1. Chapter One Homework due tomorrow in lab Numbers 10, 12 and 17

2. Managerial Economics & Business Strategy Chapter 1 The Fundamentals of Managerial Economics

3. Net Benefits Net Benefits = Total Benefits - Total Costs Profits = Revenue - Costs

4. Marginal Benefit (MB) Change in total benefits arising from a change in the control variable, Q: Slope (first derivative) of the total benefit curve.

5. Marginal Cost (MC) Change in total costs arising from a change in the control variable, Q: Slope (first derivative) of the total cost curve

6. Marginal Principle To maximize net benefits MB = MC. MB > MC means the last unit of the control variable increased benefits more than it increased costs. MB < MC means the last unit of the control variable increased costs more than it increased benefits. Can we do it??? Start with a control variable that can only be used in WHOLE units (discrete)

7. Control Variable Total Benefits Total Costs Net Benefits Marginal Benefits Marginal Costs Marginal Net Benefits QB(Q)C(Q)N(Q)MB(Q)MC(Q)MNB(Q) 000 19010 217030 324060 4300100 5350150 6390210 7420280 8440360 9450 10450550

8. Control Variable Total Benefits Total Costs Net Benefits Marginal Benefits Marginal Costs Marginal Net Benefits QB(Q)C(Q)N(Q)MB(Q)MC(Q)MNB(Q) 0000 1901080 217030140 324060180 4300100200 5350150200 6390210180 7420280140 844036080 9450 0 10450550-100

9. Control Variable Total Benefits Total Costs Net Benefits Marginal Benefits Marginal Costs Marginal Net Benefits QB(Q)C(Q)N(Q)MB(Q)MC(Q)MNB(Q) 0000--- 190108090 21703014080 32406018070 430010020060 535015020050 639021018040 742028014030 84403608020 9450 010 450550-1000

10. Control Variable Total Benefits Total Costs Net Benefits Marginal Benefits Marginal Costs Marginal Net Benefits QB(Q)C(Q)N(Q)MB(Q)MC(Q)MNB(Q) 0000--- 19010809010 2170301408020 3240601807030 43001002006040 535015020050 63902101804060 74202801403070 8440360802080 9450 01090 10450550-1000100

11. Control Variable Total Benefits Total Costs Net Benefits Marginal Benefits Marginal Costs Marginal Net Benefits QB(Q)C(Q)N(Q)MB(Q)MC(Q)MNB(Q) 0000--- 1901080901080 217030140802060 324060180703040 4300100200604020 535015020050 0 63902101804060-20 74202801403070-40 8440360802080-60 9450 01090-80 10450550-1000100-100

12. What if we can use fractional parts of the control variable? Q Total Benefits & Total Costs Benefits Costs Q* B C Slope = MC Slope =MB

13. Let’s talk calculus… What is the MB? n 300-12Y What is the MC? n 8Y What is the profit max level of Y? n 300-12Y = 8Y n 300=20Y n Y=15 What are the Net Benefits at this level of Y? n NB = ((300*15)-(6*15^2))-(4*15^2) n NB = 2250

14. One more check….Is it a maximum point?? Second derivative of the Net Benefit equation must be negative N(Y) = B(Y)-C(Y) First derivative n (300-12Y)-8Y Second derivative n -12-8= -20 n Negative  Maximum Shows n N(Y) is concave n Slope of MB curve < slope of MC curve