Tutorial 7: Production (cont.)
Returns to Scale
To keep our model of the production process as simple as
possible (but not simpler!) we will assume there are only
two inputs available to produce goods. Varying both
inputs varies the scale of operations, and, by definition,
the scale of operations can change only in the long run.
That is, the short run is characterized as that time period
during which at least one input is fixed. The long run is
characterized as that time period during which all inputs
can vary. For a small, T-shirt shop, in might take half
a year to vary all of its inputs, so the long run might
be 6 months. For a large, automobile producing plant, the
long run might be five years.
What might happen to output if both inputs were to
double? There are three possible outcomes:
- Double inputs and output increases by double ("constant
returns to scale").
- Double inputs and output increases by more than double
("increasing returns to scale").
- Double inputs and output increases by less than double
("decreasing returns to scale").
Let's see how this works. Open Production.xls.
The production model illustrated in this workbook is based
on the Cobb-Douglas production function, Q = A * La
* Kb. (We are assuming no other inputs are involved...)
Let's do some exploring:
- Initially, a + b = 1, and at L = 10 and K = 10, output
is 10 units/t. What happens to Q if L and K are doubled?
(HINT: Look at the table to find the output that is highlighted
at the intersection of L = 20 and K = 20.) [Check
- Change a and b so that a + b > 1. Now what happens
to Q if L and K are doubled? [Check
- Finally, change a and b so that a + b < 1. Now what
happens to Q if L and K are doubled? [Check
So what have we witnessed? In the short run a firm
has at least one fixed input. As a result, as more of a
variable input is employed, the additional output of that
variable input (MP) diminishes. But in the long run
all inputs are variable -- so the concept of diminishing
marginal returns does not apply. What does matter in the
long run are the returns to scale exhibited by the
production function. When both inputs are allowed to vary,
the size of the increase in output depends on the relative
productivity of the inputs. It's possible to double the
inputs and have output double, in which case the firm's
production has constant returns to scale. Then again,
the firm could double the inputs and have output more than
double, in which case the firm's production enjoys increasing
returns to scale. Finally, the firm could double the
inputs and have output less than double, in which case the
firm's production suffers decreasing returns to scale.
This concludes our discussion of production. But employing
these inputs adds to the firm's costs. So now we will see
what these principles of production tell us about the firm's
costs in the short run and in the long run.
Next: Tutorial 8 - The Cost