
M. V. BORLAND ET AL.
necessarily or sufficiently informative for the systematic deter-
mination of utility-increasing reallocations of educational re-
sources. The relative position of an individual school or school
district is determined not only by their decision to allocate re-
sources to the various academic areas for which comparisons
are made, but the decision to allocate resources by other
schools or school districts over which they have no control .
Summary and Conclusion
Is the typical suggestion of change in resource allocation
given the report of comparative test scores by academic area
necessarily utility-increasing? If different school administrators
allocate resources under utility-maximizing conditions, but with
respect to different educational utility functions, then even in
this case, the students in such schools or school districts would
be expected to have comparative test scores that are necessarily
low in at least one academic area and high in at least one other
academic area, mutatis mutandis. To reallocate educational
resources, therefore, on the basis of the existence of compara-
tive test scores can not be expected to be utility-increasing for
any individual school or school district, despite the existence of
low and high comparative scores in such individual schools or
school districts. A claim to the contrary would violate the orig-
inal assumption that the initial allocations of resources are util-
ity-maximizing. Unless empirical work on the relationship be-
tween comparative test scores and resource allocation is under-
taken to provide knowledge of comparative marginal utilities
by academic area, reallocations of available resources sug-
gested by policy makers, educational authorities, and members
of the general public will have unknown consequences on edu-
cational utility.
Re ferences
Carroll, J. (1963). A model of school learning. Teachers College
Record, 64, 723-733.
Denham, C., & Lieberman, A. (Eds. ) (1980). Time to Learn. Washing-
ton, D.C.: National Institute of Education.
Fisher, C., Marliave, R. & Filby, N. (1979). Improving teaching by
increasing ‘academic learning time’. Educational Leadership, 37,
52-54.
Karweit, N. (1984). Time-on-task reconsidered: Synthesis of research
on time and learning. Educational Leadership, 41, 32-35.
Leithwood, K., & Stager, M. (1989). Expertise in principals’ problem
solving. Educational Administration Quarterly, 25, 126-161.
doi:10.1177/0013161X89025002003
Levin, H., & Tsang, M. (1987). Economics of student time. Ec onomics
of Education Review, 6, 357-364. doi:10.1016/0272-7757(87)90
019-7
Roberts, R., Schrader, R., & Harryman, M. (1986). Productive use of
time: an attack on declining achievement. Journal of Human Beha-
vior and Learning, 3, 32-40.
Simon, H. (1976). Administrative Behavior: A Study of Decision- Mak-
ing Processes in Administrative Organization, 3rd ed., New York:
The Free Press.
Wiley, D., & Harnischfeger, A. (1974). Explosion of a myth: Quantity
of schooling and exposure to in instruction, major educational ve-
hicles. Educational Researcher, 3, 7-12.
Endnotes
1Such comparative test scores most commonly take the form of per-
centile scores by academic area derived from absolute scores for com-
parisons to other individual schools or school districts. Sometimes,
however, absolute test scores are transformed into stanines, despite the
condition that neither parents nor counselors are likely to be able to
provide a definition of a stanine.
2Such a question with respect to the results of administrative deci-
sions has long existed and is currently relevant. See K. Leithwood and
M. Stager, “Expertise in Principals’ Problem Solving,” Educational
Administration Quarterly, v25, n2 (May 1989), and H. Simon, Admini-
strative Behavior: A Study of Decision-Making Processes in Adminis-
trative Organization
3Equation (1) is assumed to be continuous, with first and second par-
tial derivatives that are continuous, and strictly quasi-concave in its
arguments. The first partials of Equation (1) are assumed to be strictly
positive. Attempts, in general, to affect levels of achievement, in terms
of scores associated with the various areas of testing, are not con-
strained to those that redistribute a fixed quantity of educational re-
sources, but include those that increase educational resources by trans-
fers from non-educational areas and by increases in the educational day
and/or year. Nevertheless, given the determination for R in a more
general equilibrium framework, distributions of educational resources
are assumed to be constrained to R.
, 3rd. ed., New York: The Free Press, 1976.
4Equation (4) is also assumed to be continuous, with first and second
partial derivatives that are continuous, and strictly quasi-concave in its
arguments. The first partials of Equation (4) are assumed to be strictly
positive, as well. An analysis over time can be simplified by invoking a
composite-resource theorem that states that, if prices of a group of
resources change in the same proportion over time, the optimal choice
of resources is consistent with the solution implied by the consideration
of resources as a single resource.
5See H. Levin and M. Tsang, “Economics of Student Time,” Eco-
nomics of Education Review, v6, n4 (1987), pp. 357-364; R. Roberts, R.
Schrader, and M. Harryman, “Productive Use of Time: An Attack on
Declining Achievement,” Journal of Human Behavior and Learning, v3,
n3 (1986), pp.32-40; N. Karweit, “Time-on-Task Reconsidered: Syn-
thesis of Research on Time and Learning,” Educational Leadership, v41,
n8 (May 1984), pp. 32-35; C. Denham and A. Lieberman,
co-editors, Time to Learn, Washington, D.C.: National Institute of
Education (1980); C. Fisher, R., and N. Filby, “Improving Teaaching
by Increasing ‘Academic Learning Time’,” Educational Leadership,
v37, n1 (October 1979), pp. 52-54; D. Wiley and A. Harnischfeger,
“Explosion of a Myth: Quantity of Schooling and Exposure to Instruc-
tion, Major Educational Vehicles,” Educational Researcher, v3, n4
(April 1974), pp. 7-12; J. Carroll, “A Model of School Learn-
ing,” Teachers College Record
6The terms, urq = urv, represent the 1st partials of u with respect to rq
and rv, res pecti ve ly.
, v64, n8 (May 1963), pp. 723-733.
7The 2nd-order conditions require that the score transformation func-
tion is increasing at the quantities at which the 1st-order conditions are
satisfied. If the educational utility function in terms of rq and rv is a
regular strictly quasi-concave function over a domain, the quantities at
which the 1st-order conditions are satisfied are unique educational