Preference Ordering
This refers to ordering choices of alternatives that determine preferences. Different sets of consumption bundles face the consumer but only one is an optimal choice. Therefore, a consumer will order available products and services in order of utility derived from each based on reflexivity and transitivity. If X > Y and Y > Z then X > Z. If good X and Y are available to the consumer, only one can be chosen. If X > Y the consumer strictly prefers good X to Y and vice versa. Alternatively an order X ≥ Y implies the consumer weakly prefers X to Y. An order X ≥ Y, X ≤ Y indicates X=Y implying that the consumer is indifferent.
Endowment
Endowment refers to natural resources available that give an individual or an economy a comparative advantage. Different countries have varied natural resources whereas one natural resource such as land or human capital is found in most countries. However, some possess an advantage in mobilization of these resources making them more preferred. For example, China has an endowment in labor due to its high population giving it a comparative advantage over most countries they engage in business.
Boundness of sets of points
This term implies the possibility of enclosing a budget set in a large finite size. This holds as long as income is finite and the prices are strictly positive. If there is a more preferred good X and a less preferred one Y. Boundedness exists for any t in ∟, X ≥ t ≥ Y.
Convexity of a set of points
Convexity of two sets of points combination implies that those two bundles in the budget set are also feasible. Preferences are convex; therefore, any intermediate bundle will be cheaper than the most expensive one. The property of convexity follows from convexity of preferences as indicated in an indifference curve. F(x) is a convex set for all xs.
F(x)
The Slutskys equation
This is an equation in the theory of the consumer relating the substitution and income effects following a price change. It decomposes the changes in demand following price change. Price change has an income effect and a substitution effect. Price decrease affects the consumption preference as one item becomes more expensive than the other-substitution effect and consumers purchasing power will increase- Income effect.
∆xj ≈ ∂xj(p, m)/∂pi.∆pi = ∂hi(p, u)/∂pi.∆pi - ∂xi(p, m)/∂m .xi∆pi
The negative semi definite matrix
This is a matrix whose main diagonal terms are negative. This property requires a hessian matrix relating to a cost function and for concavity to be fulfilled in production functions. To check for negativity of the leading diagonal terms, we obtain the determinant of the matrix, which should be negative.
Closedness of set of points
This is a property of input requirement set implying that in a sequence of production plans yi, where i = 1,2,., are in Y and yi → y. The limit of production plan y is in Y. Therefore, all points on boundary Y are also feasible. Since Y is closed, the input requirement set V(y) is a closed set for all y ≥ 0. V(y) = {x : f(x) ≥ y} is a closed set.
Compactness of a set of points
Compactness refers to a closed and bounded budget set. If p > 0 (ie. Pi > 0, ɏi = 1, ..,L). Therefore, it follows that if Yj is compact and strictly convex, then the supply correspondence is yj (p) is a well-defined single valued and continuous function.
Lexicographic preferences
This is a preference that exists in a two good case. Lexicographic preferences satisfy completeness, convexity, transitivity, and non-satiation. However, they do not meet continuity. If X ≥ y ie. x1 > y1 or x1 = y1 and x2 ≥ y2.
Giffen goods
Giffen goods refer to an inferior good whose demand increases with the increase in prices and demand decrease following a price decrease. Such goods exhibit an upward sloping demand curve because an increase in price is directly related to the quantity demanded meaning that the substitution effect is less than the income effect.
However, it reaches a point where the consumption of the Giffen good takes up the entire consumption budget of the consumer. At this point, an increase in price leads to a reduction in the quantity the consumer is capable of buying thereby causing the good to exhibit a downward sloping curve (Jensen, and Miller 1554).
Testing
Testing implies evaluation to find out if models are reliable or not. Tests include t test, f test, Z test, and likelihood test among others. We test a hypothesis ie. null hypothesis against an alternative hypothesis. This involves observation of parameter estimates to judge if they actually make sense.
Likelihood ratio test
This is a statistical test used to evaluate model assumptions using two models one as a null model and the other as the alternative model. D = -2 ln{likelihood for the null model} + 2ln{likelihood for an alternative model}
Theory consistent parameter restriction
These are theoretical restrictions on indirect utility functions that satisfy theoretical properties (Varian, 102). Restriction is imposed in order to provide estimators that are more precise. To impose restriction requires that an explanatory parameter be considered as zero.
Work Cited
Jensen, Robert and Nolan, Miller. “Giffen Behaviour and Subsistence Consumption.”
American Economic Review 98.4 (2008): 1553-77.
Varian, Hal. Microeconomic Analysis. New York: Norton & Company, 1992. Print.
