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?

$


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?

(Click to select) No Yes

Explanation / Answer

let q = q1 +q2

then C(Q)=4(Q1+Q2)

P= 160 - 2(Q1+Q2)

THEN PQ1=160Q1-2Q12-2Q1Q2

PROFIT = TR - TC

SO = 160Q1-2Q12-2Q1Q2-4(Q1+Q2)

differentiate w.r.t q1

160-4q1-2q2-4 = 156-4Q1-2Q2 (1)

SIMILARLY EQ2 IS 156-4Q2-2Q1

SOLVE FOR 1 AND 2

Q1=26 ,Q2=26 and P=56

USE P AND Q to find profit

THEN PROFIT =TR - TC =$2704

without

PROFIT =TR - TC

160Q-2Q2 - 4Q=156Q-2Q2

156-4Q = 0

Q=39 AND P=82

However , a rising fixed cost w

ould make it costly for the firms to release the product . The fixed investment should be avoided

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.