AGEC 317 Review of Key Algebraic Concepts and

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 2

Topics v Mathematical operations with algebraic expressions v Addition, subtraction, multiplication, division v Solving equations v Linear functions v v Graphical analysis Slope Intercept Nonlinear functions v v v Graphical analysis Rate of change (marginal effects) Optimal points (minima, maxima) 3

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Solving Equation(s) 5

The Economic Optimization Process The Univariate Case 6

Derivatives Ø Ø Y=f(x) The value of the ratio of X. for extremely small change in 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. 7

Illustration of Derivatives 8

Rules of Derivatives 9

Rules of Derivatives 10

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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: (a) Slope (b) Intercepts 12

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

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Locating Maximum and Minimum Values of a Function 15

Locating Maximum and Minimum Values of a Function 16

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

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

Locating Maximum and Minimum Values of a Function 19

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. 20