2008年美国中学生数学建模试题 HiMCM

AromaRhyme

2008 Problems
High School Mathematical Contest in Modeling (HiMCM)
Problem A: National Debt and National Crisis
Mathematical modeling involves two equally important steps – building models based on
real world situations and interpreting predictions made by those models back in the real
world. This problem places equal emphasis on both steps.
We are at the start of the 2008 U.S. presidential elections, and one important area of
debate is sure to be the national debt. As high school students, you have a particular
interest in this subject since you are the people who will pay off or at least manage the
national debt in the future. The rate at which the national debt changes depends on the
difference between federal income (primarily taxes) and federal expenditures. Your first
task is to build a model that can be used to help understand the national debt and make
forecasts based on different assumptions. As usual, modeling involves a balance between
so much complexity that the model may be intractable and so little complexity that it is
unrealistic and useless. Your model needs, at the very least, to allow you to consider
different tax policies and different expenditure policies.
As usual, raw numbers don't carry much information. Those numbers must be placed in
context. For example, total national debt is less meaningful than national debt per capita.
In addition, you must be careful about inflation. Many analysts look at the ratio between
national debt and gross domestic product as a good indicator of the impact of the national
debt. Others worry about the cost of servicing the national debt. This cost is affected by
both the size of the national debt and the interest rate the government must pay to borrow
money. You may want to look at the Wikipedia article
http://en.wikipedia.org/wiki/Nat ... _presidential_terms
for some figures involving the ratio between national debt and gross domestic product.
TASKS:
1. Build a model that can be used to help understand the national debt and make
forecasts based on different assumptions. You must provide justification for the
various elements of your model and you must also test the sensitivity of your
model to various parameters.
2. Use your model to compare at least two alternative plans for the years
2009─2017. Your plans should be based on different tax and spending policies
that are reasonable and politically feasible. Use your model to compare the impact
on the national debt and then impact on the nation in general of your policies.
3. Prepare a letter to the new president advising him of your model.

AromaRhyme

Problem B: Going Green.
The United States can address its national carbon footprint in two ways: by reducing
carbon dioxide emissions or by increasing carbon dioxide consumption (sequestration).
Assume that the total U.S. carbon dioxide emissions are capped at 2007─2008 levels
indefinitely. What should the U.S. do to increase carbon dioxide consumption to achieve
national carbon neutrality with minimal economic and cultural impact? Is it even
possible to achieve neutrality? Model your solution to show feasibility, effectiveness,
and costs. Prepare a short summary paper for the U.S. Congress to persuade them to
adopt your plan.

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