Utility Functions:
Rational individuals always choose their most preferred alternative from a set of alternatives. Imbedded in the set of choices, is information about the marginal value a decision maker places upon the goods that define each state.
This marginal value determination is subjective and dynamic, which does not easily result in tractable quantitative analysis. The concept of utility functions enables comparison of different states by defining a preference relation as continuous when small changes in a particular good result in a small change in the preference level. Thus, any continuous preference can be represented by a continuous function known as a utility function. Utility functions are convenient constructs, however it should be emphasized that, except in special cases, utility functions may not be representative of the decision maker’s value determination.
Constraints on Choice
Budgetary, time, knowledge, moral, resource, and other limitations place constraints upon the alternatives available to decision makers. Therefore, the available set of choice states is a subset of all choice states.
A consumption choice set is the collection of all consumption choices available to the consumer. A consumption bundle, previously defined as a choice state, is denoted by the vector (x1, x2, … , xn) and contains x1 units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity and is so defined because they are the choice states that are actually consumable, given all constraints.
Constrained Choice – combining constraints and preferences
The principal behavioral postulate is that a decision maker chooses its most preferred alternative from those available to it. The available choices constitute the consumption choice set. How is the most preferred state in the consumption choice set located?
Economic agents seek to maximize the satisfaction of their wants and needs. Therefore, assuming rationality, agents will choose the state that maximizes utility within a given set of constraints. This state is defined by a tangency condition.
The tangency is the state that uniquely and simultaneously defines the intersection of the set of constraints and the set of choice states. Thus, an economic decision maker undertakes a dynamic constrained optimization problem with every choice.
If we hold preferences constant, and assume constraints depend primarily on prices and income, then we can write create demand functions that describe the optimal amounts of goods chosen as a function of only prices and income.
x1 = x1(p1,p2…pn, m)
x2 = x2(p1,p2…pn,m)
The output of these functions are the quantity demanded of each good given the prevailing market prices of all available goods in their choice set. |
