We are a regional leader in industrial ice machines and only face competition from one other vendor in our relevant market. Because of our preferred supplier contracts we are able to bring our product to the market before our rival does, so we currently have a Stackelberg leadership advantage.

Moreover, we are out competing our rival in terms of marginal costs. Our accounting department has informed me that our monthly costs are roughly C(Q1) = 1,200 + 4Q1, while those of the competitor are C(Q2) = 1,000 + 8Q2.

According to our sales department we are both facing the following inverse monthly market demand curve: P(Q) = 600 - 2Q.

Since we have enough capacity to supply the entire relevant market in this time period, we are considering buying the rights of our competitor to become the sole supplier to the relevant market. Before I go into negotiations, I would like you to estimate what our maximum willingness to pay should be for monopoly control of the relevant market. I want to make sure that I do not over-pay!