OUTLINE OF CLASS: ROLE OF MARGINAL COST IN PRICING Private firm (profit-maximizing)

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

2. 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

3. 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

4. PRICING IN A PUBLIC ENTERPRISE ASSUMPTIONS FOR P = MC: • 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) • REDISTRIBUTION NOT AN ISSUE (Distribution of incomes and opportunities is fair or better corrected by other measures) • NO UNCORRECTED EXTERNALITIES (E.g., no uncorrected pollution or congestion externalities) • OTHER GOODS AND SERVICES ARE PRICED AT MC (E.g., no monopolies or distorting taxes or subsidies) • NO CONFLICTING MANAGERIAL OR BUDGETARY CONSIDERATIONS (E.g., if P = MC means TR  TC subsidizing the public enterprise through tax revenue is acceptable.)

5. 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

6. 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 PAUTO < MCAUTO • PTRANSIT MCTRANSIT ? • PTRANSIT MCTRANSIT ? • LESSONS • NO OBVIOUS SOLUTION (P  =  MC ?) • IGNORE IF LOW CROSS PRICE ELASTICITY

7. 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 AC = MC MC AC IF P = MC, this means TR = TC TR  TC TR  TC

8. 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

9. 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)

10. 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!

11. 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: • Broaden definition of peak (Peak will shift if peak period defined too narrowly) • If shifting peak persists, allocate joint costs so that peak and off-peak volumes equal

12. 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 DOFFPEAK DPEAK PPEAK OC + CC CC POFFPEAK OC VOFFPEAK VPEAK VOLUME

13. COMPLICATIONS IN DETERMINING MC:(2) ECONOMIES OF SCOPE OR JOINT COSTS PEAK LOAD EXAMPLE • SHIFTING PEAK DOFFPEAK DPEAK PPEAK OC + CC CC POFFPEAK OC VPEAK VOFFPEAK VOLUME

14. COMPLICATIONS IN DETERMINING MC:(2) ECONOMIES OF SCOPE OR JOINT COSTS PEAK LOAD EXAMPLE • SOLUTION TO JOINT COST ALLOCATION IN SHIFTING PEAK DCOMBINED PEAK AND OFF PEAK DOFFPEAK DPEAK 2OC + CC OC + CC PPEAK CC POFFPEAK OC VPEAK AND OFFPEAK VOLUME

15. 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 SRAC1SRAC2SRAC3SRAC4 LRAC = LRMC SRMC1SRMC2SRMC3SRMC4

16. 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

17. 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

18. 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

19. TIPS ON BACK OF THE ENVELOPECOSTING AND PRICING • ESTIMATE MC • WHAT DO VARIOUS COSTS DEPEND ON? (COST DRIVERS) E.g, peak vehicles, vehicle miles, passengers? • ARE THERE (DIS)ECONOMIES OF SCALE OR DENSITY? If not, can use AC. If so, what is source and size? • ARE THERE JOINT COSTS OR (DIS)ECONOMIES OF SCOPE? If so, who is responsible for joint costs? Beware shifting peak • 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