University:
University of Michigan
Course:
ECON 613 | Advanced Topic in Mathematics for Economists
Academic year:

2024
Views:

8

Pages:

2
Author:

Alvinska H.

Linear Direction Coefficient: Determining the Relationship of Variables in an Economic Function Name: Alvinska Hebat Grade: 910-Math Relationship between Straight Lines: Intersecting, Intersecting, Parallel Two straight lines will intersect if the two lines have unequal direction coefficients. Two straight lines are said to coincide if the intercept and direction coefficients are the same. Two straight lines are said to be parallel if the direction coefficients arethesame but have different intercepts Role and Description of Constants in Economic Concepts In economic concepts, each constant in a mathematical function has its own term/name, such as: 1. In the consumption function: C = a + bY where C = consumption; Y = income then in the economic concept the amount "a" indicates Autonomous / Initial Consumption. 2. In the investment function: I = Io - bR where I = investment; R = interest rate then in the economic concept the amount of Io = Autonomous Investment 3. In the total cost function: TC = a + bQ where TC = total cost; Q = total output then in the concept of economics the amount of "a" indicates the fixed cost. 4. In the tax function: T = To + tY where t = tax rate (in %), Y = income then in the economic concept the amount of "To" shows Lump Sum (Fixed) Tax Linear Direction Coefficient versus Nature of Functional Relationship Between Variables In a linear function Y= f(X) =a+mX m = The coefficient of the direction of the line Y = f (X) which shows the nature of the relationship between variable Y and X. A positive direction coefficient indicates that the relationship between Y and X is unidirectional (positive), meaning that if X goes up then Y also goes up, and if X goes down then Y also goes down. A negative direction coefficient indicates that the relationship between Y and X is in the opposite direction (negative), meaning that if X goes up then Y goes down, and if X goes down then Y goes up. The direction coefficient of the line for autonomous functions will be zero for a straight line parallel to the flat axis (X-axis) such as Y = Yo where Yo = constant, but for a line perpendicular to the flat axis (X-axis) such as X = Xo, the direction coefficient value is infinite. Determine the coefficient of the direction of the line and the equation of the function for each of the data sets below and draw the curve, which satisfies the function Y=f(X):