2. 1 Civil Systems Planning Benefit/Cost Analysis Scott Matthews 12-706 / 19-702

3. Announcements  (Group) Project 1 Feedback so Far  HW 3 Out  Read Facility Case for Wednesday  Case Study Writeup Due (NO late accepted) 12-706 and 73-3592

4. Profit Maximization under Perfect Competition 12-706 and 73-3593 Q P S D Q P S = MC p D p = MR q

5. 12-706 and 73-3594 Allocative Efficiency Allocative efficiency occurs when MC = MB (or S = D) Equilibrium is max social surplus - prove by considering Q1,Q2 Q* P* S D = MB = MC Q1Q1 Q2Q2 a b Price Quantity Is the market equilibrium Pareto efficient? Yes - if increase CS, decrease PS and vice versa.

6. 12-706 and 73-3595 Deadweight Loss  Yellow paid to gov’t as tax  Green is pure cost (no offsetting benefit)  Called deadweight loss  Consumers buy less than they would w/o tax (exceeds some people’s WTP!) - loss of CS  There will always be DWL when tax imposed Price Quantity P2 0 1 2 Q* Q1 A B P* CS1

7. 12-706 and 73-3596 Monopoly - the real game  One producer of good w/o substitute  Not example of perfect comp!  Deviation that results in DWL  There tend to be barriers to entry  Monopolist is a price setter not taker  Monopolist is only firm in market  Thus it can set prices based on output

8. 12-706 and 73-3597 Monopoly - the real game (2)  Could have shown that in perf. comp. Profit maximized where p=MR=MC (why?)  Same is true for a monopolist -> she can make the most money where additional revenue = added cost  But unlike perf comp, p not equal to MR

9. 12-706 and 73-3598 Monopoly Analysis MR D MC Qc Pc In perfect competition, Equilibrium was at (Pc,Qc) - where S=D. Demand – horizontal line But a monopolist has a Function of MR that Does not equal Demand So where do they supply?

10. 12-706 and 73-3599 Monopoly Analysis (cont.) MR D MC Qc Pc Monopolist supplies where MR=MC for quantity to max. profits (at Qm) But at Qm, consumers are willing to pay Pm! What is social surplus, Is it maximized? Qm Pm

11. 12-706 and 73-35910 Monopoly Analysis (cont.) MR D MC Qc Pc What is social surplus? Orange = CS Yellow = PS (bigger!) Grey = DWL (from not Producing at Pc,Qc) thus Soc. Surplus is not maximized Breaking monopoly Would transfer DWL to Social Surplus Qm Pm

12. 12-706 and 73-35911 Natural Monopoly  Fixed costs very large relative to variable costs  Ex: public utilities (gas, power, water)  Average costs high at low output  AC usually higher than MC  One firm can provide good or service cheaper than 2+ firms  In this case, government allows monopoly but usually regulates it

13. 12-706 and 73-35912 Natural Monopoly MR D Q* P* Faced with these curves Normal monop would Produce at Qm and Charge Pm. We would have same Social surplus. But natural monopolies Are regulated. What are options? Qm Pm MC AC a b c d e

14. 12-706 and 73-35913 Natural Monopoly MR D Q* P* Forcing the price P* Means that the social surplus is increased. DWL decreases from abc to dec Society gains adeb Other options? Qm Pm MC AC a b c d e Q0

15. 12-706 and 73-35914 Monopoly – Other Options  Other options - set P = MC  But then the firm loses money  Subsidies needed to keep in business  Give away good for free (e.g. road)  Free rider problems  Also new deadweight loss from cost exceeding WTP Phone service

16. Making Cost Functions  Fundamental to analysis and policies  Three stages:  Technical knowledge of alternatives  Apply input (material) prices to options  Relate price to cost  Obvious need for engineering/economics  Main point: consider cost of all parties  Included: labor, materials, hazard costs

17. Pricing Strategies  Highway pricing  If price set equal to AC (which is assumed to be TC/q then at q, total costs covered  p ~ AVC: manages usage of highway  p = f(fares, fees, travel times, discomfort)  Price increase=> less users (BCA)  P=MC: maximizes economic efficiency (why?)  more users, higher price  Might want to set p=MSC

18. PA Turnpike Commission Revenues and Costs  Also Post-Gazette, “Turnpike tolls to rise”, 9/14/03  2005 Data: Toll Revenue $545 million  Distribution: 57% commercial, 43% cars y537 miles in length x5.62 billion vehicle miles travelled xAnnual maintenance $43 million y60 fare collection facilities xAnnual fare collection costs $60million zOverall tolls $545 M/ 5760 M miles yAverage toll: X cents per mile zLooks like $500M revenue, $100 M cost zNewer data http://www.paturnpike.com/geninfo/2006_Annual_Report_PTC.pdf

19. Where is the rest of cost?  “Construction” or major renovations are not paid for out of operating revenues  They are paid for by selling bonds  Then the yearly interest is paid as cost  What must current debt load be, assuming the rest of the ‘cost’ is debt expense?  If ‘rest of cost’ is $300M, then at 10% bond rate it would be about $3 billion  In reality, there are other costs, and rate is not 10%, and current outstanding debt is about $2.1 billion

20.  “New” exit numbers are mile markers  How is turnpike doing pricing? 12-706 and 73-35919

21. Toll Road Pricing  How can we represent costs in this domain? Average? Marginal?  At proposed rates, how are they charging?  What costs would you charge?  Average cost? What and how?  Marginal cost? What and how?  What would be good/bad aspects of each?

22. Marginal Cost Pricing  If srmc pricing is used in natural monopolies, total costs will not be covered and subsidies will be needed to keep the service at breakeven  Idea is to charge the incremental cost to all users (marginal social cost) to the newest user  Highways: show marginal cost of travel delay, congestion, pollution from additional car on road  Note this is very different from simply charging the marginal private cost of the highway (which is likely near $0)  Also note that operator, not users, get revenues

23. Other Markets - Pricing?  Railroads  SRMC pricing - “cost of running another train” (generally excludes infrastructure upgrades)  Amtrak - if pricing at srmc, need big subsidies  Ramsey pricing- different prices can be charged to recover cost  Originally a way of minimizing distortion from taxes  Highest taxes on goods with inelastic demand, lowest on goods with elastic demand (inverse elasticity rule)  Transit - Higher prices for those least responsive to price (  )

24. Another Option - 2 part tariffs  Charge separately for fixed, variable cost  Fixed charge is entry fee  Variable set to srmc  Where do we see this?

25. Notes - Pricing Chapter (Hendrickson/Wohl)  Sufficient revenue must often be raised from tolls to cover operation and debt repayment funds  Inverse elasticity: higher fares during times of day when demand inelastic  Differential pricing may be problematic

26. Cost Function Example  Avg var cost expresses average user cost in time, effort, money (without toll)  Is “private cost of transportation”- i.e. what people pay  If sravc 1 (q)=  1 + v/(V 1 -  1 q)  Then srmc 1 (q)= sravc 1 (q)+ v  1 q/(V 1 -  1 q) 2  Appropriate ‘marg. cost toll’ is srmc 1 - sravc 1  Cost of disutility of time to the q-1 drivers when q enters the road  Otherwise the qth driver only considers her own costs  Use sravc =6.2 + 350/ (28-0.008q) (cents/v-mi)

27. From Our Example Marginal change in time is very small (1 second) for adding 1 trip after 1999 trips already taken. q is flow rate (trips/hr)

28. Who is Better Off?  Society gains the toll revenues  Society gains environmental benefits.  The benefits to society should exceed (in theory) the losses to the drivers.  Can some form of compensation be used to make everyone better off?  Hard to do. 12-706 and 73-35927

29. Another Approach  If demand linear (for 5 mile trips):  Demand ~ Marginal Benefit (MB)  q=3060 - 2.857p p = MB= 1071 - 0.35q  For MC pricing, find where p = MB = srmc  Now p=371(cents) and q=2000  Sravc=177, toll = 194 cents, time=25 mins