Environmental Decisionmaking

Nordhaus Glossary

Aggregate model (p. 5) One that includes everything.

Analytical solutions (p. 11) Solutions that can be found using algebra and calculus, rather than having to model with a computer. Economists love analytical solutions because you can make broad statements about economic systems with them. The drawback is that you usually have to make strong assumptions in order to get analytical solutions, and that weakens your model considerably.

Auctionable quotas (p. 3) A system where the government issues a limited nunmber of pollution credits, and companies must purchase these at an auction if they wish to emit pollutants

Command-and-control (p. 41) A type of regulation where the government spells out the requirements that companies comply with. Often this takes the form of requiring "best available technology" or something along these lines. Command-and-control has been out of fashion since the success of market-based mechanisms in the early 90s. Market-based mechanisms tell companies how much they can emit, but do not tell them how to get there. This allows for people to make efficient decisions about implementation. Still, command-and-control remains common because it is often difficult to measure emissions. For example, all cars are required to install catalytic converters, even if a company could demonstrate that their cars are clean enough not to need them.

Constant-returns-to-scale (p. 9) If the scale is doubled, returns are doubled. For example, if my labor production function displays constant returns to scale, then if I have twice as much labor I can produce twice as many widgets.

Consumption deflator (footnote, p. 8) A factor used to relate consumption values over time (related to changes in quality of life and inflation).

Derivative (footnote, p. 11) A calculus term meaning the change in something given a teensy-tiny change in something else.

Difference equations (p. 5) An equation where the value of a variable at time t is a function of that variable and others at time t-1. For example, our rabbit/fox models were difference equations because they looked at population in a given time period as a function of population in the time period before (after we have included births and deaths). In fact, Nordhaus is wrong here, because the Meadows model is a system of nonlinear differential equations, which avoid some of the fluctuation that we found inherent in our difference equations. It is an important distinction, but not particularly informative here.

Diminishing returns (p. 9) As you get more of something, the benefits per unit decrease. Most economic functions assume diminishing returns.

Disamenities (p. 9) Bad things.

Elasticities (p. 9) The change in something given a change in something else. For example, the elasticity of output with respect to input is how much more output you get if you add a little more input. These are written in terms of fractions, rather than absolute values, so if the elasticity of output to input is 2, that means that if I increase input by 10%, I will increase output by 20%

Empirical (p. 16) Based on experience or observation. An empirical debate is one that can be answered with data

Endogenous (p. 5) Part of the model. In our lake model, the outflow was endogenous, because it was a function of how much water was in the lake. Therefore, it is something that we model. see exogenous

Exogenous (p. 5) Not part of the model. An exogenous variable or value is one that, as far as the modeler is concerned is "given from on high." In our lake problem, the inflow was exogenous because we just said "assume 500 gallons is flowing into the lake." Many of you wanted to include rationales for how much water would flow in, but then how could we define exogenous? see endogenous

Factors (p. 9) In economics, factors are things like labor, capital, land, and other things which go into the production of goods.

Functions If I write Y = G(X,P), that means "Y is equal to G, which is a function of X and P." Economists can do a lot just knowing what the variables are in a function, because they make certain restrictive assumptions about about them. If I write F(L, R, T, K; H), that means "F is a function of L, R, T, and K, given the level of H."

Hicks-neutral (p. 10) A change affects labor and capital in the same way. In this case he means that technological changes can be used to increase the efficiency of both labor and capital, without benefitting one primarily.

Imaginary roots to the characteristic equation (footnote, p. 12) If you use matrix algebra to analyze complex sets of difference equations, you can figure out what is going to happen at any time by figuring out the "characteristic equation" and playing with that rather than with Excel. The characteristic equation more complex than we want to get into, but it turns out that if you find the eigenvalues of this equation it can tell you a lot about the stability of the system (will it go directly to a steady state, will it blow up to huge (or tiny) numbers, will it show oscillations, etc.). An "imaginary number" is a quite reasonable thing to get in this case--it is just that some numbers are multiplied by the square root of negative one, and that is OK. If this happens, it means that your system will oscillate (show overshoot and collapse, perhaps indefinitely). I will not get into how you actually work with eigenvalues or find them, although it is a fascinating topic.

Lag (p. 18) A lag just means that something in time t is a function of stuff in time t-1. For example, in the case in the text where Nordhaus discusses lagged labor inputs, he is saying that production today is a function of labor inputs last year and the year before.

Marginal products (p. 9) The return from the last unit. For example, if I have one person working to restore a prairie, then the marginal product from adding another will be large. However, if I already have 15,000 people working on the same prairie, then adding another will not bring much benefit. The marginal product in the second example is small.

Market failure (p. 4) A market failure occurs when something interferes with a market. For example, externalities are a type of market failure because the costs are not fully included in the market, and so the market does not work as expected. To a true Chicago-school economist, a market failure is the only thing that can keep the invisible hand from optimizing social welfare.

Monotonic (p. 47) Moves in only one direction.

Negentropy (p. 32) A term used to refer to the opposite of entropy. Entropy is a measure of the disorder of a system, and so negentropy would be the order. As you do stuff, the Second Law of Thermodynamics requires that entropy increases. There is a fixed amount of energy in the universe, and as it is turned into heat it is no longer available to do work. So, we can assume that negentropy + entropy = constant. In that case, negentropy is the thing that decreases as entropy increases.

Nonlinear (p. 5) Not linear. For example, our rabbit/fox models were nonlinear in that they involved feedbacks which sometimes made populations grow slowly, sometimes quickly, and sometimes the direction changed dramatically.

OECD Countries (p. 8) The OECD is the "Organization of Economic Cooperation and Development." It includes the US, Canada, Japan, Europe, Australia and New Zealand. Essentially, when you see OECD, just think "rich".

Parameters (p. 5) values of constants in a model. For example, birth rates and death rates are parameters. Models are essentially a bunch of variables and parameters set up in equations. Variables generally change, parameters generally don't.

Production function (p. 5) The equation that determines how much of a good is produced. A "time-invariant agricultural production function" is an equation that does not change in time and that shows how much food we can grow on a given amount of land. Here, Nordhaus is dissing Meadows et al., because they acknowledge that agricultural production changed in time without allowing it to change in their model

Purchasing-power-parity (p. 8) As anyone who has spent time in a developing country knows, life is cheaper there. Some things cost the same (consumer electronics, for example), but things like basic foods and so on are much cheaper. Hence, it isn't really fair to compare the income of an average American with that of an average Sudanese, because they can get a lot more food and shelter for $100 than we can. Economists take this into account by using PPP, where instead of comparing incomes, they compare how much of a standardized bundle of goods people can buy with their income. Poor countries still have lower per capita incomes than rich countries, but it is not as much lower as it is if we just compare per capita GDP. A cynic would think that Nordhaus chose PPP because it makes his argument seem stronger.

Shadow prices (p. 29) Shadow prices are the amount that an objective would improve if you increased a constraint by one unit. That's not a good definition, but, you know, I never really understood shadow prices. You don't need to either; just think of it as a price.

Superabundant (p. 29) Nordhaus uses superabundant to mean infinitely available at a given price. Notice, this does not mean that the goods are free, just that you can get as much as you like for a given price. This is in contrast to the normal situation where you might expect price to rise as you try to get a lot more of something.

Time-invariant (p. 5) Doesn't change in time.

Unity (p. 10) "Unity" is just a way for researchers to say "1" and sound fancy.