1. CDAE 266 - Class 08 Sept. 20 Last class: 2. Review of economic and business concepts Today: 2. Review of economic and business concepts Quiz 2 (Time value of money) Next class: Result of Quiz 2 2. Review of economic and business concepts Important dates: Problem set 1: due today Project 1: due Thursday, Sept. 27 (Download files from http://vermontchineseschool.org/CDAE266.html)

2. 2. Review of Economics Concepts 2.1. Overview of an economy 2.2. Ten principles of economics 2.3. Theory of the firm 2.4. Time value of money 2.5. Marginal analysis 2.6. Break-even analysis

3. 2.4. Time value of money 2.4.1. What is the time value of money? 2.4.2. How to calculate the TVM? 2.4.3. Future value and compounding 2.4.4. Present value and discounting 2.4.5. Future value of an annuity 2.4.6. Present value of an annuity 2.4.7. Compounding & discounting periods 2.4.8. Perpetuities 2.4.9. How to calculate the TVM using Excel?

4. General procedures of solving a TVM problem Step 1. List the information you have Step 2. Determine what we are looking for Step 3. Decide which formula or Table to use Step 4. Do the calculation Step 5. Answer the question For example: Suppose a small business has been estimated to make a net profit of $20,000 per year in the next five years and the business can be sold at $95,000 in the end of the fifth year. What is the present value of this business if the annual interest rate is 5%?

5. Group projects 1. Groups: 2-4 students in each group (organize your own group by Tuesday, Sept. 18) 2. Format requirements for project reports (available in the class website) 3. How will I grade your project reports?

6. Project 1 -- What is the business problem? -- What information do we have? -- How to analyze the problem? -- How to write your business memo?

7. 2.5. Marginal analysis 2.5.1. Basic concepts 2.5.2. Major steps of using quantitative methods 2.5.3. Methods of expressing economic relations 2.5.4. Total, average and marginal relations 2.5.5. How to derive derivatives? 2.5.6. Profit maximization 2.5.7. Average cost minimization

8. 2.5.1. Basic concepts (1) Decision making: The process of deriving the best possible solution to a given problem. (2)Optimal decision: The action that produces the results most consistent with the decision objective or objectives.

9. 2.5.2. Major steps of using quantitative methods: (1) The economic relations must be expressed in a form suitable for analysis. (2)Various techniques are used to determine the optimal solution. An example: Profit = -100 + 2 Q - 0.01 Q 2 where Q is the level of output

10. 2.5.3. Major ways to present economic relations: (1) Graphs (2) Tables (3) Functions (4) Computer programs

11. 2.5.4. Total, average and marginal relations (1) General notations: P = price of a product (output) Q = quantity of a product (output) TR = P Q = Total revenue FC = total fixed costs VC = total variable costs TC = FC + VC = total costs AC = TC / Q = average cost  = TR - TC = total profit A  =  / Q = average profit

12. 2.5.4. Total, average and marginal relations (2) Marginal concepts: Marginal revenue (MR) = the change in total revenue (TR) when output quantity (Q) changes by one unit. Marginal cost (MC) = the change in total costs (TC) when output quantity (Q) changes by one unit. Marginal profit (M  ) = the change in total profit (  ) when output quantity (Q) changes by one unit.

13. 2.5.4. Total, average and marginal relations (3) An example Q MAQ MA 0 0 ------ 119 1919 252 3326 393 4131 4 136 4334 5 175 3935 6 210 3535 7 217 731 8 208 -926

14. 2.5.4. Total, average and marginal relations (4) Graph the data (5) Relation between total profit (  ) and marginal profit (M  ) when M  > 0,  is increasing when M  < 0,  is decreasing when M  = 0,  reaches the maximum.

15. 2.5.5. How to derive derivatives? The first-order derivative of a function (curve) is the slope of the curve. (1) Constant-function rule (2) Power-function rule (3) Sum-difference rule (4) Examples

16. 2.5.6. Profit maximization (1) With a profit function ( relation between profit and output quantity ): (a) Profit function: (b) What is the profit-maximizing Q? -- A graphical analysis -- A mathematical analysis Set M  = 0 ==> Q* = 100 (c) Maximum profit = 10,000