Tournaments, reward structures based on rank order, are compared with individual contracts in a model with one riskneutral principal and many risk-averse agents. Each agent's output is a stochastic function of his effort level plus an additive shock term that is common to all the agents. The principal observes only the output levels of the agents. It is shown that, in the absence of a common shock, using optimal independent contracts dominates using the optimal tournament. Conversely, if the distribution of the common shock is sufficiendy diffuse, using the optimal tournament dominates using optimal independent contracts. Finally, it is shown that for a sufficiently large number of agents, a principal who cannot observe the common shock but uses the optimal tournament does as well as one who can observe the shock and uses independent contracts.

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Three main types of mortgages are fixed interest contracts which automatically fall due on the sale of a dwelling, fixed rate loans which are assumable by a buyer, and floating rate instruments. When interest rates rise, the fall in the economic value of these assets in savings and loan associations' portfolios varies from one form of mortgage to another. For either of the fixed interest rate contracts, the cash flow from the mortgage is constant as long as it has not been prepaid. If the interest rate rises, the homeowner has a nominal capital gain, since his loan is then at a below market interest rate. He would therefore be less likely to prepay. The fall in the savings and loans' net worth arises from two factors: (1) the interest rate differential for mortgages of a fixed duration, and (2) the endogenous lengthening of the duration. This paper is an attempt to measure the dependence of the duration of mortgages on the implicit unrealized capital gain of mortgage holders resulting from interest rate changes. Our estimate is based on a sample of 4,000 mortgages issued in California which were active in 1975. We follow their payment history from 1975 to 1982. Using a Proportional Hazards Model, we estimate the percentage reduction in prepayment probability associated with interest rate changes. Our results indicate that for due-on-sale fixed interest rate mortgages, a sudden increase in the interest rate from 10 to 15 percent would induce a 23 percent loss in the economic value of the mortgage. If the mortgage were assumable, this loss would be 28 percent. Correspondingly, the 6-year average time to repayment of mortgages at a constant interest rate would be lengthened to nine years for due-on-sale mortgages, and 13-1/2 years for assumable ones.

In a double-blind placebo-controlled trial carried out from 1980 to 1982, 20 patients with established Lyme arthritis were assigned treatment with 2.4 million U of intramuscular benzathine penicillin weekly for three weeks (total, 7.2 million U) and 20 patients received saline. Seven of the 20 penicillin-treated patients (35 per cent) had complete resolution of arthritis soon after the injections and have remained well during a mean follow-up period of 33 months. In contrast, all 20 patients given placebo continued to have attacks of arthritis (P less than 0.02). In 1983, of 20 patients treated with intravenous penicillin G, 20 million U a day for 10 days, 11 (55 per cent) had complete resolution of arthritis and have remained well since. As compared with nonresponders, penicillin-responsive patients in both studies were more likely to have previously received antibiotics for erythema chronicum migrans (P less than 0.02) and less likely to have been given intraarticular corticosteroids during or at the conclusion of parenteral therapy (P less than 0.1). The Lyme spirochete was not cultured from synovium or joint fluid. We conclude that established Lyme arthritis can often be treated successfully with parenteral penicillin. However, neither of the regimens that we tested is uniformly effective, and further experience will be needed to determine the optimal course of therapy.