Suppose that spot market wages fluctuate between the two values $50 and $100, each with probability 1/2. Suppose that a risk-averse worker dislikes fluctuations in income and wants to smooth out these wages. He therefore approaches a large employer, who is risk-neutral and goes by expected values. They agree on a contract (w_l, w₂), where w₁ is paid by the employer to the employee in case the spot market wage is $50, and where w₂ is paid in case the spot market wage is $100.

(a) Describe precisely the set of contracts [(w₁, w₂) pairs] that would be acceptable to the employer, in the sense that he would prefer to pay using such a contract rather than pay spot wages.

(b) Using part (a), argue that if the employer and the employee settle on a contract, then it must be the case that (w₁ + w₂)/2 < 75, and, moreover, that w₁ > 50 and w₂ < 100.

(c) Now consider an ongoing form of this contract between employer and laborer. Notice that in each period, if the going spot wage happens to be $100, the laborer has an incentive to break the contract and run away. Why is this? What is the laborer’s short-run gain from doing so?

(d) Now we think about the long-run loss to the laborer for breaking the contract. He will surely lose future contracts with the current employer. This is a source of real loss if, in the original contract, the employer desisted from driving the laborer’s compensation down to the equivalent of what he could have obtained elsewhere. Observe that this becomes more and more important if the laborer can get a permanent contract elsewhere without the current employer’s knowledge. Argue that if this problem becomes very serious, then the employer will not agree to offer the permanent contract in the first place.