Abstract
This chapter develops a model of a perfectly competitive economy. It does so from a viewpoint of general equilibrium, rather than examining subsets of the economy. The chapter begins with production and then addresses consumption. General equilibrium values for quantities produced, product prices, and input prices are determined.
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Notes
- 1.
The rest of the system consists of utility functions of the consumers, who are also resource owners, and a specification about how much of each resource each consumer owns.
- 2.
Most of the algebra that follows is phrased in terms of LX and KX. The analyst must keep track of the corresponding values of LY and KY.
- 3.
Strictly speaking, the Edgeworth box, named after the nineteenth-century economist who first popularized its use, is defined by the bold line in the graph and segments of the x and y axes.
- 4.
If the edge of the lens is included, then it is possible to increase the output of one good without decreasing the production of the other good.
- 5.
For the functions used in this illustration, this is a curve with a constantly increasing positive slope. Contract curves can be wavy. The curve lies below the diagonal of the Edgeworth box because X production is relatively labor intensive.
- 6.
The line is drawn by placing the logical expression inside the draw command, in contrast to the approach used when graphing the supply curve above. Maxima treats the two approaches as identical, so the choice depends on user preference.
- 7.
We can limit attention to good X because of Walras’s Law, which says that in a system of n markets equilibrium in n − 1 of the markets implies equilibrium in the nth market. Our system consists of four markets. We specify that LX + LY = LT and KX + KY = KT. Thus, these two markets are in equilibrium. Therefore, equilibrium in the market for X is all that is required. The market for Y must also be in equilibrium.
- 8.
These values are: the quantity of good Y; the price of good X with the price of good Y set at one; the per-unit prices of resources; and the allocation of resources between the two goods; and Anderson’s and Brooks’s income, consumption, and utility levels.
References
Bator FM (1957) The simple analytics of welfare maximization. Am Econ Rev 47:22–59
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Hammock, M.R., Mixon, J.W. (2013). General Equilibrium. In: Microeconomic Theory and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9417-1_11
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DOI: https://doi.org/10.1007/978-1-4614-9417-1_11
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