Industrial Organization and Regulation - Questions and Answers - Organization Management Assessment answer

Assessment Task:

Q1. HotellingModelwithCollusion
Two?rmsarelocatedattheendpointsofalineofunitlength[0,1]. Firmsinteractrepeatedlyoveranin?nitetimehorizon t =0,1,2,....andfaceacommon per-period discount factor δ∈(0,1). Firms compete in prices in each period and do not change their location over time. Both ?rms incur zero marginalcostsofproduction.
Consumers are uniformly distributed over the same interval with their location denoted by x ∈[0,1]. In every period, each consumer demands at most one unit of the product and derive utilityU1 =V −x−p1 from buying from?rm1(locatedatposition0),andutilityU2 =V−(1−x)−p2 frombuying from?rm2(locatedatposition1). x and1−x representthelineardisutility fromhavingtotraveltoeither?rm’slocationtopurchasetheproduct. Consumers do not change their location over time and purchase the product if theygetnon-negativeutility. Furthermore,weassumethatV >2,suchthat ?rmswillalwaysprefertoselltotheentiremarket.
Wewillbeginbyconsideringaone-shotinteractionbetween?rms. First, suppose that ?rms do not collude (think normal Hotelling price competition)andconsidertheequilibriuminasingle-stagegame.
a.Findtheindifferentconsumer,b x,intermsofp1 andp2.
b.Using your answer from a), write out the pro?t maximisation problemforboth?rms1and2.
c.Hence?ndthenon-collusiveequilibriumpricesp∗ 1,NC andp∗ 2,NC set by either ?rm in equilibrium. Furthermore, ?nd the equilibrium pro?ts earned by each ?rm, π∗ 1,NC and π∗ 2,NC, and the industry pro?t Π∗NC.
Now,considerwhenthe?rmscollude. Theymaycolludeintwoways: eitherbyconcentratingalltheirproductiononone?rm(locatedatposition0) andchargingasingleprice,p =p∗ C,1,orbycontinuingtooperateboth?rms such that they both charge a common price p1 =p2 =p∗ C,2 (while remaining at positions 0 and 1). You can imagine that ?rm 2 agrees to set a sky-high price in the former case so that all consumers will only buy from ?rm 1. In
bothcases,?rmswillequallysharethecollusivepro?t. Assumethatregardlessofeithercase,?rmsareobligedtosettheirpricesuchthatthemarketis fullycovered(allconsumermustbewillingtobuytheproduct).
d.Firstly,wewillassumethat?rmsconcentratealltheirproductionononestore. Whatwillbetheoptimalpriceinequilibrium? [Hint: Consider the furthest positioned consumer - what price will entice himtopurchasetheproduct?] e. (1 pt) What will be the resulting industry pro?t Π∗ C,1? Is this higher or lowerthan Π∗NC inc)?
f.Now, wewillassume that ?rms chooseto continueproducing at both stores and charging a common price. In this case, each ?rm sellstohalfthemarket. Whatwillbetheoptimalpriceinequilibrium? [Hint: Consider the indifferent consumer’s decision - what price will enticehimtopurchasetheproduct?] g. (1 pt) What will be the resulting industry pro?t Π∗ C,2? Is this higher or lowerthan Π∗NC inc)?
h.Compare your answers from e) and g). Which of the two arrangementsdothe?rmsprefer? Justifyyouranswer.
We will now move on to the in?nite period game in which ?rms collude by choosing the latter collusive arrangement, that is, to continue operating at both stores and equally share Π∗ C,2. Firms will continue to collude until a ?rm deviates by setting a different p at time t. If deviation occurs, both ?rms will revert to playing the non-cooperative equilibrium for all subsequentperiods.
i.Considerthescenariothat?rm1deviatesattimet. Giventhat p2 =p∗ C,2,writeoutthepro?tmaximisationproblemfor?rm1. j. (1 pt) Hence ?nd the optimal deviation price, p∗ D charged by ?rm 1 in equilibrium and the associated deviation pro?t. Is it higher than undercollusion?
k.Findthepositionoftheindifferentconsumerinthiscase. How doesitchangewithregardstoV ?
We will now check ?rm 1’s incentive to deviate. Remember that ?rm 1 accountsforbothcurrentandfuturepro?ts.
l.Supposethat?rm1isdecidingwhethertodeviateatperiod t. Writeoutunderwhatcondition?rm1choosestodeviateatperiod t.
m.Findthevaluesof δ suchthat?rm1willdecidetodeviate.
n.DoesanincreaseinV facilitatecollusion? Explainyouranswer.

Q2. ToEnterortoMerge? 
Mitch(M)andIndra(I)arecompetinginquantitiesinthemarketforretail mobileservices. TheinversedemandfunctionofthemarketisgivenbyP = 1−Q,whereP representsthepricesetinthemarketandQ representstotal marketdemand. M andI faceaconstantmarginalcostofcM ∈(0, 1 2)andcI ∈ (0, 1 2)respectively. WefurtherassumethatM ismoreef?cientinproduction suchthat cM <cI. Neither?rmfacesany?xedcosts.
An entrant, Chris (K ), may either enter the market as a separate competitorormergewith I toformanewentity I0. K possessesadvancedtechnology such that he faces a marginal cost of 0 if operating separately, or, if K merges, reduces the marginal cost of I0 to 0. If K enters the market independently, he incurs an entry cost of F > 0. There are also no additional costsif K isallowedtomergewith I.
The current mobile network regulator is unsure as to which option will providethehighestwelfare. Assuch,theregulatorhasturnedtoyou,abudding Economist, to help it decide whether it should allow K to enter separatelyormergetoform I0.
We will ?rst begin by investigating the benchmark case such that K has notenterednormergedwith I.
a.Writedownthepro?tmaximisationproblemforeachofM and I.
b.WriteoutthebestresponsefunctionsforeachofM and I.
c.Solve for each ?rm’s production quantity and pro?ts, the equilibriummarketpriceandconsumersurplus.
WewillnowassumethatK entersasaseparatecompetitorinthemarket (alongsideM and I).
d.Write down the pro?t maximisation problem for each of M, I and K .
e.Writeoutthebestresponsefunctionsforeach?rm.
f.Solveforeach?rm’s productionquantityandpro?ts. Consideringthissituationinisolation,when will K decidetoenterthemarket?
g.Given that K enters the market, ?nd the equilibrium market priceandconsumersurplus. Doconsumersbene?tfromtheentrance of K?
Now assume that K instead merges with I to form I0. I0 and M now competeinthemarket.
h.Writedownthepro?tmaximisationproblemforeachofM and I0.
i. Solve for each ?rm’s production quantity and pro?ts, the equilibrium market price and consumer surplus. Do consumers bene?t fromthemergerbetween K and I?
The regulator will now decide whether to allow the K to enter independentlyortomergewithincumbent I.
j.Suppose that the regulator is concerned with maximising consumer welfare. Compare your answer in g.) to that of j.). When will the merger bene?t consumer welfare more than K entering the market separately? [Hint: if comparing consumer surplus proves to be too dif?cult, consider comparing prices instead]. Explain the meaning/intuitionbehindyouranswer(max3-4sentences).
For the remainder of the question, we will assume that cM = 1 20 and cI = 1 10.
k.Usingyouranswerfromj)or otherwise, will consumers prefer themergerorfor K toenterindependently?
l.Now suppose that the regulator is concerned with maximising total welfare (that is, the sum of consumer welfare and ?rm pro?ts). Is ForwhatvaluesofKwillthemergerbene?ttotalwelfaremorethan K entering the market separately? (you may round your ?nal answer to threesigni?cant?gures).
m.Compare your answers from k) and l). Are the preferences of consumers and the regulator for the merger/independent entry always the same? If they are (or are not), explain why (max 3-4 sentences).

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