AGEC 317



AGEC 317

Basic Economic / Mathematic Definitions Review

Basic Definitions - Economic Models

(Source A.C. Chiang. Chapter 2 in Fundamentals Methods of Mathematical Economics. Second edition. McGraw-Hill Book Company. New York, NY. 1974.)

Variables - something whose magnitudes can change, that is something that can take on different values.

Endogenous variables - variables whose solution values we seek from the model.

Exogenous variables - variables that are assumed to be determined by forces external to the model.

Constant - magnitude does not change (i.e., fixed number) and is, therefore, the antithesis of variable. When a constant is joined to a variable, it is often referred to as the coefficient of that variable.

Parameter (sometimes called parametric constant) - special status for a constant in that the constant has not been assigned a specific number, it can take virtually any value.

Definitional equation - sets up an identity between two alternative expressions that have exactly the same meaning. An example would be profit defined as the excess of total revenue over total costs, [pic]; note ≡ is read is identically equal to. In general, the = can be used in place of the ≡ symbol.

Behavioral equation - specifies the manner in which a variable behaves in response to changes in other variables. An example would be a cost equation defined as costs as a function of output,[pic], where C is total costs, 75 are fixed costs, and Q is the quantity of output.

Equilibrium conditions - relevant only if the model involves the notion of equilibrium. Equilibrium conditions are equations that describe the prerequisite for attainment of equilibrium. Two common conditions are quantity demanded equals quantity supplied and intended savings equals intended investment.

Set - a collection of distinct objects.

Ordered pairs - a way of writing elements in which the order of the elements is important. One important use of ordered pairs is in graphing in the (x, y) coordinate space.

Function (used to be called single-valued function) - is a relation such that for each x value there exists only one corresponding y value, denoted by [pic] and is read y equals f of x. A function is, therefore, a set of ordered pairs that have the property that any value of x uniquely determines y, however the converse may not be true.

In the function[pic], x is the argument of the function and y is the value of the function. Alternatively and more common in economics, x is the independent variable and y is the dependent variable.

Constant function - a function whose range consists of only one element, example [pic]

Polynomial functions - have the general form [pic] in which each term contains a coefficient and a nonnegative power-integer power of the variable x.

Exponential functions - such as [pic] in which the independent variable appears in the exponent. This is an example of a nonalgebraic function, which is also known by the more esoteric name of transcendental function.

Logarithmic functions - contain logarithmic operations such as [pic], which is also a nonalgebraic function.

Multivariate functions - functions of two or more independent variables such as [pic] in this case, the function is a set of ordered triples (x, y, z).

Review Questions

In answering the following questions, consider the following simple supply and demand model:

[pic]

where qd is quantity demanded, qs is quantity supplied, and p is price.

1. List all variables in the model. Which variables are exogenous and endogenous?

2. List all constants in the model.

3. In terms of the previous definitions, what is the difference between the intercepts in the quantity supplied and quantity demanded intercepts?

4. What equation is a definitional equation? Behavioral equation? Equilibrium condition?

5. What is (are) the independent (dependent) variable(s)?

6. If a = 25 and b = -3, find the order pairs for quantity demanded for prices of 1, 3 and 6.

7. Rewrite the equations in a semi logarithmic form; only the independent variable is in logarithmic form. Use natural logs, ln.

8. Rewrite the equation in double logarithmic form; both the independent and dependent variables are in logarithmic form. Use natural logs, ln.

9. In words, how would the equations differ if the form was polynomial instead of linear.

10. What variables might you include to make the simple demand equation multivariate?

Answers to Basic Economic / Math Modeling Definitions Review

1. qd, qs, and p - all variables in this model are endogenous

2. a, b, 4, c

3. quantity demanded intercept is a parameter or parametric constant (does not yet take on a specific value), whereas quantity supplied intercept is a constant, it takes on the specific value of 4

4. qd and qs are behavioral equations specifying how quantity demanded and supplied varies as price changes. The equation qd = qs is an equilibrium condition. There are no definitional equations in this model.

5. independent variables - p dependent variables - qd and qs

6. order pairs for (qd, p) are (1, 22), (3, 16), (6, 7)

7. [pic]

with appropriate redefinitions of the constants to be discussed later in class.

8. [pic]

with appropriate redefinitions of the constants to be discussed later in class.

9. Price would be taken to a non-negative integer power.

10. Variables such as income, price of substitutes and compliments, and population if aggregate quantity demanded.

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