onsider a market that will last two years, and assume no discount (the interest

Question

onsider a market that will last two years, and assume no discount (the interest rate is zero). There are two players, an incumbent firm A that starts producing and X at the beginning of the first year, and a potential entrant E that contemplates entry at the beginning of the second year. Firm E is producing a good that serves the same needs as X, but is of lower quality. Serving this market requires XE each firm paying a fixed cost F-200 in order to install capacity, this cost is paid only once, even if the firm produces in both periods. During the first year the incumbent A pays F and operates alone in the market, choosing a price between the following: Pm, the monopoly price, or Pi, a very low price that threatens (in conjunction with the superiority of X over XE) to leave any potential entrant with zero sales (stage 1 of the game). If A charges Pm it gets a first-period revenue equal to 2550, whereas the same revenue under Pi is 1950. At the beginning of the second year, E contemplates entry (stage 2). If E does not enter, the incumbent must charge the same price it did during period one (whether P or P) and make the same revenue. If E enters, the incumbent revises its price having now two choices (stage 3): to either fight the entrant charging Pi, or to accommodate it, charging P The latter is a price between Pm and Pi (Pm> Pe>P) that allows E to make positive sales and revenue equal to 400. If A accommodates entry, its revenue is equal to 650. If following entry A decides to fight charging the price P, A's revenue is 250 and E's revenue is zero. a) Is it possible for the incumbent to deter entry by threatening to charge Pi during the first and the second period? Is charging Pi during the first period a rational choice for the incumbent? b) Find the equilibrium path (outcome) and the profits at the SPNE

Explanation / Answer

a).

Consider the given game problem here there are 2 firm. So, for “incumbent firm A” have to choices either charge “Pm” with payoff “2550 – 200 = 2350” or charge “Pc” with payoff “1950 – 200 = 1750”, because the “firm A” have to pay a fixed cost of “200” in order to install capacity .

Now, in the 2nd stage if “entrant E” will decide to not enter into the market, then “firm A” will continue to charge same price as “1st stage”. So, if “E” decides not to enter into the market then “A’s” payoff under “Pm” is “2550 + 2350 = 4900”, similarly “A’s” payoff under “P1” is “1950 + 1750 = 3700”, since in the 2nd stage “A” don’t have to pay the fixed cost.

Now, if “E” decides to enter in to the market then “A’s” have two possibilities either to charge “Pc” to accommodate “E” other wise to charge “P1” to prevent “E” out of market in the 2nd stage. So, under the 1st possibility “A’s” payoff is “2350+650=3000” if “A” charged “Pm” and “1750+650=2400” if “A” charged “P1” in the 1st stage. Now, “E’s” payoff is “400-200=200”.

Now, under the 2nd possibility “A’s” payoff is “2350+250=2600” if “A” charged “Pm” and “1750+17500=3700” if “A” charged “P1” in the 1st stage. Now, “E’s” payoff is “0”.

So, we can see that it is possible for the incumbent to deter entry by threating to charge “P1” in the 1st and 2nd period.

Now, if “A” want to charge the monopoly price then “E” will try to enter into the market in the 2nd stage and will charge “Pc” in the 2nd stage (since Pc < Pm) if “A” accommodates “E”, there are 2 possibilities if “A” accommodate then will get “3000” as payoff otherwise (not accommodate) will get “2600” as a payoff . Now, if “A” charge “P1 < Pc” in the 1st stage then “E” will not enter into the market because “A” already charging very low price so “E” can’t survive in the market by charging “Pc”. So, “E” will decide not to enter into the market if “A” charge “P1” in the 1st stage. So, here “A” will get “3700” as payoff. So, charging “P1” during the 1st stage is rational choice.

b).

So, SPNE of this game is “A” will charge “P1” in the stage and since “P1 < Pc” then “E” will enter into the market and “A” will continue to charge the same price “P1” and will get “3700” as a payoff.

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