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.
Shame on you! This appears to be a situation where the marginal abatement costs are not equalized:
While details of the E.P.A.’s proposal remain confidential, experts predict that it will include separate standards for carbon dioxide emissions from plants fired by natural gas and by coal. Plants using comparatively clean gas would be permitted to emit perhaps 1,000 pounds of carbon dioxide per megawatt-hour, a ceiling within easy reach using modern technologies.
Coal-fired plants, meanwhile, may be allowed to emit as many as 1,400 pounds per megawatt-hour. But coal is so heavily laden with carbon that meeting even that higher limit would require operators to scrub carbon dioxide from their emissions before they reach the smokestack, and then pump it into permanent storage underground.
One of the more useful things about the field environmental economics is that it can help reduce the costs of achieving any environmental quality target. When there are multiple sources of pollution, costs are minimized when the last unit of abatement costs the same for each source. In other words, when the marginal abatement costs are equalized total costs are minimized. To see this imagine if the last unit of abatement for a new coal plant is higher, say $80, than for a new natural gas plant, which is $50. Costs would be reduced by $30 if the natural gas plant was required to reduce one more unit and the coal plant reduced one less unit. Environmental quality does not suffer and money is saved.
The article goes on to say that 1400 pounds per megawatt hour might not be technically feasible. This suggests that the marginal abatement cost for natural gas is lower than the marginal abatement cost for coal at these standards. Therefore, costs of achieving the policy goal would be lowered if the standard for natural gas plants is tightened (i.e., fewer pounds of CO2 per megawatt hour) and the standard for coal is loosened. Regulating by prices (e.g., carbon tax) or quantities (e.g., cap-and-trade) are two ways to achieve equalized marginal abatement costs without knowing what the marginal abatement cost curves look like.
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?
I'm risking biting a hand that partially feeds me with this post:
Bruised from the defeat of a massive farm bill last month, Republicans are giving the legislation another chance by bringing a pared-down version to the House floor.
GOP leaders were still counting how many votes they could muster for the new measure, which drops the politically sensitive food stamp portion of the bill, when they released the legislation late Wednesday. The White House swiftly issued a veto threat, and House Democrats reacted angrily to the last-minute move. A vote is expected Thursday.
The dropped section would have made a 3 percent cut to the $80 billion-a-year food stamp program. Many Republicans say that isn't enough since the program's cost has doubled in the last five years. Democrats have opposed any cuts.
The White House said food stamps should not be left out of the bill. The Obama administration had also threatened to veto the original bill, saying it did not include enough reductions to farm subsidies and the food stamp cuts were too severe.
Republicans are proposing a measure containing only farm programs, with a food stamp bill to come at a later date. Farm groups, anti-hunger groups and conservative groups have all opposed the idea, for different reasons.
I have often stated (in private of course) that food stamps and farm provisions of the farm bill should be separate pieces of legislation. The food stamp program is an equity program designed to redistribute income from those who have to those who don't. It has little to do with efficiency of markets. I'm not saying that's a bad thing, but it is difficult to design an effective program when it is paired with legislation that is supposedly aimed at improving market efficiency.
The farm provisions are a highly bastardized attempt to deal with market failures in agriculture. About the only farm provision left in the Farm Bill that is even partially defensible on efficiency grounds is subsidized crop insurance designed to help alleviate systemic regional risks (like drought). Private insurers have trouble staying afloat in the presence of systemic risk, and actuarily fair pricing would be prohibitively expensive for many farmers. Beyond that, many of the farm provisions in the farm bill bear little resemblance to efficiency improving market policies and we would all benefit from an examination of the provisions independent from food stamps. If that happens (and that's a big if) I'm not sure Republicans (or farmers) would like the outcome.
Now I will sit and wait for my boss' phone call...
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?
Republican presidential candidate Mitt Romney will lay out policies on Thursday aimed at achieving North American energy independence by 2020 by pursuing a sharp increase in production of oil and natural gas on federal lands and off the U.S. coast.
I know I'm dense, but can someone please explain to me why a market-favoring conservative would want complete North American energy independence? This is like saying I want food independence for my neighborhood. Sure, it reduces reliance on food from those other evil suburbs around Columbus, but it also makes my food more expensive, reduces my choices--where am I going to get my unsustainable seafood if I can't import from the Chesapeake Bay region--and makes me generally worse off.
Romney is to predict that a full-blown energy plan will create 3 million jobs in energy sectors and other areas, part of an ambitious effort to create 12 million jobs during a Romney presidency.
"I want every American who wants a good job to be able to have one," Romney told Republicans at a fund-raising event in Little Rock on Wednesday.
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.
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