Two firms compete by setting prices of identical products. Consumer purchase fro
ID: 1147313 • Letter: T
Question
Two firms compete by setting prices of identical products. Consumer purchase from whichever firm offers the lowest price. Market demand is given by P 300-Q (a) If MCA 100 and MCB 100, briefly explain why the Nash equilibrium is where both firms set b) Suppose the firms have different marginal costs (e.g., MCA 90, MC 100). What is the Nash (c) Return to case (a) in which both firms have identical marginal cost, but the firms compete agairn price equal to marginal cost. equilibrium in this situation? and again. The firms' discount factors are 0.75 Explain whether it would be possible for the firms to tacitly collude such that they both charged the monopoly price. If so, how would they collude. If not, why not? d) Would your answer to part (c) change if a firm could deviate for three periods before it was detected?Explanation / Answer
1) Both firms will be setting price that equal to marginal cost in the Nash equilibrium. This will be a point where neither firm can deviate and make themselves better off. If the price is set higher than customers will not purchase from them; and if lower price is set, the whole market will be captured however at a point below marginal cost, thus they will lose money on every unit they sell.
Why won’t they set same prices above marginal cost, you ask? In such scenario, each would have the incentive to undercut the other by a penny and thus whole market will be captured. Therefore, pa = pb > mc is not a Nash equilibrium
2) Firm B will, at majority, reduce prices to p = MCB = 100. In such scenario firm A could set the identical price and split the market, however can make itself better off by undercutting firm B by a smal fraction and capturing the entire market demand for thus the whole market will be captured. Hence, it will set a price just below 100, for instance $99 if it’s setting prices in whole dollars, or $99.99 in case pricing in dollars and cents)
3) In this scenario, the firms could coordinate on the monopoly price in the below mentioned approach. Assuming that both firms agreed to start playing the monopoly price, however switching to the Bertrand equilibrium strategy forever after in case competitor deviates from the monopoly price.
If they cooperate, the firms will split the monopoly profits, as provided by MR = MC.
Thus, MR = 300 – 2Q = 100; Qm = 100, Pm=200; ITm= (200 – 100)*100 = 10,000
If collude, both firms will set P = 200 and thus split the monopoly profits among tjem and get 5,000 each period.
So, will the firms prefer to collude or deviate from this strategy?
If firms collude, they get 5,000 each period. At a discount factor of 0.75, the NPV of the stream of profits will be computed as 5000 X (1/(1-d)) = 5000x(1/.25) = 5000x4 = 20,000.
In case a firm deviates, then will capture the entire monopoly profit for a single period, however earns 0 afterwards. Hence, the NPV of the profits associated with deviation equals 10,000.
Because NPV of collusion exceeds NPV of deviating, thus firms will not deviate from the above agreement.
4) Assuming a firm could deviate for three turns, deviation would provide profits of 23,125 computed as 10,000 + 10,000*.75 + 10,000*.75^2 + 0*.75^3+0*.75^4+0*.75^3… = 10,000 + 7,500 + 5,625 = 23,125.
Because it exceeds the profits from collusion, thus the firms would prefer to deviate from the agreement.
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