The economics of proposal writing

How much effort should a Principal Investigator (PI) spend writing a proposal? This is a complicated question. The short, convenient, but only moderately useful answer is you should write so long as the marginal benefits of additional writing exceed the marginal costs. But this begs two questions:

  1. What are the marginal benefits?
  2. What are the marginal costs?

The marginal benefit is not the value of the proposal. Say it is a $1,000,000 proposal. The marginal benefit is not $1 million.

  1. First, you need to consider the expected value of the proposal. What is the likelihood of the proposal being funded. If it is for NSF, this is around 10% (I have heard as low as 8% … in any case, this is pathetic, and suggests many other problems in our academic funding system). Now of course 10%*$1,000,000 is $100,000. But that is still not the marginal benefit of the proposal. Further, the probability of success is probably a positive function of the amount of time spent writing, but it is subject to diminishing returns. The first draft takes the probably from 0 (you will not get funded if there is no proposal) to a positive number. The second draft (or second day) increases this probability, but not as much as the first, and so on. In short, the benefits depend in part on the costs.
  2. Second, From the point of view of the PI, we need to think about “profit”. So for $100,000 proposal, University overhead is a bit over 50% (it’s more complicated, since overhead is charged differently on different items). This leaves us $66,666 of revenue. But that is still not the “profit”. Let’s say the proposal funds 1 month of summer salary, an RA, and a few other things. A purely and irrationally selfish PI might treat the 1 month of summer salary as the “profit”, and ignore the RA time, overhead, etc.
    • That would wrong (too high) though, since the 1 month of summer salary is not the profit, it is the 1 month of summer salary working on this project minus the alternative use (cost) of that time, which is not valued at 0. In the absence of this project, the PI would work on some other project (which might be less interesting, but still pays a salary, in which case the cost includes the difference of interestingness) or get to experience leisure over the summer. Valuing this is not obvious. What salary would the PI require to switch from leisure to work. It is in all likelihood lower than the salary the PI actually receives, but higher than 0.
    • That would also be wrong (too low) since the PI presumably gets some social capital from funding RAs, getting grants, and paying the University, social capital which is eventually translated into tenure or a higher salary or job offers elsewhere. This is even harder to value, and depends on the characteristics of the PI (does the PI already have tenure? then this is lower; is this a prestigious grant?; is the PI looking to move? how old is the PI? what is the net present value of additional expected future earnings if this proposal gets funded? )
  3. Third, we should consider positive spillovers. This proposal, if funded, may open up other good research directions and funding opportunities, and the Net Present Value of those should be considered.

The marginal cost is similarly complicated.

The cost spent writing the proposal is of course in part the value of the time spent writing the proposal (the time spent multiplied by the dollars per hour).

This cost might be lowered if the proposal is not written from scratch, but instead is comprised at least in part of recycled materials (all environmentally conscious PIs recycle good but unfunded ideas). It might also be discounted if the time spent writing is multi-purpose, so that the text that is written can be recycled into an academic paper or some future proposal if this proposal is not funded.

We also need to think about opportunity cost, what is the next best use of the time that was spent writing this proposal. If that time was otherwise leisure, we can add the value of the leisure foregone. If that time would otherwise be spent writing a different proposal, we then need to consider the marginal benefits and marginal costs of that proposal, and add the net of those as the opportunity cost.

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Now suppose an Investigator has been invited to contribute to someone else’s proposal. There are several reasons this might occur. The PI might value the other-investigator’s talents and see some synergies from collaboration. The PI might see some value in the investigator’s CV and reputation, this is crudely referred to as “renting a CV”.

The same math applies to the fraction of the proposal that is committed to the Investigator. But there is also a set of equity checks we can employ. The co-PI should not write more of the proposal than their share of the proposals funding. The senior co-PI should write less than the junior PI for a variety of reasons.

    • First, his relative benefits are less (less future NPV from success).
    • Second his value added includes the more valuable CV.
    • Third, his value of time is presumably higher.

This does not mean the senior co-Investigator should leave everything to the junior PI. First the senior co-PI does have value in framing and editing the structure of the document, second he needs to ensure quality since his CV is being rented, and he doesn’t want to be associated with a truly bad proposal.

In short this is a complicated question, without an obvious answer, but with an order of magnitude for the upper bound … the amount of time spending the proposal should not exceed the expected value of the proposal.

Introduction to Transportation Engineering – Introduction to Queueing