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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:

  1. 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 your work.]
  2. Change a and b so that a + b > 1. Now what happens to Q if L and K are doubled? [Check your work.]
  3. Finally, change a and b so that a + b < 1. Now what happens to Q if L and K are doubled? [Check your work.]

 

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.