2. Average/Marginal Cost Pricing Lecture 9 September 29, 2004 12-706 / 73-359

3. Administrative zHW 2 posted last week (due Monday) zComments on final grades in this course

4. Pricing Strategies zHighway pricing yIf price set equal to AC (which is assumed to be TC/q then at q, total costs covered yp ~ AVC: manages usage of highway yp = f(fares, fees, travel times, discomfort) yPrice increase=> less users (BCA) yMC pricing: more users, higher price yWhat about social/external costs? yMight want to set p=MSC

5. PA Turnpike Commission Revenues and Costs zAlso Post-Gazette, “Turnpike tolls to rise”, 9/14/03 z2002 Data:Toll Revenue $376 million xDistribution: 57% commercial, 43% cars xOther Income $20 million (total $396 million) y531 miles in length x5.67 billion vehicle miles travelled xAnnual maintenance $43 million y57 fare collection facilities xAnnual fare collection costs $55 million zOverall tolls $376M / 5760 M miles y6.6 cents per mile zLooks like $400 M revenue, $100 M cost

6. Toll Road Pricing zHow can we represent costs in this domain? Average? Marginal? zAt proposed rates, how are they charging? zWhat costs would you charge? yAverage cost? What and how? yMarginal cost? What and how? zWhat would be good/bad aspects of each?

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

8. Other Markets - Pricing? zRailroads ySRMC pricing - “cost of running another train” (generally excludes infrastructure upgrades) yAmtrak - if pricing at srmc, need big subsidies zRamsey pricing- different prices can be charged to recover cost yOriginally a way of minimizing distortion from taxes yHighest taxes on goods with inelastic demand, lowest on goods with elastic demand (inverse elasticity rule)  Transit - Higher prices for those least responsive to price (  )

9. More on Ramsey pricing zCosts recovered disproportionately yBut done only to recover unattibutable costs yNot to return monopoly profits zDo turnpike tolls do this? zWhere do we find ‘inelastic demand’ for transport? yWhere there are no/few substitutes yE.g., trucking where no rail/water around zDoing this right requires lots of data!

10. Another Option - 2 part tariffs zCharge separately for fixed, variable cost yFixed charge is entry fee yVariable set to srmc zWhere do we see this? y Phone service

11. Notes - Pricing Handout (Hendrickson/Wohl) zSufficient revenue must often be raised from tolls to cover operation and debt repayment funds zInverse elasticity: higher fares during times of day when demand inelastic yDifferential pricing may be problematic

12. Cost Function Example zAvg var cost expresses average user cost in time, effort, money (without toll) yIs “private cost of transportation”  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 zAppropriate ‘marg. cost toll’ is srmc 1 - sravc 1 yCost of disutility of time to the q-1 drivers when q enters the road yOtherwise the qth driver only considers her own costs zUse sravc =6.2 + 350/ (28-0.008q) (cents/v-mi)

13. 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)

14. Another Approach zIf demand linear (for 5 mile trips): yDemand ~ Marginal Benefit (MB) yq=3060 - 2.857p p = MB= 1071 - 0.35q yFor MC pricing, find where p = MB = srmc yNow p=371(cents) and q=2000 ySravc=177, toll = 194 cents, time=25 mins