Question

Suppose that an entrepreneur is deciding whether or not to build a new highspeed railroad on the West Coast. Building the railroad will require an initial sunk \(\operatorname{cost} F\). If operated, the new railroad will generate revenue \(R\). Operating the railroad will cost \(M\) in fuel and \(n w\) in wages, where \(n\) is the number of full-time jobs needed to operate the new railroad and \(w\) is the career wage per worker. If a rail worker does not work on the new railroad, then he can get a wage of \(\bar{w}\) at some other job. Assume that \(R>M+F+n \bar{w}\), so it would be profitable to build and operate the new railroad even if rail workers had to be paid somewhat more than the going rate \(\bar{w}\). The entrepreneur, however, must decide whether to invest the initial sunk cost \(F\) before knowing the wages she must pay. (a) Suppose that if the railroad is built, after \(F\) is invested, the local rail workers' union can make a "take it or leave it" wage demand \(w\) to the entrepreneur. That is, the entrepreneur can only choose to accept and pay the wage demand \(w\) or to shut down. If the railroad shuts down, each worker receives \(\bar{w}\). Will the railroad be built? Why? (b) Next suppose that the wage is jointly selected by the union and the entrepreneur, where the union has bargaining weight \(\pi_{\mathrm{U}}\) and the entrepreneur has bargaining weight \(\pi_{\mathrm{E}}=1-\pi_{\mathrm{U}}\). Use the concept of negotiation equilibrium to state the conditions under which the railroad will be built. (c) Explain the nature of the hold-up problem in this example. Discuss why the hold-up problem disappears when the entrepreneur has all of the bargaining power. Finally, describe ways in which people try to avoid the hold-up problem in practice.

Short answer

No, not if union wages are too high (a). It may be built with balanced bargaining weights (b). Hold-up occurs due to post-investment wage hikes (c).

Step-by-step solution

Analyze Profitability Condition for Building

The condition given is that revenue \( R \) must be greater than the sum of operating costs \( M \), sunk cost \( F \), and competitive wages \( n \bar{w} \), i.e., \( R > M + F + n \bar{w} \). This condition implies that the railroad can be profitable if operated at or slightly above competitive wage rates.

Evaluate Union Wage Demands Scenario (Part a)

If the union can make a 'take it or leave it' offer with wage \( w \) to the entrepreneur after the sunk cost \( F \) is invested, the entrepreneur must decide whether \( R > M + n w \). If the union demands \( w = \bar{w} + \epsilon \) such that \( R \leq M + n w \), the entrepreneur cannot profitably operate, and the railroad will not be built.

Negotiation Equilibrium Analysis (Part b)

With joint wage selection, the negotiation considers the bargaining weights \( \pi_{\mathrm{U}} \) and \( \pi_{\mathrm{E}} \). The wage \( w \) that maximizes the joint surplus is negotiated where the profit \( R - M - n w \) and surplus \( n(w - \bar{w}) \) are considered. The Nash bargaining solution relates to these functions' optimal intersection point considering both parties' weights.

Identify the Hold-up Problem (Part c)

The hold-up problem arises because, after the initial investment \( F \), the union can leverage the situation to demand higher wages \( w > \bar{w} \), leading to potential non-recovery of \( F \) by the entrepreneur. When the entrepreneur has all bargaining power (\( \pi_{\mathrm{E}} = 1 \)), they would set \( w = \bar{w} \), avoiding the hold-up problem. Solutions in practice include contracts that fix wages before sunk costs are incurred, thus preventing opportunistic wage increases after investment.

Key concepts

Sunk Cost

Sunk cost refers to money that has already been spent and cannot be recovered. In the context of building a new high-speed railroad, the sunk cost is denoted as \( F \), representing the initial investment required to construct the railroad. Once the entrepreneur has committed this money for building, it is a sunk cost because it is irreversible. Therefore, the decision to operate the railroad should not be influenced by the sunk cost, as this money cannot be retrieved.
This concept is crucial because once the initial investment \( F \) is made, any further decisions about operating the railroad depend on the additional costs and revenues. The entrepreneur must assess whether the remaining revenue \( R \) exceeds the additional operating costs \( M + n w \), where \( n \) is the number of jobs and \( w \) is the wage per worker.
Sunk costs can lead to distortion in decision-making if they are not ignored in future calculations. It's important to focus on potential future costs and benefits instead. Understanding sunk costs helps avoid the common pitfall of continuing a venture just because substantial amounts have already been sunk.

Bargaining Power

Bargaining power in negotiation determines the influence each party has over the outcome. In the railroad scenario, the union and the entrepreneur share bargaining power to decide workers' wages. The union's bargaining weight is represented by \( \pi_\text{U} \), and the entrepreneur's weight is \( \pi_\text{E} = 1 - \pi_\text{U} \).
With equal bargaining, outcomes are decided from a position where each party's influences are considered. Greater bargaining power allows a party to tilt the wage negotiation closer to their preferred outcomes. For instance, if \( \pi_\text{U} \) is larger, the union could negotiate for higher wages. Conversely, if \( \pi_\text{E} \) is greater, the entrepreneur can press for lower labor costs.

• Bargaining power affects profitability. Higher union power might squeeze the entrepreneur's profits through increased wage demands, whereas more entrepreneur power could push wages towards the competitive level \( \bar{w} \).
• It shapes negotiation dynamics; equilibrium wages hinge on the relative power balance, impacting whether the project remains viable post-negotiation.

Hold-up Problem

The hold-up problem arises in business when one party in a transaction becomes vulnerable after investing, allowing the other party to exploit the situation. In the railroad case, after the investment \( F \) is made, the union could potentially demand excessive wages, undermining the project's profitability.
This problem becomes more prominent in situations with specific assets, like the railroad, where the investment is highly tailored and cannot easily be repurposed. After the investment is sunk, the entrepreneur has less leverage, and the union can leverage this to push for higher wages than initially feasible.
When the entrepreneur holds all bargaining power, the hold-up problem is less likely to emerge because they can enforce the wage at \( \bar{w} \).

• Contracts can mitigate hold-up issues by fixing wages before any critical investment, ensuring stable expectations for both parties.
• Strategic alliances or vertical integration are other solutions where businesses tightly coordinate to reduce power imbalance post-investment.

Negotiation Equilibrium

Negotiation equilibrium refers to an agreement where both parties' interests are balanced based on their respective bargaining powers. It's a state of balance in negotiations, ensuring no party is better off changing their proposal unilaterally. For the railroad scenario, this equilibrium examines the interests of the entrepreneurs and the union around wage determination.
Using the Nash bargaining solution, negotiations focus on maximizing joint benefits. Both the entrepreneur, looking to minimize costs, and the union, aiming to raise wages, negotiate to find a compatible wage \( w \).
In practice, reaching negotiation equilibrium requires understanding and accommodating the opposing party's strengths and limitations.

• It involves strategic negotiation, taking into account how wage settings impact overall profits \( R - M - n w \).
• It helps avoid disputes and operational delays, ensuring smooth collaboration and project success.
• This equilibrium ensures the railroad operates under mutually beneficial terms, fostering long-term project sustainability.