AGEC 317 Review of Key Algebraic Concepts and Applications to Economic Issues
Readings Review of fundamental algebra concepts (Consult any math textbook) Chapter 2, pp. 23-43, Managerial Economics
Topics Mathematical operations with algebraic expressions Addition, subtraction, multiplication, division Solving equations Linear functions Graphical analysis Slope Intercept Nonlinear functions Rate of change (marginal effects) Optimal points (minima, maxima)
Solving Equation(s)
The Economic Optimization Process The Univariate Case
Derivatives Y=f(x) The value of the ratio of for extremely small change in X. Derivative of Y with respect to X at point A is the slope of a line that is tangent to the curve at the point A.
Illustration of Derivatives
Rules of Derivatives
Rules of Derivatives
Linear Function: Y = aX + b Slope = dY / dX = a Interpretation: a one unit increase in X leads to an increase in Y of a units; basis of regression Intercepts On x-axis; the value of X is y = o: aX + b = 0; the x intercept is –b/a; put another way (-b/a,o) On y-axis; the value of Y is x = o: The y intercept is b; put another way (o,b) Graph Y = -2X + 2, x intercept is 1 or (1,0); y intercept is 2 or (0,2) Y = 2X + 4, x intercept is -2 or (-2,0); y intercept is 4 or (0,4)
Application of Linear Function: Revenue & Output Total Revenue Output $1.50 1 3.00 2 4.50 3 6.00 4 7.50 5 9.00 6 Questions: Slope Intercepts
Nonlinear function: Total, Marginal, and Average Profits Curvilinear expression of profit and output
Locating Maximum and Minimum Values of a Function
Locating Maximum and Minimum Values of a Function
Locating Maximum and Minimum Values of a Function (Con’t)
Locating Maximum and Minimum Values of a Function (con’t)
Locating Maximum and Minimum Values of a Function Locating Maximum and Minimum Values of a Function
Assignment Do the Self-Test problem in Hirschey (pp 43-45) concerning profit versus revenue maximization for Presto Products, Inc. Do the Self-Test problem in Hirschey (pp 45-48) for Pharmed Caplets, an antibiotic product.