Average/Marginal Cost Pricing Lecture 8 September 27, /

Administrative zHW 2 posted last week (due next Mon.) zHW 1 returned today yAvg 40, High:50 Low: 20 zComments on final grades in this course

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

Making Cost Functions zFundamental to analysis and policies zThree stages: y Technical knowledge of alternatives y Apply input (material) prices to options y Relate price to cost zObvious need for engineering/economics zMain point: consider cost of all parties zIncluded: labor, materials, hazard costs

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

Where is the rest of cost? z“Construction” or major renovations are not paid for out of operating revenues yThey are paid for by selling bonds yThen the yearly interest is paid as cost yWhat must current debt load be, assuming the rest of the ‘cost’ is debt expense? zIf ‘rest of cost’ is $300M, then at 10% bond rate it would be about $3 billion yIn reality, there are other costs, and rate is not 10%, and current outstanding debt is about $2.1 billion

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?

Other Markets - Pricing? zElectricity

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

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 zUse sravc = / ( q)

From Our Example Marginal change in time is very small (1 second) for adding 1 trip after 1999 trips already taken.

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