This paper presents a detailed theoretical derivation and justification for methods used to compute solutions to a multi-period (including infinite-period), continuum-agent, unobservedeffort economy. Actual solutions are displayed illustrating cross-sectional variability in consumption and labour effort in the population at a point in time and variability for a typical individual over time. The optimal tradeoff between insurance and incentives is explored and the issue of excess variability is addressed by consideration of the analogue full-information economy and various restricted-contracting regimes.