1. AGEC 317
Review of Key Algebraic Concepts and Applications to Economic Issues

2. Readings
Review of fundamental algebra concepts (Consult any math textbook)
Chapter 2, pp , Managerial Economics

3. 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)

5. Solving Equation(s)

6. The Economic Optimization Process
The Univariate Case

7. 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.

8. Illustration of Derivatives

9. Rules of Derivatives

10. Rules of Derivatives

11. 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)

12. Application of Linear Function: Revenue & Output
Total Revenue Output $
Questions:
Slope
Intercepts

13. Nonlinear function: Total, Marginal, and Average Profits
Curvilinear expression of profit and output

15. Locating Maximum and Minimum Values of a Function

16. Locating Maximum and Minimum Values of a Function

17. Locating Maximum and Minimum Values of a Function (Con’t)

18. Locating Maximum and Minimum Values of a Function (con’t)

19. Locating Maximum and Minimum Values of a Function
Locating Maximum and Minimum Values of a Function

20. 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.