AverageMarginal Cost Pricing

1
Average/Marginal CostPricing

• Lecture 9
• September 29, 2004
• 12-706 / 73-359

2
Administrative

• HW 2 posted last week (due Monday)
• Comments on final grades in this course

3
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)
• MC pricing more users, higher price
• What about social/external costs?
• Might want to set pMSC

4
PA Turnpike CommissionRevenues and Costs

• Also Post-Gazette, Turnpike tolls to rise,
  9/14/03
  
• 2002 DataToll Revenue 376 million
• Distribution 57 commercial, 43 cars
• Other Income 20 million (total 396 million)
• 531 miles in length
• 5.67 billion vehicle miles travelled
• Annual maintenance 43 million
• 57 fare collection facilities
• Annual fare collection costs 55 million
• Overall tolls 376M / 5760 M miles
• 6.6 cents per mile
• Looks like 400 M revenue, 100 M cost

5
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?

6
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

7
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 (e)
  

8
More on Ramsey pricing

• Costs recovered disproportionately
• But done only to recover unattibutable costs
• Not to return monopoly profits
• Do turnpike tolls do this?
• Where do we find inelastic demand for
  transport?
  
• Where there are no/few substitutes
• E.g., trucking where no rail/water around
• Doing this right requires lots of data!

9
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?
• Phone service

10
Notes - Pricing Handout (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

11
Cost Function Example

• Avg var cost expresses average user cost in time,
  effort, money (without toll)
  
• Is private cost of transportation
• If sravc1(q)t1 v/(V1-d1q)
• Then srmc1(q) sravc1(q) vd1q/(V1-d1q)2
• Appropriate marg. cost toll is srmc1- sravc1
• 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)

12
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)
13
Another Approach

• If demand linear (for 5 mile trips)
• Demand Marginal Benefit (MB)
• q3060 - 2.857p p MB 1071 - 0.35q
• For MC pricing, find where p MB srmc
• Now p371(cents) and q2000
• Sravc177, toll 194 cents, time25 mins