5. We include “family-held corporations” within “partnerships” because such corporations are often established
under “subchapter S” of the Internal Revenue Service code and are more like small partnerships than large-scale
corporations. For the issues we study, this distinction is not important.
6. Eleven stages of growth, from planting to ripening, exist in “Feeke's Scale of Wheat Development.” See The
Wheat Grower (September 1994): WF-8.
7. Recognizing that ownership is not constant across stages of production points out the ambiguity of questions
like “How big is the farm?” A farm may be 1,000 acres at planting but harvesting may be done by another “farm”
over 80,000 acres.
8. Ellickson and Brewster (1947) also recognize the common cumulative feature of agriculture: “For the number
of simultaneous operations in agriculture varies little with either the size of farm or the 'state of the industrial arts.'
It makes little difference, for example, whether a corn-hog farm covers the whole state of Iowa or on 160 acres,
or whether farming is done with oxen, flails, and sickles or with high-powered tractors and combines; the number
of production steps that can be done at the same time on such farms remains substantially unchanged” (841).
9. For example, the harvest season for spring wheat might be three weeks but can be several months for sugarcane.
In the simple case of homogeneous stages, L = 365 /(C ∗ S) so that if just one stage requires a year to complete
the process, then L = 365 days.
10. In making this assumption, we assert that the reduction in capital costs outweighs the moral hazard problems
that might arise with multiple owners or users of capital. Compared to labor effort, capital levels are easily observed
and often assigned to a specific partner or hired worker.
11. Once again, the random input
play no direct role in the objective function or
the optimality conditions. None of the organizations we discuss are first-best: this requires full specialization
( a = 1, r = r
and its variance
min ), no moral hazard, and optimal timing.
12. Our model of partnership is distinct from recent studies by Gaynor and Gertler (1995) and Lang and Gordon
(1995) that emphasize risk sharing as the motivation for partnerships.
13. This is because a = 1 / 2 in both cases.
14. We recognize that a firm with a corps of hired labor is likely to have hired managers as well. Our model simply
lumps together the adverse selection and moral hazard problems of managers with the moral hazard of workers.
Analysis of these issues can be found in the burgeoning literature on the internal workings of the firm (Baker,
Gibbs, and H olstrom 1994; Lazear 1995).
15. Mighell and Jones (1963) also discuss “interstage” incentives. More recently, Hennessy (1996) develops a
model in which intermediate product quality is costly to measure, thus creating incentives for vertical coordination.
This justification has the same impact as our timelines argument.
16. In practice, the importance of timing can vary greatly across crops and stages. Harvest timing, for example, is
crucial ( δ is large) in spring wheat, where delays can result in large losses from hail, rain, or wind. Once wheat
is threshed, however, there is almost no timing problem associated with milling the wheat into flour ( δ ≈ 0).
Sugarcane, on the other hand, must be processed into raw sugar within 24 hours after cutting or the cane's sugar
content will decline dramatically (again δ is large).
17. This is most likely to hold for small partnerships (for example, if
2) and when capital is relatively
unimportant because the marginal deadweight losses from moral hazard fall with an increase in partners while
the marginal benefits of capital cost savings increase with the number of partners.
18. This holds because increases in the number of partners lead to approximately quadratic increases in moral
hazard losses. This relationship is essentially that derived from the analysis of the deadweight losses from
19. A $50,000 limit per person was created in 1981. “Persons” include individuals, partnerships, estates, and
20. The crop failures and famines in China and the Soviet Union are the most obvious cases, but other important
examples abound. See Nerlove (1996) and Pryor (1992). Closer to home, farming on Indian reservations in the
western United States has been tremendously unproductive because typical land tenure institutions do not allow