Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

lines and isoquants. This locus is known as the expansion path. If
inputs were freely variable, production would take place along the ex-
pansion path.
Cost functions may be derived from knowledge of the production
function, the expansion path, and input prices. In the short run, how-
ever, an input combination on the expansion path cannot always be chosen
because of the fixity of one or more inputs. In this case, a "short-
run" expansion path may be obtained from the first-order conditions of
the usual constrained cost minimization, except that the production
function and isocost equation will reflect the condition of input fix-
ity. The system of these equations, consisting of short-run production
function, short-run isocost equation, and short-run expansion path, can
be reduced to a single equation in which cost is stated as an explicit
function of the level of output plus the cost of the fixed inputs, i.e.,
a short-run total cost curve. However, this is only true where the
three functions have the appropriate properties. 4
In cases where the production function is not amenable to mathe-
matical manipulation, an alternative method may be used to deter-
mine cost curves. Of course, both methods should be equivalent. 5 The
following steps are involved: (1) choose a level for all inputs;
(2) compute cost: (3) compute output; (4) change level of one input;
(5) compute cost; (6) compute output; (7) repeat (4), (5), and (6) a
number of times to generate a.series of cost-output combinations;
(8) plot cost against output; (9) repeat process with a new level of
the "fixed" input(s) to get another short-run cost curve. By doing
this successively for various levels of the fixed inputs, one would
4