reference for the improvement of productivity. Much different from the production
function theory, economy of scale and economy of scope are two approaches to
examine afirm’s internal efficiency based on cost function.^2 Economy of scale, also
called“economic benefit of scale”, is the economy or economic return obtained by
reasonably allocating the proportion and quantity of every production factors. It is a
phenomenon that the cost of per unit production decreases and the return increases
accompanying the enlarged scale of operation in afirm. Otherwise, it’s called
diseconomy of scale. Different from the return to scale based on production
function, economy of scale means a decreasing long-term average cost. To a uni-
versity, it achieves economy of scale when its average cost decreases as output
increases. Otherwise, it falls into diseconomy of scale. Economy of scope is present
when there are cost efficiency to be gained by joint production for multiple prod-
ucts, rather than by being produced separately (Panzar and Willig 1981 ). This
concept is closely associated with multi-product organization. Generally, university
is recognized as a typical multi-product organization combining teaching, research,
and social services all together, which is deemed to perform economy of scope to
some extent. Discovering the rules of economies of scope in the production of a
university would enable us to reduce costs without increasing inputs, through
transforming the mode of production within university and between universities or
changing the current allocation pattern of resources (Hou et al. 2009 ).
It’s common to use the terms of productivity and efficiency interchangeably.
Even some academic articles don’t make clear distinction between the two con-
cepts. Nevertheless, their interpretations are not precisely the same. Thus, we will
try to further clarify the two concepts by Fig.2.1.
For simplicity, we consider a simple production process in which a single input
(x) is used to produce a single output (y). Since there is only one input, this
production process involves no allocative efficiency. The curve OF in Fig.2.1
represents production frontier, which means the maximum output attainable from
each input level, hence it reflects the current state of technology in thefirm.
A production unit operates either on that frontier if it’s technically efficient, or
beneath the frontier if it’s technically inefficient. In Fig.2.1, we use a ray through
the origin to measure productivity of a particular data point. The slope of this ray is
y/x and hence provides a measure of productivity. To some technically inefficient
point A in the feasible production set, we can improve productivity in several ways.
Thefirst is to improve technical efficiency, that is, moving from point A to point B
on the production frontier. In this case, the slope of ray OB would be greater than
the slope of OA, implying higher productivity at point B. The second is to improve
economy of scale, that is, moving from point B to point C, where the ray OC is at a
tangent to the production frontier and hence defines the point C of maximum
possible productivity, or the point of (technically) optimal scale. Operation at any
other point on the production frontier results in lower productivity. Based on this,
(^2) As a result of the duality between production function and cost function, the issue of return to
scale in production can be transformed into the one of economy of scale in cost.
14 2 Evaluation on University Research Efficiency and Productivity...