1. 1 Civil Systems Planning Benefit/Cost Analysis Scott Matthews 12-706/19-702 / 73-359 Lecture 10

2. 12-706 and 73-3592 Sorta Timely Analysis zHow sensitive is gasoline demand to price changes? zHistorically, we have seen relatively little change in demand. Recently? zNew AAA report: higher gasoline prices have caused a 3 percent reduction in demand from a year ago.  What was  p?  q?  ? zWhat does that tell us about gasoline?

3. 12-706 and 73-3593 Distorted Market - Vouchers  Example: rodent control vouchers  Give residents vouchers worth $v of cost  Producers subtract $v - and gov’t pays them  Likely have spillover effects  Neighbors receive benefits since less rodents nearby means less for them too  Thus ‘social demand’ for rodent control is higher than ‘market demand’

4. 12-706 and 73-3594 Distortion : p0,q0 too low Q P Q0 P0 S-v DMDM S D S: represents higher WTP for rodent control P1 Q1 What is NSB? What are CS, PS? Social WTP

5. 12-706 and 73-3595 Social Surplus - locals Q P Q0 P0 S-v DMDM S DSDS P1 Q1 B P E P1+v A C Make decisions based on S-v, Dm What about others in society, e.g. neighbors? Because of vouchers, Residents buy Q1

6. 12-706 and 73-3596 Nearby Residents Q P Q0 P0 S-v DMDM S DSDS P1 Q1 B P E P1+v A C Added benefits are area between demand above consumption increase What is cost voucher program? F G

7. 12-706 and 73-3597 Voucher Market Benefits  Program cost (vouchers):A+B+C+G+E ----  Gain (CS) from target pop: B+E  Gain (CS) in nearby: C+G+F  Producers (PS): A+C  ---------  Net: C+F

8. 12-706 and 73-3598 Opportunity Cost: Land Q P D b Price Case of inelastic supply Government decides to buy Q acres of land, pays P per acre Alternative is parceling of land to private homebuyers What is total cost of project? S Can assume quantity of land is fixed (Q)

9. 12-706 and 73-3599 Opportunity Cost: Land Q P D b Price Government pays PbQ0, but society ‘loses’ CS that they would have had if government had not bought land. This lost CS is the ‘opportunity cost’ of other people using/buying land. Total cost is entire area under demand up to Q (colored) S 0

10. 12-706 and 73-35910 Example: Change in Demand for Concrete Dam Project  If Q high enough, could effect market  Shifts demand -> price higher for all buyers  Moves from (P0,Q0) to (P1,Q1).. Then?? Q0 P0 D a Price Quantity D+q’ S P1 Q1

11. 12-706 and 73-35911 Another Example: Change in Demand  Original buyers: look at D, buy Q2  Total purchases still increase by q’  What is net cost/benefit to society? Q0 P0 D a Price Quantity D+q’ S P1 Q1 Q2

12. 12-706 and 73-35912 Another Example: Change in Demand  Project spends B+C+E+F+G on q’ units  Project causes change in social surplus!  Rule: consider expenditure and social surplus change Q0 P0 D Price Quantity D+q’ S P1 Q1 Q2 E B C FA G G G

13. 12-706 and 73-35913 Dam Example: Change in Demand  Decrease in CS: A+B (negative)  Increase in PS: A+B+C (positive)  Net social benefit of project is B+G+E+F Q0 P0 D Price Quantity D+q’ S P1 Q1 Q2 E B C FA G G G

14. 12-706 and 73-35914 Final Thoughts: Change in Demand  When prices change, budgetary outlay does not equal the total social cost  Unless rise in prices high, C negligible  So project outlays ~ social cost usually  Opp. Cost equals direct expenditures adjusted by social surplus changes Quantity

15. 12-706 and 73-35915 Secondary Markets  When secondary markets affected  Can and should ignore impacts as long as primary effects measured and undistorted secondary market prices unchanged  Measuring both usually leads to double counting (since primary markets tend to show all effects)  Don’t forget that benefit changes are a function of price changes (Campbell pp. 167)

16. 16 Decision Analysis Clemen - Chapter 3 (and a little reminder from Chapter 2)

17. 12-706 and 73-35917 Structuring Decisions  All about the objectives (what you want to achieve)  Decision context: setting for the decision  Decision: choice between options (there is always an option, including status quo)  Waiting for more information also an option  Uncertainty: as we’ve seen, always exists  Outcomes: possible results of uncertain events  Many uncertain events lead to complexity  Next week we’ll play with models for that

18. 12-706 and 73-35918 Structuring Decisions (2)  But this week, we’ll start simple  Steps:  Identifying objectives  Structuring elements into framework  Refining/precisely defining all elements

19. 12-706 and 73-35919 Example: Who to Nominate as a Supreme Court Justice  Objectives?  Categories?  Means/fundamentals? Hierarchy?

20. 12-706 and 73-35920 Influence Diagrams /Decision Trees  Probably cause confusion. If one confuses you, do the other.  Important parts: Decisions Chance Events Consequence/payoff Calculation/constant

21. 12-706 and 73-35921 Other Notes  Chance node branches need to be mutually exclusive/exhaustive  Only one can happen, all covered  “One and only one can occur”  Timing of decisions along the way influences how trees are drawn (left to right)  As with NPV, sensitivity analysis, etc, should be able to do these by hand before resorting to software tools.

22. 12-706 and 73-35922 Solving Decision Trees  We read/write them left to right, but “solve” them right to left.  Because we need to know expected values of options before choosing.  Calculate values for chance nodes  Picking best option at decision nodes  We typically make trees with “expected value” or NPV or profit as our consequence  Thus, as with BCA, we choose highest value.

23. 12-706 and 73-35923 For Next Class  Be able to solve by hand the Texaco decision tree (Figure 4.2)  Ideally also the same one with PrecisionTree (@RISK) or Treeplan (on course website)