AverageMarginal Cost Pricing

1
Average/Marginal CostPricing

• Lecture 9
• September 29, 2003
• 12-706 / 73-359

2
Making Cost Functions

• Fundamental to analysis and policies
• Three stages
• Technical knowledge of alternatives
• Apply input (material) prices to options
• Relate price to cost
• Obvious need for engineering/economics
• Main point consider cost of all parties
• Included labor, materials, hazard costs

3
Estimation in the Course

• We will encounter estimation problems in sections
  on demand, cost and risks.
• We will encounter estimation problems in several
  case studies.
• Projects will likely have estimation problems.
• Need to make quick, back-of-the-envelope
  estimates in many cases.
• Dont be afraid to do so!

4
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

5
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

6
Where is the rest of cost?

• Construction or major renovations are not paid
  for out of operating revenues
• They are paid for by selling bonds
• Then the yearly interest is paid as cost
• What must current debt load be, assuming the rest
  of the cost is debt expense?
• If rest of cost is 300M, then at 10 bond rate
  it would be about 3 billion
• In reality, there are other costs, and rate is
  not 10, and current outstanding debt is about
  2.1 billion

7
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
• Use sravc 6.2 350/ (28-0.008q)

8
From Our Example
Marginal change in time is very small (1 second)
for adding 1 trip after 1999 trips already taken.
9
Another Approach

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