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 (Q) = 5,000 - Q. Note that currently the Cournot 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 Stackelberg leadership is worth it.