Economics 454 — Assignment 2
Economics代写 It is up to you to find someone to work with. Consider a market of homogeneous products in which firms compete on quantity.
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.
Consider a market of homogeneous products in which firms compete on quantity. Demand in this market is given by
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)Suppose that Ce = ∞. What are the equilibrium price, quantity for each firm, and profit for each firm?
(b)Suppose that Ce = 0. What are the equilibrium price, quantity for each firm, and profit for each firm?
(c)What is the maximum value of Ce for which E does not make a loss if it enters?
(d)What is the maximum value of Ce for 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 enter.)
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.Economics代写
The game consists of three stages:
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 Economics代写
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. Economics代写
(a)Suppose that E decided to stay out. How much profit would M make?
(b)Suppose that M chooses Km to 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 Ce for which E would not lose money if it entered?
(d)Suppose that M chooses Km to be equal to the Stackelberg equilibrium value of qm and E enters. Determine the equilibrium profits of E,M.
(e)What would be the largest value of Ce for which E would not lose money if it entered in this case?
(f)Now suppose that M chooses Km so large that it will not be using all of it in stage 3 and E enters.Determine the equilibrium profits of E,M.
(g)What would 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 graph.
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 chooses the wholesale price and the retailer the retail price.
The demand function is 26 − p.
(a)Write down the retailer’s profit function as a function of the retail price p and the wholesale price w.
(b)What is the optimal retail price choice as a function of the wholesale price?
(c)What is the corresponding quantity?
(d)What is the producer’s profit as a function of w?
(e)What are hence the equilibrium values of w, p, q?
(f)What are the equilibrium producer and retailer profits (both separate and in aggregate)?
(g)Now suppose that the producer and retailer merge without a change in retail or production costs. Then what would be the new equilibrium price, quantity, and profit?
(h)Provide a brief intuitive explanation for why the retail price is now less but profits are higher.
(i)If the producer and retailer are still separate firms, then how much of a $1 increase in the unit producer cost gets passed through to the retailer and how much to the consumer?
(j)How would a $1 increase in the unit retail cost aGect the wholesale and retail prices? Please explain.
(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 this example?
(l)What would be the profit of the producer and that of the retailer? Express the profit in terms of R.
(m)Show that R should be between 8 and 12 (both inclusive) for both producer and retailer to be ok with this arrangement.
(n)What is the relevance of the nonlinear pricing example for mergers?
Suppose that there is a nut manufacturer and a bolt manufacturer. Consumers need one of each. The cost of producing a nut is 10 and 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 here.
(b)What would be the corresponding numbers if the firms merged? You only need to set one combined price for a nut–bolt pair.
(c)Explain why the price of a nut–bolt pair went down yet profits went up.
Consider a market for diGerentiated products with two producers. 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,(3)
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, p2 as a function of w1, w2.
(b)Express q1, q2 as a function of w1, w2
(c)Express the producers’ profit functions in terms of w1, w2.
(d)What are the optimal wholesale prices?
(e)What are the optimal retail prices? (f) What are quantities sold？
(g)What are retailer profits per firm?
(h)What are producer profits per firm?
(i)What would have been per firm profits absent a retail channel?
(j)What is the range of franchise fee amounts that would make both the producer and the retailer better oG with a retail channel?
Which three ongoing merger cases would you like to be discussed in class and why?
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