale price w.

(b)Whatis the optimal retail price choice as a function of the wholesale price?

(c)What is the correspondingquantity?

(d)What is the producer’s profit as a function ofw?

(e)What are hence the equilibrium values of w, p,q?

(f)What are the equilibrium producer and retailer profits (both separate and inaggregate)?

(g)Nowsuppose that the producer and retailer merge without a change in retail or production  Then what would be the new equilibrium price, quantity, and profit?

(h)Providea brief intuitive explanation for why the retail price is now less but profits are

(i)If the producer and retailer are still separate firms, then how much of a $1 increase in the unit producer costgets passed through to the retailer and how much to the consumer?

(j)Howwould a $1 increase in the unit retail cost aGect the wholesale and retail prices? 

(k)Now suppose that the producer oGers to sell its products to the retailer at the producer’s marginal cost  (w = 14) in return for a fixed fee R. So the retailer pays  the producer 14 per unit plus R.  What would  be the equilibrium retail price in thisexample?

(l)Whatwould be the profit of the producer and that of the retailer? Express the profit in terms of 

(m)Showthat R should be between 8 and 12 (both inclusive) for both producer and retailer to be ok with this

(n)Whatis the relevance of the nonlinear pricing example for mergers?

4.Suppose that there is a nut manufacturer and a bolt manufacturer.

Consumers need one of each.  The cost     of producing a nut is 10and the cost of producing a bolt is 4. Demand is

q(pn, pb) = 26 − pn − pb. (2)

(a)What are the equilibrium prices, quantities, and profits? Equilibrium prices will not be the same

(b)What would be the corresponding numbers if the firms merged? You only need to set one combined price for a nut–bolt

(c)Explainwhy the price of a nut–bolt pair went down yet profits went

5.Considera market for diGerentiated products with two  Each producer is tied to a single retailer.

Each producer first sets a wholesale price. Then, the retailer chooses a retail price. The demand functions are

q1(p1, p2) = 488 − 4p1 + 2p2,

q2(p1, p2) = 488 + 2p1 − 4p2.

The production cost of each unit of either good is 28. There are no retail costs and no fixed costs.

(a)For given wholesale prices w1, w2, derive the optimal retail prices p1, p2as a function of w1, w2.

(b)Express q1, q2as a function of w1, w2

(c)Express the producers’ profit functions in terms ofw1, w2.

(d)What are the optimal wholesaleprices?

(e)What are the optimal retail prices? (f) What are quantitiessold?

(f)What are retailer profits perfirm?

(g)What are producer profits perfirm?

(h)What would have been per firm profits absent a retailchannel?

(i)What is the range of franchise fee amounts that would make both the producer and the retailer better    oG with a retailchannel?

  1. Whichthree ongoing merger cases would you like to be discussed in class and why?
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