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ECON 445 Final Exam
创建日期：2024-08-17 17:25:14
所属分类：经济Economics
标签： ECON 445
Final Exam

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The exam has a total of 100 points. Please answer all questions.


Students are not permitted to engage in group work or collaborate with other students on this exam.  Collaboration on exams is a violation of academic integrity.

1 Short Questions (20 pts)

Provide brief  answers to each of the following questions (ideally no more than three to four sentences).

1.  (4 pts) A price-setting dominant firm (firm 1) operates in a market produc- ing a homogenous good, but faces competition from a competitive fringe. The supply curve of the fringe firms is given by S(p) = 2p.  You don’t know exactly what the demand curve is or the dominant firm’s marginal cost, but you do know that in the 2023 equilibrium, the dominant firm has a market share of 70%.

However in 2024, the dominant firm decides to exit the industry, so con- sumers can only buy from the competitive fringe.   Will  prices in 2024 decrease, increase or stay the same compared to 2023?  Briefly explain the reasoning behind your answer.

2.  (4 pts) Firms in an industry produce a homogeneous good. You have data on prices P, quantity Q, a demand shifter y and a cost shifter w.  The demand curve is linear, and marginal costs are constant.  Based on this information, is it possible to estimate the conduct parameter λ? Why or why not?

3.  (4 pts) Consider the following game, where player  1 can choose between T, M, and B; while player 2 chooses beween L, C and R. The table below shows the payoffs to the players from each pair of actions. For example if player 1 chooses T and player 2 chooses L, player 1 gets a payoff of 1 and player 2 gets a payoff of 7.

                    Player 2

                    L   C    R

                T 1,7 3,3 4,2

Player 1     M 5,0 4,2 8,1

                 B 7,2 3,1 2,9

Find all the pure-strategy Nash equilibria of this game.

4.  (4 pts)  An industry consists of two firms producing an identical good, with demand curve D(p) and identical marginal costs c.  Both firms are capacity-constrained, with each firm having capacity K, where K > D(c). The firms compete in prices.

What would happen to the equilibrium price and quantity if firm 1 were to invest in building more capacity?  Explain your answer carefully but briefly.

5.  (4  pts)  Suppose  the  coffee  shop  in  Terminal  3  of Toronto Pearson In- ternational Airport engages in monopoly pricing of lattes, with constant marginal cost c > 0.  The price of a latte there is $8, and through diligent market research you discover that the elasticity of demand is -2 at that price. What is c?

2 Longer Questions

2.1    Bertrand competition with differences in pricing tech- nology (20 pts)

An industry consists of 2 firms that produce a homogeneous, identical good and compete in prices  (Bertrand competition).  Demand for the good equals D(p) = 40 -p where p is the price.

Firm 1 can produce at a constant marginal cost c1 , and chooses price p1 . Firm 2 can produce at a constant marginal cost c2 , and chooses price p2 .  For now, let’s assume c1  = c2  = 4.

However, the two firms differ in their pricing technology.

(a) Firm 1 can set prices with exact precision, meaning they can set any price to the cent, such as $9.43 or $10.22 (but not, for example, a price of $9.437).    (b) Firm 2 has a less precise pricing technology and can only set prices in the tens of cents.  For instance, firm 2 can charge a price of $9.4 or $10.2, but it cannot set a price of $9.43 or $10.22.

Initially, assume the firms choose prices simultaneously.

1.  (9 pts) Solve for all pure-strategy Nash equilibria of this game. What are the profits of each firm under each Nash equilibrium?

2.  (5 pts) Suppose firm 1’s marginal cost equalled c1  = 4.05 instead.  Find all pure-strategy Nash equilibria of this game.

3.  (3  pts) Let’s go back to assuming c1  = c2  = 4.   Suppose that the game was sequential:  firm  2 gets to choose their price p2  first, and then firm 1 observes this price and chooses their own price p1 .  Which of the Nash equilibria that you worked out in part (a) are subgame-perfect?

4.  (3 pts) Going back to the simultaneous game with c1  = c2  = 4:  suppose the products that the firms produced were differentiated.  How do you think this will affect the Nash equilibria that you worked out in part (a)?  Ex- plain the intuition behind your answer.  (Note:  you do not need to work out the new Nash equilibria).

2.2 Avocado price collusion (30 pts)

There  are  two  producers  of  avocado:   CaliCado,  located  in  California;  and ChileCado,  located in Chile.     Sometimes I will refer to  CaliCado as firm  1 and ChileCado as firm 2.

For simplicity, we will divide each year into summer and winter as experi- enced in North America.   Demand for avocados is stable across time, and is given by D(p) = 55 -p.

However, the cost of producing avocado differs by firm and by season.  Specif- ically, the marginal cost of producing avocados equals c1  = 5 for CaliCado in summer (because that is the growing season in California), but equals c1  = 10 in winter.  By contrast, the marginal cost of producing avocados equals c2  = 5 for ChileCado in “winter” (which is summer in Chile, and therefore the growing season) and equals c2  = 15 in summer.  (See table below)

Producer

Summer

Winter

CaliCado, c1

$5

$10

ChileCado, c2

$15

$5

Table 1:  Marginal cost of producing avocados for CaliCado and ChileCado by season

1.  (4 pts) Non-cooperative Bertrand: Derive the equilibrium prices and quantities under Bertrand competition (i) during summer and (ii) during winter. What  are the profits earned by each firm in summer and in winter?

2.  (6 pts) Merger: Suppose  CaliCado  and  ChileCado were able to merge with each other and form a joint monopoly (“CaCado”).  What are the new equilibrium quantities and prices during (i) summer (ii) winter? What is the total profit of the merged firm (πm )?  Do consumers benefit from the merger?

Collusion:

The US FTC blocks the merger of the two firms.  So they decide instead to collude, using a grim trigger strategy.  From now on, assume that the pricing game is repeated an infinite number of period (where each period or season is defined as a six-month length of time, either summer or winter). Each firm discounts their future profits by a discount factor δ that lies between 0 and 1.

The firms decide to collude and set the monopoly price and produce the monopoly quantity every period (that you derived in the previous ques- tion).

The firm adopt a grim trigger strategy to punish any firm that cheats on the agreement.  If in any period t either firm ever deviates from the agreed prices, then both firms will revert back to Bertrand competition in all future periods.

3.  (4 pts) Carefully describe a grim trigger collusive strategy for the infinitely repeated game. Make sure to specify prices and quantities in both summer and winter, and describe what the firms will do in the event that one firm deviates.

4.  (4 pts) What is the discounted present value of profits for  (i) CaliCado if it keeps colluding (ii) ChileCado if it keeps colluding?  Work these out separately for winter and summer.

5.  (4 pts) What is the discounted present value of profits for (i) CaliCado if it deviates from the collusive arrangement (ii) ChileCado if it deviates from the collusive arrangement?  Again, work these out separately for winter and summer.

6.  (5 pts) Under the collusive strategy you specified in part  (3),  for what values of δ will collusion be viable?

7.  (3 pts) Suppose that δ is too low by some small amount.  Describe what the two firms can do to preserve the collusive arrangement (you do not need to work out the exact prices they should charge).

2.3 Coffee Meets Bagel (25 pts)

You own a cafe where you sell two kinds of products (i) coffee (ii) bagels. Each morning, there are two types of consumers who visit the cafe.  For simplicity assume the marginal cost of producing a coffee or a bagel is zero.

? Each type  A consumer is willing to pay $6 per coffee, and is willing to buy 2 coffees; and is willing to pay $3 per bagel, and buy up to 2 bagels. There are 20 consumers of type A.

? Each type B consumer is willing to pay  $2 per coffee, and will only buy at most one coffee; and is willing to pay $2 per bagel, and buy up to 4 bagels. There are 40 consumers of type B.

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PHIL2617 PHYS3116 MIE250 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 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