1. Material for Week 2: Optimization Techniques

2. 100 + 800 Problem 3: Interest rate (i) = 15%

3. Problem 12: Current Job = $30,000 New Job = $40,000 Return From Pharmacy = $200,000 Explicit Cost = 80,000+40,000+10,000+5,000 +8,000 = 143,000 Business Profit = 200,000 – 143,000 = 57,000

4. Implicit Cost = 40,000 + 2,000 = 42,000 Economic Profit = Business Profit – Implicit cost = 57,000 – 42,000 = 15,000 (b) Total Revenue now is $200,000 which includes a $15,000 economic profit. So in three years when the new pharmacy will drive down the economic profit to zero, total revenue of the pharmacy will be $200,000 - $15,000 = $185,000.

5. c. Samantha shall purchase the pharmacy if the present value of the pharmacy is positive. 15,000 – 50,000

6. Demand Curve: It shows the relationship between the quantity demanded of a commodity with variations in its own price while everything else is considered constant.

7. Demand Curve: Q d = 20 -.5P Q P 0 P = 40 - 2Q d 40

8. Supply Curve: Shows the relationship between the quantity supplied of a commodity with variations in its own price while everything else is considered to be constant.

9. Q s = –.15 +.3P 0 Q P Supply Curve P =.5 + (10/3) Q s

10. 0 Q P 7 25 Supply Demand Excess Supply

11. Profit = TR - TC TR = P × Q Q = 10 –.10P P = 100 – 10Q TR = (100 – 10Q)×Q = 100Q – 10Q 2 AR = TR/Q = 100 - 10Qwhen, Q  0

12. TR = 100Q – 10Q 2

13. TR MR AR Q Q MR Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Q6Q6

14. Q1Q1 Q2Q2 MC Q Q 0 0 TC AC TC AC, MC

15. Profit Maximization: TR TC Q1Q1 Q2Q2 MR MC Q Q 

16. Optimization & Marginal Analysis : Marginal Cost is defined as the change in total cost per unit change in output and is given by the slope of the TC curve. As long as the slope of the TR curve or MR exceeds the slope of the TC curve or MC, it pays for the firm to expand output and sales. The firm would be adding more to its total revenue than to its total costs and so its total profit would increase. To make it general, according to the marginal analysis as long as the marginal benefit of an activity (such as expanding output or sales) exceeds the marginal cost, it pays for the organization (firm) to increase the activity (expand output). The total net benefit (profit) is maximized when the marginal benefit equals marginal cost.