Abstract
This chapter and the next two examine price-searching firms. Such firms inhabit one of the three types of industries: simple monopoly (one firm constitutes the industry), monopolistic competition (many firms inhabit an industry for which each firm’s product differs slightly from those of other firms), and oligopoly (a few firms inhabit an industry, and the firms’ products may be either identical or similar). This chapter addresses the first two cases.
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Notes
- 1.
We use arc_mr, arc marginal revenue, to indicate marginal revenue for a discrete quantity change. Most of the material below involves analysis of marginal revenue at a point: \(mr = \frac{dtr} {dx}\).
- 2.
Exercise: Create three separate graphs, replacing gr2d with wxdraw2d. Add the average cost and average variable cost curves to these graphs.
- 3.
Exercise: Demonstrate that this result must hold if c = 0, that is if marginal cost is constant and the demand curve exhibits constant elasticity.
- 4.
Bishop [1] provides a more general discussion of the relevance of the demand curve’s curvature to deadweight loss.
- 5.
Exit is possible, of course. If the monopolist exits the industry, however, nothing remains to be analyzed in this partial-equilibrium framework.
- 6.
This specification is more general than it might appear. We can select product units such that x = 1 at the average cost curve’s minimum point, and we can select monetary units such that the height of the curve at that point is 1.
- 7.
The table shows that the elasticity of the total variable cost function equals c + 1. The elasticity of total cost with respect to output approaches c + 1 from below and that the elasticity of average cost with respect to output approaches c from below.
- 8.
One line of input creates a list of x values. We do not use that list, but Maxima retains the values.
References
Bishop RL (1968) The effects of specific and ad valorem taxes. Q J Econ 82:198–218
Krugman PR, Obstfeld M (2004) International economics: theory and policy, 8th edn. Prentice-Hall, Saddle River
Wainwright K, Chiang AC (2004) Fundamental methods of mathematical economics, 4th edn. McGraw-Hill, New York
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Hammock, M.R., Mixon, J.W. (2013). Price-Searcher Markets. In: Microeconomic Theory and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9417-1_12
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DOI: https://doi.org/10.1007/978-1-4614-9417-1_12
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