Abstract
The cost structure of a firm is reflected in its costs functions: total cost TC; average cost AC; and marginal cost MC. Total cost, the sum of total variable and total fixed costs, is generally expressed as a function of the level of output Q. While a firm’s production function is often a bivariate or multivariate function relating its output to various inputs, the cost functions are usually univariate functions relating different costs to only one variable, output. It is therefore much easier to specify and estimate various cost functions for a firm than specify and estimate its production function.
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Notes
- 1.
A detailed discussion of production functions and related topics is presented in Chap. 10.
- 2.
I am ignoring the possibility of an upward sloping marginal revenue curve here.
- 3.
This is not actually an assumption but rather the implication of the assumptions needed for the existence of perfect competition.
- 4.
Can you show that in light of other restrictions (\(R5\)) might be redundant?
- 5.
See the chapter’s Appendix II for application of a simple numerical method using Microsoft Excel and use of other tools in solving cubic and other nonlinear functions.
- 6.
We should carefully distinguish between a single-period and multi-period profit maximization strategy. A noncompetitive firm, especially a monopoly with substantial market power, may follow a strategy of maximizing profit over several production cycles rather than over a single cycle. This is dynamic optimization strategy and is beyond the scope of this book. Here, and in other parts of the book, by “profit maximization” we simply mean single period maximization.
- 7.
Again, see Chap. 10 for a comprehensive discussion of the production function.
- 8.
My presentation here is based on the assumption (very likely unrealistic) that the reader is not familiar with Excel. For this reason the mechanics of implementing Excel is explained in an elementary fashion. Those who know Excel can use more advanced features of the software.
- 9.
Most colleges and universities have license for a mathematical software like Maple.
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Vali, S. (2014). Optimal Level of Output and Long Run Price. In: Principles of Mathematical Economics. Mathematics Textbooks for Science and Engineering, vol 3. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-036-2_6
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DOI: https://doi.org/10.2991/978-94-6239-036-2_6
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