Demonstrating discount rates with a reverse auction of presentation dates

This page authored and based on an activity by James Peyton, Highline College
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This material is replicated on a number of sites as part of the SERC Pedagogic Service Project


In this reverse auction of presentation dates, student groups submit their "offers" for taking weekly presentation dates 2,3,4 or 5 weeks away in order to illustrate the discounting of future effort. The offers state how many bonus points the group would want to receive to be assigned to the earlier rather than the later days, with those groups presenting on the final day receiving no bonus points. The groups complete an exercise using the bids to calculate a simple discount rate. Group presentations are scheduled by offers. Groups receive bonus points based on the lowest bid set. Setup document and worksheet included.

Learning Goals

Students observe the discounting of future effort and calculate a simple discount rate. If desired, the discounting concept can be applied to economics of climate change.

Context for Use

This reverse auction can be applied to any assignment that has different turn-in dates that students could select. It complements discussions of present value or the economics of climate change mitigation versus adaptation. It is designed to fit within a 50-minute class for the auction, related exercise and discussion, with additional time for subsequent assessment.

Description and Teaching Materials

Assignment groups of 3-4 submit offers for sequential delivery dates
Students use their offers to calculate the implied discount rate on future effort, using the total points possible for the assignment plus their highest bid as the base

Offer sheet for each group (see example)
Exercise worksheet for each student relating offers and the concept of discounting (see example)

Running the Auction:
The idea of a reverse auction where the lowest offer wins is introduced in the first few minutes.
Groups are given about 5-8 minutes to privately determine their offers.

Exercise Components:
Groups of 3-4 work through the steps to calculate their implied discount rate for future effort. Where assignment groups are smaller than 3-4, the assignment groups can be combined for larger small-group discussions.
The worksheet (example attached) starts with a table where the students take the total points possible for the assignment, add their highest bid (hopefully for the most proximate date), then use that sum as the denominator for point ratios for subsequent delivery dates. The difference between the calculated ratios converted into percentages and 100% then gives a simple discount rate of future effort compared to the first delivery date.

Class Discussion:
Groups are asked to post their discount rates and explore why we expect different groups to have different discount rates. This discussion ties back to subjective valuation and opportunity cost.
If desired, the discount rate concept can be tied into a broader discussion of the economics of climate change.
Offer sheet example (Microsoft Word 2007 (.docx) 12kB Apr4 17)
Discount Rate Calculation Worksheet Example (Microsoft Word 2007 (.docx) 14kB Apr4 17)
Sample Economics of Climate Change Activity using Discount Rates (Microsoft Word 2007 (.docx) 516kB Apr4 17)
Assessment activity for discount rates (Microsoft Word 2007 (.docx) 14kB Apr4 17)

Teaching Notes and Tips

Several notes:
  • Construction project bids are one real-world example of reverse auctions where the lowest offer gets the contract.
  • In this exercise, setting the bonus points to zero for the final presentation day anchors the offers and guides groups to give increasing offers for more proximate delivery dates. I told the class that groups will receive bonus points for the different weeks based on lowest offer set, as long as it is reasonable.
  • There's a balance in the time given for the offer development. Students need enough time to understand what they are doing, but not enough time to collude among groups and drive up offer prices.


I have assessed the learning outcomes of the reverse-auction activity with a short in-class written assignment about discount rates and the economics of climate change (example attached). The prompt is

Write a thoughtful response to the following prompt that uses what we have been learning in class:

Public opinion surveys in the US show that some people support taking major steps to cut back on carbon emissions as a way to fight climate change, but others oppose taking those steps. If both sides agree that the additional costs to the US economy of reducing climate change 40-60 years from now will be about $250 billion per year starting today, why could they disagree on whether it is worth it to take on those costs now?

Include the following elements in your response:
- Briefly explain at least two major difficulties, related to economics in some way, of determining how we should respond to climate change.
- Use some hypothetical numbers and the idea of discount rates as part of your answer to the question above.
- Refer to material from the text and from class discussions as appropriate.

The scoring rubric was set as follows (where 70% at a 3 or above would be the goal)
5- two major difficulties of determining how to respond to climate change related to economics, strong connection to prompt scenario, hypothetical numbers and discount rates correctly interpreted, includes some reference to class material
4- two major difficulties, hypothetical numbers and discount rates correctly interpreted, includes some reference to class material, acceptable connection to prompt scenario
3- one major difficulty and hypothetical numbers and discount rates correctly interpreted or two major difficulties with minor errors in discount rate interpretation, some reference to class material
2- two major difficulties and weak or no discount rate interpretation
1- one major difficulty and weak or no discount rate interpretation
0- answer does not address prompt

where students scoring 3 would be viewed as having met the learning objective as applied to this content area.

In my Fall 2017 class, just over 30% of students achieved a score of 3 or higher. While that level is not at the stated goal of 70%, I am encouraged by the results and I will continue to use this activity as part of my instructional efforts in this area. In the past, very few students were understanding discount rates enough to apply them to the economics of climate change. This activity gives me a different foundation to build from.

References and Resources

The report "The Economics of Global Climate Change" from Tufts University has tables and graphs that are directly connected to discount rates and the political economy of climate change policies: