Problem 1: You Are The Manager Of Taurus Technologies

Problem 1 You Are The Manager Of Taurus Technologies And Your Sole

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) = 4 qi , and the inverse market demand curve for this unique product is given by P = 160 – 2 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 $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? What are your profits if you do make the investment? Instruction: Do not include the investment of $200 as part of your profit calculation. Should you invest the $200?

Paper For Above instruction

The competitive landscape between Taurus Technologies and Spyder Technologies mirrors a classic Cournot duopoly scenario, where both firms decide simultaneously on production quantities with the understanding that their profits depend on market output. The key strategic consideration revolves around the potential advantage of making a fixed, unrecoverable investment of $200 that could afford Taurus pre-market entry, potentially altering incentives and outcomes within the equilibrium framework.

Scenario Without the Investment

In the absence of the fixed investment, both firms play a simultaneous game of quantity setting. The inverse demand function P = 160 – 2Q indicates that total market quantity Q = q1 + q2, where q1 and q2 are the outputs of Taurus and Spyder, respectively. The firms' cost functions are identical, with C(qi) = 4qi, implying marginal costs (MC) of $4 per unit produced.

The profit function for Taurus without the investment is given by:

π1 = (P - MC) q1 = (160 – 2q1 – 2q2 – 4) q1

Similarly, Spyder maximizes its profit based on its output, assuming Taurus's quantity q1. Given symmetry and equilibrium conditions, the Cournot equilibrium yields the following best response functions:

• q1 = (78 – q2)/2
• q2 = (78 – q1)/2

Solving this system results in the Cournot equilibrium quantities:

• q1 = q2 = 26

Substituting back into the demand function gives the market price:

P = 160 – 2(26 + 26) = 160 – 104 = $56

The profit for Taurus is:

π1 = (56 – 4) 26 = 52 26 = $1,352

Scenario With the Investment

If Taurus makes the fixed investment of $200, it gains a pre-market entry advantage, potentially enabling it to commit to production quantity before Spyder decides. This pre-emption could enable Taurus to capture a larger market share or influence Spyder's production decisions favorably.

In the pre-emption case, assuming Taurus commits to a certain quantity q1', Spyder responds optimally. Given the fixed costs are not part of profit calculations, the firm evaluates whether the benefit from increased market control outweighs the $200 investment cost.

If Taurus can fully preempt the market or secure higher sales, its profit could increase. For example, suppose Taurus can set a quantity q1' that maximizes its pre-market profit, with Spyder reactive response. A simplified analysis suggests that preemptive entry allows Taurus to set a higher quantity, increasing profits above the non-investment equilibrium.

Estimating the profits post-investment involves calculating the max profit achievable through pre-commitment, minus the $200 investment. If this net benefit exceeds $1,352 (the non-investment profit), the investment is justified. Therefore, Taurus should proceed if the maximum net profit from pre-emptive entry exceeds its existing equilibrium profit.

In conclusion, the decision hinges on the strategic advantage gained through pre-entry, which, if significant, justifies the $200 investment. The precise quantitative benefit depends on detailed pre-emption modeling, but typically, if the advantage substantially raises profits beyond the original $1,352, Taurus should invest.

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