Abstract
This chapter illustrates two models using Maxima. The first model is the production possibilities curve, which is a simple model of economy-wide production. The second model is that of competitive markets, where demand and supply determine the equilibrium price and quantity of a good. We also extend this model to examine disequilibrium and the effects of shifts in demand or supply, along with the relevance of elasticities, the impact of taxes, and the value that markets generate.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
If this value is set too low, an error message will occur, showing the values of y at the endpoints. Executing the command again with an increased maximum value of x will lead to a solution.
- 2.
The values are defined in terms of x1max. This is not necessary. Specific numbers can be entered if you prefer, as long as the values are within the range determined above. The changes are discrete, so the Greek letter Delta, Δ is used.
- 3.
Economic theory does not dictate that opportunity cost must increase. The simple Ricardian model of comparative advantage, with a linear PPC, exhibits constant opportunity cost. PPCs can bow in, at least over some range, so that opportunity cost decreases.
- 4.
(x1 + x1 +Δ x)∕2 = x1 +Δ x∕2
- 5.
Evaluating the oc function at x = x1 +Δ x∕2 and at x = x2 +Δ x∕2 yields values that differ from the values computed over the ranges only at the third decimal point. These values are 1.76 and 6.274, respectively.
- 6.
This implies, however, that the opportunity cost of y increases: At each level of x, increasing y by an additional unit requires that more units of x be forgone than before the shift.
- 7.
We could use Maxima to determine the equations for the inverse demand and supply curves. The accompanying exercise set takes this approach.
- 8.
Actually, solve does work in this case, but it yields four solutions, three of which involve imaginary numbers or negative values. The fourth is the positive real solution that find_root provides directly.
- 9.
If the upper bound had been set too low, find_root would have returned an error message because the difference between the demand price and the supply price would have been positive at both ends of the range. If this happens, increase the upper end of the range and repeat the command. Or draw a simple graph to determine the approximate value.
- 10.
Rounding error resulting from the use of a numerical method to find the equilibrium price results in the reported value, which is nearly zero.
- 11.
If multiple > 1, then a price floor is established. An exercise using these demand and supply curves but analyzing a price floor appears in the online exercises.
- 12.
A more likely outcome is that some units will sell in the black market for a price higher than this mandated price, some will sell for a price between the free-market equilibrium price and the mandated price, and still others will sell at the mandated price.
- 13.
We use binding rather than functional expressions because, in this setting, doing so is simpler. Binding the result of the diff command is somewhat easier than expressing the relationship as a function.
- 14.
Be aware that many textbooks, by tradition, use the absolute value of own-price elasticity of demand, so that it is reported as a positive number.
- 15.
Also keep in mind that elasticity is a quite general concept. Although economists define some other elasticities, such as output elasticity and cost elasticity, one should think of an elasticity as a general way of specifying the response of a variable to a change, rather than a list of standard formulas.
- 16.
For some specifications, the income shares might exceed 1.0. This result represents economic nonsense. If such a result occurs, reduce a0 and rerun the entire sheet, using ctrl-r.
- 17.
For this function, we can determine the area under the demand curve. We do not, because in general such an exercise lacks meaning. For some goods like water and food, the marginal value of the first few units is beyond measure.
- 18.
This convention is more reasonable that it might appear. Individuals who consume commodities like automobiles make two decisions, how many units to own and how often to buy new models. If a higher price of new good rises slightly and many individuals adjust be keeping their units a bit longer, then the market quantity demanded will decrease slightly, perhaps a few hundred units in a market in which millions of units are sold.
- 19.
This caveat refers to a direct effect via the third party’s utility function. Suppose that buyer A’s purchase of the good precludes buyer B’s purchase because A is willing and able to pay more than B. Then buyer B is in a sense worse off that if A had not been in the market, but this fact implies nothing about the validity of this measure of value.
- 20.
Choose ED0 such that no elasticity equals −1.0. The three elasticity values are part of the Maxima output.
- 21.
Note the use of labels for these areas.
Each label contains a list with three elements: the text that is to appear in the graph, the horizontal distance at which the label is to be centered, and the label’s height. The alignment can be fine-tuned. See label_alignment in the Maxima user’s guide.
- 22.
This result is not general. Suppose the demand curves were shifted horizontally to the left (and truncated where they enter the second quadrant). Then the change in Consumer Surplus would be smaller than appears above, and the percentage differences among the three cases would be larger.
- 23.
This result can be predicted by examining the expression to be integrated, surpluses. Because p is subtracted from the height of the demand function and added in the definition of Producer Surplus, the function is DP(q, ED) - SP(q, ES, b). This function is integrated (the “antiderivative” is extracted) and then the derivate of the integral is extracted, returning the original function.
- 24.
The table at in the preface lists chapters in microeconomics textbooks that relate to this chapter. The following can also be of value:
Further Readings
The table at in the preface lists chapters in microeconomics textbooks that relate to this chapter. The following can also be of value:
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Hammock, M.R., Mixon, J.W. (2013). Simple Economic Models. In: Microeconomic Theory and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9417-1_2
Download citation
DOI: https://doi.org/10.1007/978-1-4614-9417-1_2
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-9416-4
Online ISBN: 978-1-4614-9417-1
eBook Packages: Business and EconomicsEconomics and Finance (R0)