Welcome on board to one of the Midwest\'s premier medical supply companies. As y
ID: 1107295 • Letter: W
Question
Welcome on board to one of the Midwest's premier medical supply companies. As you know we supply hospitals in the Midwest with mega packs of prick-numbing needles. We have only one competitor in the Midwest, and hospitals view our needle mega packs as exactly the same in quality. So, the inverse monthly market demand curve for needle mega packs is P = 5,000 - Q. Note that currently the market price is determined by the simultaneous production decisions of ourselves (Q1) and our rival (Q2), so that total monthly market production is Q = Q1 + Q2 Our accounting department has informed me that our monthly costs are roughly C1(Q) = 2,000,000 + 200Q1, while our competitor's costs are estimated to be: C2(Q2) = 500,000 + 800Q2 We are thinking about making a preferred-supplier investment with the Midwest Group Purchasing Organization (MGPO) to bring our product to the market before our rival (instead of the current situation of simultaneously supplying the market). The MGPO preferred-supplier investment will cost us $300,000 per month, and so I would like you to let me know if you think the investment in moving first is worth it.
Explanation / Answer
Because we would like to be the first mover, we would incorporate the decision of our rival in our strategy and behave like a stackelberg leader
In Stackelberg model where we as firm 1 are the first mover, we must take the reaction function of firm 2 in its computation of marginal revenue.
Derivation of firm 2’s reaction function
Total revenue of firm 2 = P*(q2) = (5000 – (q1 + q2))q2 = 5000q2 – q22 – q1q2
Marginal revenue = 5000 – 2q2 – q1
Marginal cost = 800
Solve for the reaction function
5000 – 2q2 – q1 = 800
4200 = 2q2 + q1
q2 = 2100 – 0.5q1
Incorporate this in the reaction function of firm 1
Total revenue for firm 1 = P*(q1)
(5000 – (q1 + q2))q1
=(5000q1 – q1^2 – q1q2
=(5000q1 – q1^2 – q1*(2100 – 0.5q1)
= 2900q1 – 0.5q1^2
MR = 2900 – q1
Equate MR = MC
2900 - q1 = 200
q1 = 3100
q2 = 2100 – 0.5*3100 = 550
p1 = 5000 – 3100 – 550 = $1350
Profit by our firm = TR – TC = 3100 x 1350 – (2000000 + 200 x 3100) = 1,565,000
As Cournot duopolist, we would produce 1800 at a price of 2000. Profit if we continue to work as simultaneously deciding Cournot duopolist is TR – TC = 1800 x 2000 - (2000000 + 200 x 1800) = 1,240,000.
Profits are increased by 325,000 and so the investment is worth it because it will still increase profits by 25000.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.