Another in our WWWTF (What in the World Will I ever use This For?) series:
Math Concept: Integration
Having spent multiple hours over the past week helping official oldest daughter of Env-Econ (OODEE) work through calculus problem after calculus problem in preparation for the pending AP exam, I thought it might be helpful to see how she might eventually move past solving math problems to applying the concepts. Right now I'm going to focus on integration, and hopefully later I will come back and talk about differentiation (seems backwards, but integration is fresh in my mind right now). In what follows, I assume a working knowledge of basic integral calculus--otherwise why would you care what you use this for?
As a reminder, a definite integral is defined as:
where f'(x) is the derivative of the function f(x) with respect to the variable x.
Graphically, the integral represents the area under the function y=f'(x) over the closed domain [a,b].
An example might help. Consider the simple linear function f'(x)=6-2X. What is the definite integral of f'(x) over the closed domain [1,3]?
What does this look like graphically?
Notice that for this case of a linear function (a line), the area under the function makes a triangle. A simple way to check your integration is to just find the area of the triangle on the graph.
The area of the triangle is .5(Base x Height) = .5(2 x 4) = 4. This is the same result we got for the intergral. For more complicated functions (non-linear), the area under the function isn't a nice neat geometric shape.
I know what you're thinking: Nice pictures and it's great fun to think about math, but WWWTF? (What in the World Will I ever use This For?). Keep reading for an application to environmental economics.
By: Tobias Börger, Nicola J. Beaumont, Linwood Pendleton, Kevin J. Boyle, Philip Cooper, Stephen Fletcher, Tim Haab, Michael Hanemann, Tara L. Hooper, S. Salman Hussain, Rosimeiry Portela, Mavra Stithou, Joanna Stockill, Tim Taylor, Melanie C. Austen
In: Marine Policy, Volume 46, May 2014, Pages 161-170.
Abstract: This paper scrutinises the use of ecosystem service valuation for marine planning. Lessons are drawn from the development and use of environmental valuation and cost-benefit analysis for policy-making in the US and the UK. Current approaches to marine planning in both countries are presented and the role that ecosystem service valuation could play in this context is outlined. This includes highlighting the steps in the marine planning process where valuation can inform marine planning and policy-making as well as a discussion of methodological challenges to ecosystem service valuation techniques in the context of marine planning. Recommendations to overcome existing barriers are offered based on the synergies and the thinking in the two countries regarding the application of ecosystem service valuation to marine planning.
So I was reading this CNN story this morning about the recent increase in bottlenose dolphin deaths on the east coast.
The carcasses of dozens
of the marine mammals, seven times more than normal, have been washing
up on beaches this summer, and scientists are struggling for answers to
In Virginia alone, at
least 164 dead dolphins have been found this year, said Joan M. Barns,
public relations manager for the Virginia Aquarium in Virginia Beach.
Almost half of those, 78, have washed ashore in August, she said.
As of Tuesday, federal
authorities say, they have recorded 228 dolphin deaths this year from
New York to Virginia. In all of 2012, 111 deaths were recorded.
'Why,' you ask, 'would I bother reading about dolphins?' Well, I'm glad you asked. First, dolphins are cute. And B), I seem to have spent a significant portion of my adult life studying ways to use economics to inform decision makers on environmental and natural resource disasters. So, upon reading of an anomolous (that's odd) increase in dolphin deaths, I naturally wonder, what are the costs of dolphin deaths, and what are the benefits of preventing dolphin deaths?
So how do I find teh value of a dolphin. Naturally I turn to the only reliable source for finding such information...Google. So I Googled 'value of a dolhin.' No, reallym, that's what I Googled. because my typing skills suck. Fortunately, Google planned for my sucky typing skills and gave me results for 'value of a dolphin.'*
At its most basic, the process now consuming teams of BP and
government scientists and lawyers revolves around this: How much is a
dolphin worth, and how exactly did it die?
extraordinarily difficult to monetise environmental harm. What dollar
value do we place on a destroyed marsh or the loss of a spawning ground?
What is the price associated with killing birds and marine mammals?
Even if we were capable of meaningfully establishing a price for
ecological harm, there is so much that we do not know about the harm to
the Gulf of Mexico – and will not know for years – that it may never be
possible to come up with an accurate natural resource damage
assessment," said David Uhlmann, a law professor at the University of
Michigan and a former head of the justice department's environmental
Warning: Snark ahead. Well, gee, if only the lawyers could figure out a way to value environmental harm? Or a way to place a dollar value on dead birds or marine mammals. Maybe, just maybe, a bunch of people should get together and think about how lessons learned from how people place values on things like blenders and hamburgers can be translated into ways to place values on things like oil spills, or fish kills, or fish species, or natural hazard mitigation. And, maybe, with some pie-in-the-sky thinking, these new methods for valuing the impossible might develop to the point where someone could write a book explaining the methods with an obtuse title like "Valuing Environmental and Natural Resources."
Maybe. Oh, Maybe. Someday. One can hope.
*Have I ever mentioned that I am convinced that Google is the greatest invention ever?
In a different context (Asian Carp), I have advocated for taking advantage of the Tragedy of the Commons to eliminate invasive species. The principle is simple: Given the proper incentives and open access, anglers/hunters/gatherers will overfish/overhunt/strip a common property resource into non-existence. Looks like the State of Florida may be figuring this out:
Nearly 800 people signed up for the month-long “Python Challenge” that started Saturday afternoon. The vast majority — 749 — are members of the general public who lack the permits usually required to harvest pythons on public lands.
“We feel like anybody can get out in the Everglades and figure out how to try and find these things,” said Nick Wiley, executive director of the Florida Fish and Wildlife Conservation Commission. “It’s very safe, getting out in the Everglades. People do it all the time.”
Twenty-eight python permit holders also joined the hunt at several locations in the Everglades. The state is offering cash prizes to whoever brings in the longest python and whoever bags the most pythons by the time the competition ends at midnight Feb. 10.
This is awesome. Using the power of incentives and the willingness to the many to take advantage of what would regularly be viewed as a market failure may in fact solve a different inefficient allocation of ecological resources. An odd case of the theory of second best?
I'm a simple man. And by simple I mean I seek the simplest solution to complex problems. At times that means I miss the nuance and detail that is really at the heart of many complex problems, but that doesn't stop me from offering simple analysis.
So here's my economist take on the national health insurance, health care mandate, Obamacare, socialism...whatever...debate....
It's all about the risk pooling.
Insurance markets work when non-systemic risks are pooled across a population. Let's use car insurance as an example. For the most part, the probability of me getting in an accident is independent of the probability of you getting in an accident unless you happen to be driving next to me at 75 mph while I eat a Whopper with one hand and check my Facebook status with the other. By pooling the independent risks, insurance companies can offer relatively low priced insurance against one or the other of us getting in an accident. So states require (mandate) that in order to drive, you must have insurance, thereby reducing the external costs of my bad habits on you. If you don't have insurance, you aren't supposed to drive and if you are caught driving without insurance you face stiff penalties. The result: Users of the product that causes the risk (driving) have insurance--most of the time. You can choose not to buy insurance and not drive.
So what about healthcare? Shouldn't it work the same way? In theory, yes. Users of health care could be required to buy insurance against catastrophic outcomes. By pooling the risks across large populations, the individual cost of health care will be lower than the expected cost to you if you bore the full risk of your own health. Risk pooling reduces costs and protects againsts catastrophic outcomes. And, just as with car insurance, if you choose not to buy health insurance, you lose the right to consume healthca...oh, wait.
Human decency has to be factored in.
In the absence of health insurance, individuals can still not be denied health care (at least emergency care, which is expensive). So what happens when an individual chooses to forego health insurance? The cost of the uninsured care, guaranteed by human decency, gets rolled into the premium of those already insured. In other words, health care costs rise. Further, if individuals know that health care will be provided regardless of the willingness or ability to pay or willingness or ability to be insured, there is a perverse incentive to underconsume health insurance and further reduce the size of the risk pool in the insurance market (we call that moral hazard).
So what are the possible solutions?
Rely on people to 'do the right thing.' But each person's definition of right might be different. While I think it is right to participate in the insurance market, others might think it is right to take advantage of the rules of the game. And as we know, economic incentives are powerful things.
Have the government act as the insurer of last resort. This is the model we currently have. The government offers subsidized insurance for those who are unable to afford health insurance (medicare/medicaid) and then acts as the insurer of last resort for the unisured. The result: the cost of providing insurance to the uninsured and underinsured are passed on to the insured through higher taxes and higher insurance premia.
Mandate that everyone buy health insurance and play by the same rules, and penalize those who opt out. The results 'should' be more efficiently priced insurance premia for those already insured, reduce costs of providing health care to those unable to afford insurance, and a less morally hazardous (I made that up) risk pool.
Sign #1,986 the economy might be on the upswing: We're hiring.
The Ohio State University-Assistant Professor: The Department of Agricultural, Environmental, and Development Economics (AEDE) is searching for a tenure-track assistant professor. The position is funded jointly with the university initiative in Climate, Water, and Carbon (CWC), and is one of several such positions in various departments. We seek outstanding applicants with high potential for achieving scholarly excellence in natural resource economics and modeling, with primary interests in regional and/or global water resource issues. Complementary interests in climate change, land use, and energy issues would be helpful. Expectations include teaching and research to serve AEDE’s mission, and collaboration with colleagues in the CWC initiative. Faculty members are expected to achieve national scholarly recognition, and to contribute to outreach and public engagement. The appointee will have an academic year (9 month) appointment with competitive salary and benefits package.
We had a departmental seminar yesterday by Professor Dan Sumner of the University of California at Davis and former Assistant Secretary for Economics at the U.S. Department of Agriculture. He spoke on Proposition #2 in California: the animal welfare proposition*. In particular, the passage of the proposition requires egg laying hens be housed in cages which allow them to stretch their wings for a majority of the day. In his discussion Professor Sumner raised an interesting behavioral anomaly (in a scratch-your-head kind of way). Before proposition #2, cage-free eggs were already available in supermarkets alongside traditional cage eggs. Yet, cage-free eggs accounted for only a tiny portion of total egg sales in California. Proposition #2 passed with roughly 63% of the vote, thereby banning cage-egg production in California. If Californians really cared about the welfare of hens, wouldn't they have bought cage-free eggs without the regulation?
Why would 63% of Californians vote to impose a restriction on themselves (and others) which they have failed to reveal when free to make the choice on their own?
*Here is Wikipedia's summary of Sumner's work on Prop 2: "In July 2008 the University of California, Davis conducted a study
through their University of California Agricultural Issues Center
(AIC). The study concluded that "the best evidence from a variety of
sources suggests that (non-organic) non-cage systems incur costs of
production that are at least 20 percent higher than the common cage
housing systems". This is due to higher feed costs, higher hen laying
mortality, higher direct housing costs, and higher labor costs. The
study also estimated that almost the entire California egg industry
would relocate to other states during the 5-year adjustment period. The
study does not analyze implications for animal welfare. By
demonstrating that most egg producers would leave the state, the report
estimates that the initiative would not affect how eggs are produced,
only where eggs are produced."
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