You are the manager of Taurus Technologies, and your sole competitor is Spyder T

Question

You are the manager of Taurus Technologies, and your sole competitor is Spyder Technologies. The two firm’s products are viewed as identical by most consumers. The relevant cost functions are C (Qi) = 2Qi, and the inverse market demand curve for this unique product is given by P = 50 – Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $40, Taurus Technologies can bring its product to market before Spyder finalizes production plans. Should you invest the $40? Explain.

Explanation / Answer

This problem deals with the first mover's advantage. If you can pay $40 to enter first and establish a monopoly, can you make it unprofitable for the second firm to enter. First, let's solve the Cournot game that would occur if you don't invest. V is profit. MV is marginal profit. V = P*Q1 - C(Q1) V = (50-Q1-Q2)*Q1 - 2Q1 MV = 50-2Q1-Q2 - 2 = 0 Q1 = (48-Q2)/2 This is your best response function. Since you both have the same demand and cost structure, your opponent will have an analogous best response function: Q2 = (48-Q1)/2 Plug Q2 into Q1 and solve for Q1 Q1 = (48-Q2)/2 Q1 = (48-[(48-Q1)/2])/2 (3/4)Q1 = (48-24)/2 Q1 = (4/3)*(48-24)/2 Q1 = 16 Since everything is symmetric, Q2=16. So we can solve for price. P = 50-Q1-Q2 P = 50-16-16 P = 18 Now, let's solve for our profits. V1 = P*Q1 - C(Q1) V1* = 18*16 - 2*16 V1* = 256 So, if we don't invest, then we get $256 out of the Cournot game. Now, let's say we invest and become a monopoly. V1 = P*Q1 - C(Q1) - 40 V1 = (50-Q1)*Q1 - 2Q1 - 40 MV = 50-2Q1 - 2 = 0 Q1* = 24 Plug this into inverse demand P = 50 - Q1 P = 50 - 24 P = 26 Solve for profits: V1 = P*Q1 - C(Q1) - 40 V1 = 26*24 - 2*24 - 40 V1 = 536 Awesome, so we definitely want to invest if our entry as a monopoly will keep the other guy out. Let's see if it will. His best response function was: Q2 = (48-Q1)/2 Q2 = (48-24)/2 Q2 = 12 The price is: P = 50 - Q1 - Q2 P = 50 - 24 - 12 P = 14 His profit is: V2 = Q2*P - 2*Q2 V2 = 12*14 - 2*12 V2 = 144 So, he will enter because this is positive. This means your profit is given by V1 = Q1*P - 2*Q1 - 40 V1 = 24*14 - 2*24 - 40 V1* = 248 Ok, so I know this was a lot of math, but the decision is simple. If we don't invest, we get $256. If we do invest, we only get $248 because the market is large enough to allow a second entrant. So, we're better off not investing.

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