A large firm has two divisions: an upstream division that is a monopoly supplier of an input whose only market is the downstream division that produces the final output. To produce one unit the final output, the downstream division requires one unit of the input. If the inverse demand for the final output is P = 1,000 -80Q, would the company's value be maximized by paying upstream and downstream divisional managers a percentage of their divisional profits? Explain.
To determine whether the company's value would be maximized by paying upstream and downstream divisional managers a percentage of their divisional profits, we need to analyze the potential impact of this compensation scheme on the overall performance of the firm.
First, let's define the value of the company. In this case, we can consider the value of the company as the sum of the profits generated by both the upstream and downstream divisions. Thus, the goal is to maximize the total profits earned by the company.
Under the given scenario, the upstream division holds a monopoly over the input supplied to the downstream division. This means that the upstream division has a high degree of market power and can potentially influence the price it charges for the input.
To determine the optimal pricing strategy for the upstream division, we should consider the concept of price discrimination. Price discrimination is a strategy where a firm charges different prices to different customers or market segments based on their willingness to pay.
In this case, the downstream division is the sole customer of the upstream division and requires one unit of the input to produce one unit of the final output. The downstream division's inverse demand function for the final output is P = 1,000 - 80Q, where P represents the price and Q represents the quantity.
To maximize profits, the upstream division should set its input price in a way that maximizes the downstream division's profitability while also considering its own profits. To find the optimal input price, we need to determine the downstream division's profit function.
The profit of the downstream division can be calculated by multiplying the quantity of final output (Q) by the difference between the market price (P) and the input cost (C), where C is the cost of the input from the upstream division.
Downstream division profit = Q(P - C)
= Q(1,000 - 80Q - C)
To find the maximum profit, we can take the derivative of the profit function with respect to Q and set it equal to zero:
d/dQ [Q(1,000 - 80Q - C)] = 0
Solving this equation will yield the optimal quantity of final output (Q), which can then be used to find the corresponding market price (P).
Considering the compensation scheme mentioned (paying divisional managers a percentage of their divisional profits), it may incentivize divisional managers to maximize their respective division's profitability. However, it's important to note that this may not necessarily align with the overall maximization of the company's value.
Paying managers only based on divisional profits could create conflicts of interest between the two divisions. The upstream division may want to charge a higher price for the input to maximize its own profits, while the downstream division may prefer a lower input price to increase its profitability.
This misalignment of incentives can potentially lead to suboptimal pricing decisions, resulting in lower overall profits for the company. Instead, a compensation scheme that incentivizes collaboration and a jointly optimal pricing strategy between the two divisions may be more beneficial for maximizing the company's value.
In conclusion, while paying divisional managers a percentage of their divisional profits may motivate them to individually maximize their division's profitability, this compensation scheme may not necessarily maximize the overall value of the company. It is crucial to align the incentives of both divisions and encourage collaboration to achieve the best outcome for the company as a whole.