Abstract
This chapter introduces the budget constraint and combines the budget constraint with the preferences developed in the preceding chapter to provide a model of rational consumer choice.
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Notes
- 1.
A minimal set of commands follows: [px1,py1,m1]:[100,24,2400]$ first:gr2d(explicit(BL(x,m0,px0,py0),x,0,m0/px0))$ second:explicit(BL(x,m1,px1,py1),x,0,m1/px1))$ wxdraw(first,second,columns=2)$.
- 2.
The declare and assume commands allow us to avoid a dialog with Maxima.
- 3.
The complete ICC consists of a segment of the vertical axis from 0 to 4.1667 and the horizontal line in the graph.
- 4.
We assert this for now. We demonstrate the result below.
- 5.
And in a section that follows, where Lagrangian multipliers are employed.
- 6.
Over this range, its income elasticity of demand is 1.0. Why?
- 7.
At least one good must be a normal good. Why?
- 8.
Maxima does not offer distinct notation for simple derivatives and partial derivatives. From an operational viewpoint the two do not differ. The analyst must be aware of the context.
- 9.
We consider only functions with a single local maximum or minimum value. Such functions have a global maximum or minimum value, which corresponds to the local value. Some functions can have multiple local maximum and minimum values and may or may not have a global maximum or minimum value. As an exercise, plot g(x) = sin(x) ⋅ x over a range of at least − 2 ⋅ π to 2 ⋅ π. This function has many local maximum and minimum values but no global maximum or minimum value.
- 10.
Notation: \(\frac{\partial u} {\partial x} \equiv u_{x}\). Likewise for y and z.
- 11.
The x axis is labeled. The y and z labels can be inferred.
- 12.
Be aware that the matrix command is being used in two different ways. The outermost command is used to build a table. The interior commands are used analytically.
References
Baldani J, Bradfield J, Turner RW (1996) Mathematical economics. Dryden, Fort Worth
Doi J, Iwasa K, Shimomura K (2009) Giffen behavior independent of the wealth level. Econ Theory 41:247–267
Nicholson W, Snyder C (2008) Microeconomic theory: basic principles and extensions, 11th edn. South-Western, Mason
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Hammock, M.R., Mixon, J.W. (2013). Demand Theory: Constraints and Optimization. In: Microeconomic Theory and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9417-1_4
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DOI: https://doi.org/10.1007/978-1-4614-9417-1_4
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