Abstract
This chapter contains six sections. The first considers the nature of production and a production function. The second introduces the equation that we use to illustrate production theory. The third section looks at a specific aspect of that theory, returns to scale. In this section the inputs are used in a fixed proportion, so that the output can be phrased in terms of the employment of a single input. The fourth section shows aspects of production when employment of either input can be varied over wide ranges. The fifth section considers “the short run,” a period during which the employment of only one input can be varied. The final section examines substitution between inputs.
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- 1.
When L and K vary proportionately, the function reduces to a cubic function in one variable. This important special case is examined below.
- 2.
We solve for m rather than L, because the latter results in a list of expressions that are hard to manage.
- 3.
If the values of K and L had been extended sufficiently, this contour line would define an enclosed area. As an exercise, execute the commands with K ranging from 0.1 to 30 ⋅ K0 and L ranging from 0.1 to 15 ⋅ L0 to confirm this assertion.
- 4.
This is a general relationship, not limited to the illustrative example used here. When a marginal is above an average, it is pulling the average up. When a marginal is below an average, it is pulling the average down.
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Hammock, M.R., Mixon, J.W. (2013). Production Theory. In: Microeconomic Theory and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9417-1_6
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DOI: https://doi.org/10.1007/978-1-4614-9417-1_6
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Publisher Name: Springer, New York, NY
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