TIR y VAN del proyecto

Days to Go Offer by Total Profits to Divide Amount Offered to Labor

1 Management $ 1,000 $1 2 Management 2,000 2 3 Management 3,000 3 4 Management 4,000 4 5 Management 5,000 5 … 100 Management 100,000 100 101 Management 101,000 101

This story clearly exaggerates management’s true bargaining power. Postponing agreement, even by one day, costs management $999 and labor only $1. To the extent that labor cares not only about its payments but also how these payments compare to management’s, this type of radically unequal division will not be possible. But that does not mean we must return to an even split. Management still has all the bargaining power. Its goal should be to find the minimally acceptable amount to give to labor so that labor prefers getting that amount over nothing, even though management may get more. For example, in the last period, labor might be willing to accept $334 while management gets $666 if labor’s alternative is zero. If so, management can perpetuate that 1:2 split throughout each of the 101 days and capture two-thirds of the total profit. The value of this technique for solving bargaining problems is that it suggests some of the different sources of bargaining power. Splitting the difference or even division is a common but not universal solution to a bargaining problem. Look forward and reason backward provides a reason why we might expect to find unequal division. In particular, it suggests that in the case of making offers, “’Tis better to give than to receive.”

6. A

: P

I

I

O

R

It is possible to apply backward reasoning even when problems lack a fixed endpoint.* This

is an important feature of most bargaining problems. Let us look therefore at a more typical setting, such as a steel company. A strike is in progress. If it is settled, the company can make an operating profit of $3 million each week. The union and the management are

bargaining over the division of this sum. Negotiation sessions are held weekly, and the two sides alternate in making offers.

Every week that goes by without an agreement, the two sides together sacrifice $3 million. As usual, time is money. An immediate settlement is in their joint best interest. But on what terms? Intuition suggests that the party that is more impatient for a settlement will make the earlier or the larger concessions. A more detailed look at the process confirms this intuition, and converts it into more precise predictions about the two parties’ shares.

Time is money in many different ways. Most simply, a dollar received earlier is worth more than the same dollar received later, because it can be invested and earn interest or dividends in the meantime. If the rate of return on investments is 5 percent a year, then a dollar received right now is worth $1.05 received a year later.

The same idea applies to our union and management, but there are some additional features that may add to the impatience factor. Each week the agreement is delayed, there is a risk that old, loyal customers will develop long-term relationships with other suppliers, and the firm will be threatened with permanent closure. The workers and the managers will have to move to other jobs that pay less well, the union leaders’ reputation will suffer, and the management’s stock options will become worthless. An immediate agreement is better than one a week later precisely to the extent of the probability that this will come to pass in the course of that week.

Of course the union and the management may assess the risks and their consequences differently. Just to make things precise, suppose the union regards $1.00 right now as equivalent to $1.01 a week later, and for the management the figure is $1.02. In other words, the union’s weekly “interest rate” is 1 percent; the management’s, 2 percent. The management is twice as impatient as the union.

This difference in the two sides’ impatience has a dramatic effect on their bargaining settlement: the two sides’ shares are in inverse proportion to their rates of interest, so the union gets two-thirds ($2 million per week) and the management one-third ($1 million per week).

The fact that the greater share in bargaining agreements goes to the more patient side is very unfortunate for the United States. Our system of government, and its coverage in the media, foster impatience. When negotiations with other nations on military and economic matters are making slow progress, interested lobbyists seek support from congressmen, senators, and the media, who pressure the administration for quicker results. Our rival nations in the negotiations know this very well, and are able to secure greater concessions from us.

Incentives

Why have socialist economic systems failed so miserably? The best laid Five Year Plans of Stalin and his successors “gang agley” because the workers and the managers lacked adequate incentives. Most importantly, the system offered no reward for doing a good job rather than a merely adequate one. People had no reason to show initiative or innovation, and every reason to cut corners wherever they could—fulfilling quantity quotas and slacking on quality, for example.

A market economy has a better natural incentive mechanism, namely the profit motive. A company that succeeds in cutting costs, or introducing a new product, makes a greater profit; one that lags behind stands to lose money. But even this does not work perfectly. Each employee or manager in a company is not fully exposed to the chill wind of competition in the market, and the top management of the firm has to devise its own internal carrots and sticks to obtain the desired standards of performance from those below. When two firms join forces for a particular project, they have the added problem of designing a contract that will share the incentives between them in the right way.

1. H

R

W

E

We bring out the important ideas for the design of incentive schemes through a series of examples. Imagine yourself as the owner of a high-tech company in California trying to develop and market a new computer chess game, Wizard 1.0. If you succeed, you will make a profit of $200,000 from the sales. If you fail, you make nothing. Success or failure hinges on what your expert player-programmer does. She can either put her heart and soul into the work, or just give it a routine shot. With high-quality effort, the chances of success are 80 percent, but for routine effort, the figure drops to 60 percent.

Chess programmers can be hired for $50,000, but they like to daydream, and will give only their routine effort for this sum. For high-quality effort, you have to pay $70,000. What should you do?

Chance of

Success Average Revenue Salary Payments Average Profit = Revenue—Salary Low-Quality

Effort 60% $120,000 $50,000 $70,000

High-Quality