math/economics problem

[elfprince13]

Introduction
a group of high school students in VT are working on writing, proposing, and getting passed a bill to transition VT to sustainable (both economically and ecologically) home heating. Most of the current research is spread between our wiki and this older site.

The Problem
part of our plan is as follows:
[quote name='"wiki"']We are proposing taxing fossil heating fuels at a variable rate. It would start at 0.5% and transition to a maximum that is optimum to stimulate the Vermont economy and facilitate the transition to a sustainable heating technology (bio fuels). What is the optimum rate of change for the taxation?[/quote]

if any of you guys are willing to put your crazy math skills to work on this problem and help us out, a summary of all the information we have that we thought is likely to be relevant to the problem is here. If you want anymore information, then feel free to ask.

If you choose to help with this, please show the steps you took (so we can back up your answer when we meet with our state reps to propose the bill), and of course you will be credited for your work.

Thanks, and have fun
-elfprince13

[DigiTan]

So basically you're needing to find the minimum tax rate to fund pellet production, create the Bio futures market, and create a grant for farmers to create an in-state supply of switchgrass?

[elfprince13]

there is a lag effect between when the tax is implemented (and places a drain on the state economy) and when the pelletization technologies can be put in place and the multiplier effect of the money staying in state kicks in to boost the economy back up. The lower the tax rate the lower the drag on the economy but the longer it takes to put the pelletization in place. The higher the tax rate the higher the drag, but also the shorter the lag time. So we want to find the optimal tax rate (and also, optimal rate of change to the tax rate) to minimize both the drag on the state economy and the lag time for putting in place the pelletization technologies.

due to the huge economic advantages of pellet stoves over oil/gas sources, most of the switch will pay for itself within a few years, thus the big cost to the state would be establishing the pelletizing facilities, and subsidizing families who can't afford to buy a new pellet stove while continuing to pay for their old fuel.


Home heating fuel is currently between $3 and $4 a gallon, which means within a few years, as the price rises, Vermonters will be faced with moving south or choosing between heat or food. The state can sustainably provide something like 3 cords (1 cord == 128 cubic feet) of wood a year per household which means woodstoves or wood furnaces are not a viable alternative for the whole state (our house is primarily wood heated, and we burn 6-8 cords a winter). Places like rutland that have higher concentrations of wood heating also have really bad air quality, because a traditional "high efficiency" woodstove burns at about 40% efficiency. Switchgrass and other prairie grasses on the other hand can sustainably fuel the whole state without sacrificing food production by growing on the currently 100,000 underutilized acres of crop land. Pellet stoves burn at 80-85% efficiency, which is nearly comparable to oil/gas based stoves, AND the pellet fuel is 22% the cost per equivalent BTU of oil/gas.

[TheStorm]

[elfprince13]

[elfprince13]

so, update for you guys who were interested.

I finally said screw it, and wrote a program to do the analysis, and then messed around with the rate of change by hand to find one that was as cheap + short as i could get it simultaneously.


on the political side of things, events are moving quickly, all sorts of crazy meetings at strange times cropping up. Thank God VT is a small state!