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 firms’ products are viewed as identical by most consumers. The relevant cost functions are C(Qi) = 4Qi, and the inverse market demand curve for this unique product is given by P = 160 – 2Q. 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 $200, Taurus Technologies can bring its product to market before Spyder finalizes production plans. What are your profits if you do not make the investment?

Explanation / Answer

For Firm 1

R1 = 160Q1-2Q1^2-2Q1Q2

MR1 = 160-4Q1-2Q2

MC = 4 so if MR=MC

4Q1+2Q2=156

Similarly for firm 2

R2 = 160Q2-2Q2^2-2Q1Q2

MR2 = 160-4Q2-2Q1

MC = 4 so if MR=MC

4Q2+2Q1=156

Now solving equation for both firm we get Q1=Q2=26

P = 56

Profit for each firm = 56*26-4*26 = 1352

Now for leading firm stackelberg oligopoly

Firm 2 reaction function Q2 = 39-Q1/2

P = 160 - 2Q1 - 2*29 +Q1 = 82 - Q1

MR = 82-2Q1

MC=4

As MR=MC

Q1 = 39

Q2 = 39-0.5*39 = 19.5

Q1+Q2 = 58.5

So P = 160-58.5*2 = 43

So Profit firm 1 = 43*39-4*39 = 1521

So difference = 1521-1352 = 169 So it does not even cver 200 so we should not make the investment.

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