COSTING AND PRICING IN TRANSPORTATION KSG HUT251/GSD 5302 Transportation Policy and Planning, Gomez-Ibanez OUTLINE OF CLASS: 1.ROLE OF MARGINAL COST IN PRICING  Private firm (profit-maximizing)  Public firm (welfare-maximizing) 2.COMPLICATIONS IN DETERMINING MC  Occur because Investments often high cost, durable, “lumpy” Peaking of demand  Complications 1.Increasing returns to scale or traffic density 2.Returns to scope, joint costs, and peak vs. off-peak 3.Short-run MC versus Long-run MC 4.Sunk costs

PRICING IN A PRIVATE FIRM GENERAL CASE  HOMOGENOUS PRODUCT Produce quantity where MR = MC Check shutdown (TR  TC in long run) MC P MR D  JOB SHOP Q MC is the floor Get as much above MC as possible

PRICING IN A PRIVATE FIRM COMPETITIVE MARKET “Price takers”: demand curve flat and MR = P Thus: MR = MC becomes P = MC MC D = P = MR Q

PRICING IN A PUBLIC ENTERPRISE ASSUMPTIONS FOR P = MC: 1.CONSUMER IS ALWAYS RIGHT (Consumer is best judge of his or her own welfare, consumer is reasonably well informed, welfare of society is a function of welfare of consumers) 2.REDISTRIBUTION NOT AN ISSUE (Distribution of incomes and opportunities is fair or better corrected by other measures) 3.NO UNCORRECTED EXTERNALITIES (E.g., no uncorrected pollution or congestion externalities) 4.OTHER GOODS AND SERVICES ARE PRICED AT MC (E.g., no monopolies or distorting taxes or subsidies) 5.NO CONFLICTING MANAGERIAL OR BUDGETARY CONSIDERATIONS (E.g., if P = MC means TR  TC subsidizing the public enterprise through tax revenue is acceptable.)

PRICING IN A PUBLIC ENTERPRISE ASSUMPTIONS (1) THROUGH (4) IMPLY SOCIAL BENEFIT = consumers’ willingness to pay SOCIAL COST = firms’ production costs Thus: P = MC becomes MSB = MSC MC = MSC P D = MSB Q

THEORY OF THE SECOND BEST VIOLATION OF ASSUMPTION (4)  DEFINITIONS FIRST BEST SOLUTION: price the other goods at MC too SECOND BEST SOLUTION: If first best not possible  EXAMPLE: If P AUTO < MC AUTO  P TRANSIT  MC TRANSIT ?  P TRANSIT  MC TRANSIT ?  LESSONS  NO OBVIOUS SOLUTION (P  =  MC ?)  IGNORE IF LOW CROSS PRICE ELASTICITY

COMPLICATIONS IN DETERMINING MC: (1) ECONOMIES OF SCALE OR TRAFFIC DENSITY SCALE: output or size of firm DENSITY: volume of traffic in a corridor or between a city pair RETURNS TO SCALE OR DENSITY CAN BE: CONSTANTDECREASING, OR INCREASING MC AC = MCMC AC IF P = MC, this means TR = TC TR  TCTR  TC

COMPLICATIONS IN DETERMINING MC: (1) ECONOMIES OF SCALE OR TRAFFIC DENSITY IRD, IRS COMMON BUT OFTEN EXAGGERATED  RIGHT OF WAY AND CAPITAL COSTS NOT THAT “LUMPY”  AC CURVE OFTEN STEEP ONLY WHERE DOMINATED BY OTHER MODES AC BUS RAIL AUTO CORRIDOR VOLUME

COMPLICATIONS IN DETERMINING MC: (1) ECONOMIES OF SCALE OR TRAFFIC DENSITY IMPLICATIONS OF IRD, IRS  PRICING P = MC causes deficits that may be considered undesirable due to budget or incentive concerns. Possible remedies: Price discrimination:  Descending block  Ramsey (a.k.a., inverse elasticity, value of service) Price at AC (if close to MC)  REGULATION May have “natural monopoly” (although not if competition from other modes or locations)  PROJECT EVALUATION P = MC not sufficient for project to be worthwhile. Consumers’ surplus must  deficit (Jules Dupuit’s bridge problem)

COMPLICATIONS IN DETERMINING MC: (2) ECONOMIES OF SCOPE OR JOINT COSTS ISSUE: Potential economies or diseconomies of using the same facilities, crews, etc. for different services (E.g., passenger and freight on RRs, business and leisure on airlines)  Extreme (and old) view: JOINT vs. COMMON COSTS COMMON: use same facilities but can clearly allocate all parts of the facility to one or another service JOINT: provision of facilities for one service makes them available for other service at no cost Classic examples: wool and mutton; cotton seed and fiber Real world example: peak vs. off peak  More nuanced (modern) view: ECONOMIES OF SCOPE There may be cost advantages (or disadvantages) of producing two different products with the same firm. If so, MC  AC. Beware of diseconomies of scope!

COMPLICATIONS IN DETERMINING MC: (2) ECONOMIES OF SCOPE OR JOINT COSTS PEAK LOAD PRICING: Some costs of peak and off peak are typically joint NORMAL SOLUTION: Assign all joint costs to the peak SHIFTING PEAK PROBLEM: if joint costs are assigned to peak, peak volumes may fall below off-peak volumes SOLUTIONS: 1.Broaden definition of peak (Peak will shift if peak period defined too narrowly) 2.If shifting peak persists, allocate joint costs so that peak and off-peak volumes equal

COMPLICATIONS IN DETERMINING MC: (2) ECONOMIES OF SCOPE OR JOINT COSTS SIMPLE PEAK LOAD EXAMPLE: HIGHWAY  Two periods—peak and off-peak—with zero cross-price elasticity  Two types of costs, both constant returns to scale (so AC = MC): Capacity costs (joint) = CC per unit of traffic Operating or maintenance costs (not joint) = OC per unit traffic D OFFPEAK D PEAK P PEAK OC + CC CC P OFFPEAK OC V OFFPEAK V PEAK VOLUME

COMPLICATIONS IN DETERMINING MC: (2) ECONOMIES OF SCOPE OR JOINT COSTS PEAK LOAD EXAMPLE  SHIFTING PEAK D OFFPEAK D PEAK P PEAK OC + CC CC P OFFPEAK OC V PEAK V OFFPEAK VOLUME

COMPLICATIONS IN DETERMINING MC: (2) ECONOMIES OF SCOPE OR JOINT COSTS PEAK LOAD EXAMPLE  SOLUTION TO JOINT COST ALLOCATION IN SHIFTING PEAK D COMBINED PEAK AND OFF PEAK D OFFPEAK D PEAK 2OC + CC OC + CC P PEAK CC P OFFPEAK OC V PEAK AND OFFPEAK VOLUME

COMPLICATIONS IN DETERMINING MC: (3) SHORT-RUN VS. LONG-RUN MARGINAL COSTS  DEFINITIONS SHORT-RUN COSTS: when some input fixed LONG-RUN COSTS: when all inputs variable  EXAMPLE: with CRS in long-run costs SRAC 1 SRAC 2 SRAC 3 SRAC 4 LRAC = LRMC SRMC 1 SRMC 2 SRMC 3 SRMC 4

COMPLICATIONS IN DETERMINING MC: (3) SHORT-RUN VS. LONG-RUN MARGINAL COSTS  LRMC  SRMC MEANS PLANT NOT OPTIMAL FOR CURRENT OUTPUT LRMC = SRMC  plant just right LRMC < SRMC  plant too small LRMC > SRMC  plant too big SRAC LRAC = LRMC SRMC

COMPLICATIONS IN DETERMINING MC: (3) SHORT-RUN VS. LONG-RUN MARGINAL COSTS IF LRMC  SRMC, WHICH TO USE? SRMC Optimizes use of existing plant LRMC If long-run price signals are important to consumers or prices are “sticky” because of reputational concerns or public regulation

COMPLICATIONS IN DETERMINING MC: (4) SUNK COSTS SUNK COSTS: committed, irretrievable OFTEN APPEAR LARGE because transport capital is often durable, immobile, specialized BUT RARELY COMPLETELY SUNK Usually some opportunity cost, especially in long run LOW OPPORTUNITY COST OF “SUNK” COSTS MAY INDICATE EXCESS CAPACITY Compare opportunity cost with investor or replacement cost: Opportunity cost > investment cost  buy more Opportunity cost < investment cost  buy less WHERE DIFFERENCES PERSIST, REASONING IS ANALOGOUS TO SRMC vs. LRMC Normally use opportunity cost But use investment or replacement where long-term price stability important

TIPS ON BACK OF THE ENVELOPE COSTING AND PRICING  ESTIMATE MC 1.WHAT DO VARIOUS COSTS DEPEND ON? (COST DRIVERS) E.g, peak vehicles, vehicle miles, passengers? 2.ARE THERE (DIS)ECONOMIES OF SCALE OR DENSITY? If not, can use AC. If so, what is source and size? 3.ARE THERE JOINT COSTS OR (DIS)ECONOMIES OF SCOPE? If so, who is responsible for joint costs? Beware shifting peak 4.ARE THERE SUNK COSTS OR LRMC ≠ SRMC? Can you resize the plant so it is more appropriate? Is long-run price stability important?  IF PROFIT MAXIMIZING FIRM:  GET AS MUCH ABOVE MC AS POSSIBLE  CONSIDER BROADER IMPLICATIONS Competitors reactions, effects on other business/customers  IF PUBLIC ENTERPRISE (OR REGULATOR): MORE COMPLEX: P=MC UNLESS COMPELLING SECOND BEST, EXTERNALITY, EQUITY OR BUDGETARY ISSUES