Assignment 5. Due date 12/10/98

Objectives:

• Create a spreadsheet for a multi-product, multi-driver marginal cost estimation procedure, for investigation with a simulation model.
• Answer the two questions
  • How well are overall marginal costs estimated assuming no biases in the simulation inputs?
  • If input elasticities are biased how does it impact absolute and relative marginal costs within a single cost pool, and absolute and relative marginal cost summed across cost pools?

Remember

There should be a single set of estimated (Estimation Procedure) volumes in the spreadsheet (not one for each cost pool).

Notation

(used within each cost pool):

• = elasticity of cost with respect to driver.
• = multiplicative constant term in cost driver model.
• , product volumes, i = 1,2,3,4.
• = amount of the cost driver per mail unit.
• , where D is the driver value.
• C = attributable dollars in the cost pool

Task 1. Create the spreadsheet.

Hypothetical World input values

Take the given spreadsheet and expand it to include information on a second cost pool, Purchased Transportation.

The transportation cost pool has as its driver, Cubic Foot Miles of Purchased Transportation.

This second pool has the following Hypothetical World values for the typical number of miles per piece for the 4 classes (the ):

Find the total number of cubic feet miles due to each mail class ( ), and the value of the driver ( ) which is defined as the sum over all the individual product's cubic foot miles.

The Hypothetical World elasticity ( ) for the transportation cost pool is 0.95.

Last year total costs in this pool (C) were $1,000 million. Using this cost value, baseline the hypothetical world for this cost pool by solving the log-linear cost equation for , where the cost equation asserts that:

Using the equation

find the Hypothetical World marginal cost and relative marginal cost (with respect to First class) for each of the products in this cost pool.

Estimation procedures input values.

Recall from class that the values are interpreted as the proportion of the driver due to each product, or equivalently in this context as the elasticity of the driver with respect to mail volumes.

These proportions are estimated from surveys which sample transportation movements.

Assume that the following estimates from these transportation surveys are unbiased and Normally distributed; their cv's are given in the table as well.

Enter these values into the spreadsheet defining them as assumption cells.

Assume for now that the elasticity is known correctly and with certainty, that is use an elasticity of 0.95 in the Estimation Procedure.

Construct in the spreadsheet the marginal costs and relative marginal costs for this cost pool obtained from the Estimation Procedure. You can use the existing spreadsheet as a template. Define these new cells as forecast cells. Make sure that you use the same volumes as went into the Mail Processing cost pool.

Define cells for the differences in marginal cost between the EP (Estimation Procedure) and HW (Hypothetical World) values. Make these forecast cells too.

Define cells for the differences in relative marginal cost between the EP and HW values. Make these forecast cells as well.

To check that you have done things correctly, I obtain the marginal costs and relative marginal costs from the EP for each product as:

Summing across cost pools

The last stage of setting up the spreadsheet is to define total marginal costs, which are simply obtained by summing the component marginal costs across the 2 cost pools. Also calculate relative total marginal costs.

Calculate these for both the Hypothetical World and for the Estimation Procedure. In the estimation procedure these should be defined as forecast cells.

Finally calculate differences between the HW Total Marginal Costs and the EP Total Marginal Costs, and differences between the HW Relative Total Marginal Costs and the EP Relative Total Marginal Costs. Again these should all be forecast cells.

This completes the construction of the spreadsheet.

Questions.

A table of relevant outputs with a short paragraph will suffice for each part.

1.(a) Estimate and describe the marginal costs for each product in each cost pool. Include a discussion of the uncertainty associated with the estimate.

1. (b) Estimate and describe the relative marginal costs for each product in each cost pool. Include a discussion of the uncertainty associated with the estimate.

1. (c) Estimate and describe the total marginal and relative total marginal costs for each product. Include a discussion of the uncertainty associated with the estimate.

2. Assume now that both the elasticities are estimated in a biased fashion. In particular, management assumes an elasticity of 1 in both cost pools. Include this information in the spreadsheet by entering both the EP elasticity values as 1.

Repeat questions 1 a,b,c but now under this new biased elasticity scenario.

3. Write a succinct one paragraph retort to the assertion:

``In terms of relative marginal costs, elasticities don't matter.''