This post is a follow on to my earlier post discussing what happens if we were to believe the uncertainty in the climate sensitivity rose relative to our current understanding while our best estimate of the expected value in temperature rise ($latex E[T] $) remained constant. For now, the focus will simply be numbers. For the purpose of this blog post, I make the same assumptions discussed in my previous post and assume the damage function (i.e. present value of costs ) for climate change is a function of the temperature rise due to doubling of CO2 and that it the costs in quatloos are a quadratic function of temperature with zero cost at no rise. That is $latex C(T) < T^{2} $ . This is the choice Lewandowsky made in his post on implications of uncertainty which touchted on costs. Some results I will discuss depend on the choice of damage function; others do not.
Some discussion of the economic model
I have selected the damage function of the form $latex C(T) < T^{2} $ where C is the present value of costs arising from damages from climate change denominated in Quatloos and T is the temperature rise under doubled CO2. I selected this form because it is the choice Lewandowsky made. This is a somewhat cartoonish choice is suitable for the current discussion which, despite containing numerical values, is qualitative.
Even though this is a cartoon model, I think it's important to understand the features the cartoonish economic model is intended capture. One of these features is the effect of "temporal discounting". In Lewandowsky's post that touched on costs, there was quite a bit of huffing and puffing (some of it nonsense) about economists temporally discounting costs. For example:
This is an important point to bear in mind because if the greater damage were delayed, rather than accelerated, economists could claim that its absolute value should be temporally discounted (as all economic quantities typically are; see Anthoff et al., 2009). But if greater damage arrives sooner, then any discounting would only further exacerbate the basic message of the above figure: Greater uncertainty means greater real cost.
Economists do temporally discount costs. (In fact, most engineers take engineering economics to help guide rational choices about mundane things like spending money on improvement to physical plant.) One reason costs are temporally discounted is simple and is touched on in 8th grade home economics. Here’s an example on might discuss in 8th grade:
Suppose you have the opportunity to buy a refrigerator now. It costs $700. You have $700. You currently don’t need and can’t use this refrigerator but anticipate you will need a refrigerator a year from now when you move from your dorm to an apartment. You also know you can lend your money safely to an enterprising friend who will pay you back $770 a year from now and you are 100% certain they will pay you back. You are also 100% certain the refrigerator will cost $720 a year from now. Given this fact pattern, should you buy the refrigerator now or wait a year?
Written this way, everyone knows they should defer buying the refrigerator and lend the money to their enterprising friend. The $70 you make by not spending your money and putting it to work means you will easily cover the $20 cost increase in the price of the refrigerator. The “discount rate” is the formal method of accounting for the fact that available money can generally be used to do something that creates value. In economics, these valuable things are denominated in money; in this example, the extra value is $70.
Because this post is largely motivated by Lewandowsky’s discussion, it’s worth nothing that if we are going to do the sort of cartoon analysis he did and which I largely imitate here, the damage function (i.e. estimate of the present value of costs based on the change in climate sensitivity) has already been assumed to include the temporal element. That is the discount rate has already been applied.
This must be so because mathematically speaking the damage function we chose for this exercise is only a function of climate sensitivity and so must be understood depend only on the climate sensitivity. (More complicated models can be created from more detailed damage functions by using cost models that account for time, finding more complicated probability distribution functions for scenarios of temperature. From these one might develop the simpler more cartoonish model shown here.)
The consequence of the fact that the cost function used here already accounts for the time evolution means that one ought not to suggest the the cost climate change should be further inflated to account for the fact that they may arise sooner rather than later because that effect is already accounted for in the cost model. When any such suggestion follows an analysis using a cost model of this sort, it can be taken as evidence the person making the suggestion may not understand the math underlying their cartoon analysis. Alternatively, they have forgotten the implications of their earlier assumptions.
Results of effects of uncertainty on estimated costs of climate change
Now, based on the cost model described above, I’m going to present some simple graphics showing what happens to our estimate of the probable costs of climate change if we use the sort of cost model used by Lewandowsky. The analysis is simple: To compute the probablity density function for costs I inverted my cost function to obtain the temperature rise as a function of cost, inserted that into the pdf for temperature (shown in the previous post) and used the change rule to change dCost = dT (∂C/∂T). I coded that up, and did higher mathematics also called “summing things up” (i.e. integrated.)
The results in graphical form are below. On the left, I show the cumulative probability distribution of costs computed in the ‘base case’ (i.e. lower variance.) To the right I show the values computed assuming that the best estimates of temperature is fixed but the standard deviation increases. I did this by increasing the standard deviation of our uncertainty in feedback parameter from Roe and Baker (2007).
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Examining the figure we can see some features that are independent of the cost model; others are dependent on the cost model.
The feature that is independent (or nearly independent of) the choice of economic model.
- Increases uncertainty in our ability to predict the cost. That is: the range of costs we consider possible increases. This is tautological.
Other features we predict that depend our choice of economic model. (It is worth nothing some depend on the shape of the probability distribution for the uncertainty in our ability to predict the feedback parameter.) If the expected value of the rise in temperature was correctly reflected in our first analysis, but the standard deviation our “true” uncertainty in feedback parameter is twice than value we used to compute costs:
- In both the base case and the higher uncertainty case, the expected value of the cost is greater than the cost computed based on the expected value of the temperature. That is $latex < E( C[T]) $. This will always occur when the present value of the costs are assumed to be a quadratic function of the temperature, but might not occur for other economic models. It's worth nothing that this observation doesn't need we need to "worry more". It merely means that when estimating costs, one uses $latex E( C[T]) $ not $latex C(E[T]) $. The principle that one uses $latex E( C[T]) $ is well established in economics would hold even if the inequality reversed. For this reason, reports generally mention $latex E( C[T]) $.
- In the base case, the expected cost of unmitigated climate change ( $latex E( C[T]) $ ) is 13.9 Quatloos. What this means is that under the base case, if we had only two choices: a) do nothing or b) undertake a perfect method to prevent temperature from rising at all, we should undertake that method provided the present value of its cost is less than 13.9 Quatloos. Otherwise, if we believe our cost model properly accounts for the costs at all levels of climate sensitivity and our statistical model describing the uncertainty in climate sensitivity is correct, we should select “do nothing”. That’s how economic models are used.
- In the base case, the probability that costs would fall below 13.9 Q is 62.7%. That means that if we do spend 13.9 Quatloos to avoid climate change, there is a 37.3% chance we will have spent more Quatloos than we ought to have. How much we would have wasted will depend on the actual temperature rise– which we know we cannot predict. (Note: if we spend the 13.9 Quatloos and the method works, we may never know the actual costs that would have occurred if we did not spend the Quatloos.)
In contrast, there is a 37.3% changes damages will exceed 13.9 Q if we do nothing. The damages may possibly exceed 13.9 Q by a large amount. That means that it is possible that damages could be some amount– say 35 Quatloos. If we are presented with a prefect mitigation strategy whose cost has a present value of 14 Q, and we pass that up because it costs more than 13.9 Q, we will end up being out of pocket 35 Quatloos when we could have gotten away with spending only 13.9 Quatloos.
Note however, that the skewed distribution means that if we use expected value of costs to decide whether to undertake a mitigation project we are more likely to spend too much rather than spend too little The flip side is that in cases where we spend too little, our costs might be very large. It is generally accepted that using the expected value balances these two issues properly.
- The estimate for expected value of costs ( $latex E( C[T]) $ ) computed using by doubling our estimate of the uncertainty in the standard deviation of the climate feed back is is 17% higher than anticipated using the base case. That means that means that if we estimate using the higher level of uncertainty, we should chose mitigation strategies even if they cost a 17% more than under the base case.
- Even though the the expected value of the cost of climate change increased to 16.3 Quatloos when we considered the possibility that the uncertainty in our estimate of feedback parameter, the probability that the cost will exceed 13.9 Q we fall below the value we estimated in the basecase is 64%. That is: We are still more likely to spend a little too much. That said: the item we should focus on ins the expected value of the cost: 16.3 Quatloos.
- For those who like to consider the extreme outcomes: Whereas in the base case, we anticipate there is a 90% chance the costs will fall between 3.7 Quatloos and 33.23 Quatloos, we now think the 90% range is 1.6 Quatloos to 53.6 Quatloos. Expressed in Quatloos, the width of the interval encompassing 90% of the likely outcomes increased by 76%.
- Comparing the cost estimate under higher uncertainty to that under base case (i.e. lower uncertainty), likelihood that costs will be lower than anticipated lower bound based on the base case increases from 5% to 19.8%. The likelihood that costs will be higher than the anticipated upper bound computed in the base case increases from 5% to 12.1%. So, the likelihood that costs will fall below the level we anticipated under the base case rises more rapidly than the likelihood costs will rise above the level we anticipated.
It seems to me those are the major observations one can make about how uncertainty affects costs under my assumptions about the probability distribution function for our feedback parameter using the simple cost function and using feedback parameter values from one of the cases described in Roe and Baker. Of course as with all results involving statistical models, assumptions made prior to doing any math matter. Numerical values would differ if we chose a different cost function a different probability distribution function and so on. It’s perfectly legitimate to suggest the cartoon cost function is not correct (it’s not) or that one might pick a different probability distribution function for feedback. I certainly invite debate on those issues– my goal is to show a cartoon or ‘toy’ analysis that is food for thought.
So, what should we do?
A bit later on, I’ll write a post discussing how we would use the results of analysis of this sort (whether cartoon or real) to make decisions about mitigation strategies. Much of that will be plain old discussion with no graphs or math but I’ll try to avoid rambling about how much we should “worry” or whether or not uncertainty is our “friend”. Naturally, if the analysis involves making decisions based on cost, then the discussion will involve making decisions based on costs. As we can see above, uncertainty affects those costs— generally speaking greater uncertainty increases the expected values of costs of everything. This includes both the cost of the impacts of climate change and the cost of mitigation strategies.
But who wants to go without a fridge for a year. ;P
BTW, I have never lost a Quataloo.
MrE
When I was a student, I didn’t have a refrigerator in my dorm room. That’s why I wrote the scenario this way
Of course, if we were looking at a wider range of choices, someone might do an analysis and conclude that it does make sense to spend $50 on the mini fridge advertized here:
http://chicago.craigslist.org/nwi/app/3263683086.html
In that case, one would need to consider the cost /benefit of snacks under the fridge/no fridge scenarios. But it’s unlikely a student living in a dorm and having a meal plan will want to store a $700 fridge in their dorm room as it has little incremental value over the $50 minimfridge. Plus the big fridge takes up space .
Lets say you have a 1GW coal power plant with a lifetime of 40 years remaining. And lets say you want to switch to wind power to replace that coal plant.
You could immediately purchase 5GW of wind turbines for 5 billion dollars. And lose all the money you invested in the coal plant.
20 years from now you could buy another 5GW of wind turbines (because they only last 20 years) for hopefully less (in real dollars) than you paid 20 years ago.
And 40 years from now you could buy another 5GW of wind turbines (because they only last 20 years) for hopefully less (in real dollars) than you paid 40 years ago.
And don’t forget you have to set aside money to decommission all those dead wind turbines.
And don’t forget you have to lie about how much the wind turbines will really cost or you will be fired (I wish).
Or … you could invest a much smaller amount in R & D every year with the hope that new technology would come along that would be much cheaper and even it doesn’t come along you could replace the coal plant when it finally needs replacing saving huge sums of money.
Bruce
Worse, you might have to spend money to demolish the coal plant or suffer carrying costs of keeping it. Are you putting the turbines on the former site of the coal plant? Ok. Otherwise, you pay someone to help you sell the coal plant and spend money finding a good site for the turbines.
If these are all collective costs and benefits, it might be worth while for society to come up with a method to help you cover the costs of this so others benefit. But there is no denying that switching energy sources has some cost. If the decision is going to be made on a cost basis, then someone has to account for the cost of mitigation (which might involve your switching from coal to wind). The cost estimate has to be done fairly. In this calculation, it’s likely someone doing a similar analysis where they compare costs and benefits under increasing uncertainty would likely find uncertainty in issues surrounding wind energy is “not our friend”.
And once again, the likely cost and expected benefit of R&D has to be done fairly. Here again, uncertainty is likely not “not our friend”.
Bruce–
Also, one could also consider delaying action while investing in R&D in things like carbon capture and storage. Of course, you’d find that uncertainty in climate and uncertainty in R&D would be “not our friend” because uncertainty almost never is our friend.
But the fact is, merely showing 1 path has costs associated with it cannot tell us what to do. We need to examine other choices and weigh the relative costs (or benefits.)
I think we do anticipate that climate change had a net positive cost. The question is: Given what we know about climate, CO2, technology, payoffs for R&D, alternate energy etc. what choices result in the lowest expected cost (or highest expected benefit)? To learn that, we need to do some quite detailed economic analyses. (Lewandowsky certainly did not do these in his screeds.)
Good post. Simple maths for imbeciles like me.
perhaps I did not read this carefully enough, but how do you account for the state of technology? We all know that to travel 100 iles today costs much less nthan it did for someone 100 years ago. Unless you have a good reason to say that technological costs will not continue to decrease – along the lines of Moores “Law” – then a lot of this reasoning just gets too Tobis for my liking. And I cannot see how that assumnption feeds into your curves – prob because I am innumerate. If so, just say.
Lucia,
I would be interested in sea level rise that the good doctor has done.
It was a three part post with the last part avoiding all, or most of, the very nasty economic assumptions, if I recall correctly.
I am currently doing a little work for the USACE on a probabilistic approach to sea level rise.
The good doctor makes reference to Hunter(2012) who is at CSIRO in his all too brief discussion.
In particular this has to do with the boots on the ground that the USACE has to deal with, that being always cash strapped and only doing what is necessary after the proverbial sheet hits the fan (e. g. New Orleans both before and after Katrina).
diogenes, I think that is included in the “discounted costs.”
just checking, Carrick – because mainstream scientists such as Halpern,Tobis and co seem to think that technology has run its course. And it is a key assumption…and one that is very badly handled in mainstream economic literature because it is so difficult to capture empircially. The world 50 years ago is vastly different from the world today.
Carrick – could you have conducted your research 50 years ago? No GPS…no computing power…..
Do you mean the cost of the temperature rise curve? I don’t create that. I assume someone else created it. 🙂
But I think the decrease in costs of technology is captured by the discount rate. Consider the refrigerator example. The reason your friend will be able to pay you $770 later on may very well be that he is working on improved refrigerator technology and so in future, refrigerators will be better and cheaper. He will sell his new better refrigerators, make money and pay off his debts.
This is maybe a little to cute, but he might be starting bakery, he’ll sell cupcakes and coffee to the guy improving the refrigerators, who sustained by the excess sugar and caffeine develops better refrigerators, sells them and so on. Money permits people to buy and sell refrigerators coffee and cupcakes. The discount rate helps us account for the fact that some uses of money result in outcomes more people value sufficiently to pay for and in many cases the productive desirable uses happen to be improvements in technology.
(Zeke will probably laugh at my engineers explanation of the discount rate. I’m sure there is a much better way to explain it.)
My impression was the posts became more and more incoherent as I read from 1-3. Are you asking me to comment on http://www.shapingtomorrowsworld.org/lewandowskyUncertainty_Floods.html?
I’m reading Hunter. I take it you are interested in planning with long term horizons? Or zoning? Because, after all, with respect to construction project it is at least sometimes possible to take an incrementalist approach, spend 50 Quatloos this year making it sufficient to deal with the uncertainty level of sea rise between now and 2030 and then reassess the likely sea level rise when 2030 arrives. Or, you can try to build something now that you believe will give people the protection they need in 2100. If you do the latter, you will need to build something higher.
Anyway, if you can clarify the problem you are worrying about, I may be able to do a cartoon analysis for you. It will be worth what you pay though: Blog quality.
diogenes:
Don’t forget no solar power. It would of course been absolutely impossible.
They use technology curves derived from empirical data to try and account for it. Wiki has an article on it.
However, these curves assume that technology varies in a continuous manner. There’s been speculation that we are arriving at a technology singularity (actually “kink” is probably a better term for it… a place where the derivative is discontinuous so that any data taken prior to it is essentially meaningless).
It is no doubt a very hard problem to do “right”, and it is 100% probable we will underestimate the amount of discounting needed to take into account technology advancement.
That said, this falls exactly into what Lucia has said which is basically that we will end up spending more based on the best information available at the time than post hoc analysis would tell us we need to. I smell some game theory in there somewhere.
Lucia,
Just a couple of comments on discounting.
There should be a distinction drawn between discounting for inflation and discounting for risk (or opportunity), although very often the distinction is blurred in project economics.
If I have a time series of future costs anticipated for a given scenario and expressed in “money-of-the-day” $US (sometimes called “nominal money”), and I also have an expectation that $US inflation will continue year-on-year at, say, 3% p.a. over the period of interest, then I might discount those future nominal costs back to present-day value-of-money at a discount rate of 3% to account for the fact that the inflated dollars in the future are worth less than today. I would then describe the resulting discounted costs as “REAL COSTS” as opposed to “money-of-the-day” or “nominal” costs.
However, suppose that the same cost time series is actually an estimate of the future costs of a large investment project, which also has an expected revenue stream associated with it. At a minimum we need the real revenue stream to exceed the real costs – obviously.
However, this alone is still not enough to convince me to go ahead with the project because I will have to finance the project at 7% interest, say, on the borrowings. This suggests a new hurdle-rate based on COST-OF-MONEY; I need a minimum real rate-of-return (ROR) of 4% in order to break even. Additionally, I have a number of competing projects all of which (a) appear to be very safe investments and (b) each of which offers me a 12% nominal ROR (or a 9% real ROR). Scarce resources (money and people) mean that to do the current project I would have to forego the opportunity to do the competing projects. Hence, I might re-establish my hurdle rate at 12% nominal ROR based on OPPORTUNITY COST. Finally, I note that this hypothetical project carries a far higher irreducible risk of failure than my competing projects, because it is based on untested technology. Engineering assessments suggest that there is a 30% chance of losing money (i.e. the project will produce a negative Net-Present- Value (NPV)) at a 12% nominal discount rate, but the Expected Present Value (the probability weighted NPV at 12% discount) is positive. Based on the risk profile, I might decide not to pursue the project at all, or I might decide that the unrisked project must produce at least a 20% nominal ROR to make it worthwhile considering against competing options. (This is equivalent to saying that the nominal cost and revenue streams, when discounted at 20% will still produce a positive value.)
Macro-economics do not work quite the same way as corporate economics or project economics. However, many of the concepts outlined above are applicable to the issue of AGW mitigation judged as an investment. My main point is that value-of-money is only one element. Every government also has a cost-of-money. Every government also has an opportunity cost. (In this instance, mitigation strategies are very likely to produce a negative revenue stream in the form of reduced GDP which forms part of foregone opportunity.) Finally there is the risk of “project failure†in the form of prognosis error – temperature gain being smaller than expected or damage being more limited than expected – or a failure of the mitigation strategy to have any tangible impact. Any of these outcomes could render the mitigation “investment†ineffective or needless. All of the above suggests to me that the application of a discount rate which is based solely on value-of-money (inflation adjustment) is naive.
None of the above challenges Lucia’s argument, but given how far out in time any expected benefits are, I suspect that the application of a more considered discount rate would convert the assumed damage function from being upwardly convex to being upwardly concave.
The “economic model” for cost is contrary to the current “best estimates” of damage functions.The best estimates typically have “negative damages” ie net benefits, for small temperature changes. The damage function used herein has positive damages for every change greater than zero.
“improved refrigerator technology and so in future, refrigerators will be better and cheaper”
Not sure about that. My fridge/freezer recently failed after 32 years of fault-free operation, and the replacement has required 3 engineer visits in 2 months!
Andrew_FL
Some economists tell us that.
If I change the function to (Cost= (T-T_opt)^2, I get qualitatively similar results. The numerical value of costs go down but the results under elevated uncertainty remain higher than lower uncertainty and so on. No matter what the shape of the pdf, this will always be true provided Cost is of the form (T-Topt)^n where n is even.
So: if you were trying to figure out if the estimate of 13.8 Quatloos was the correct choice for our estimate of the expected value of the cost, noting that my cost function has this flaw is important. But if you are trying to know whether the cost would be lower or higher under greater uncertainty, that particular flow “doesn’t matter”. Under greater uncertainty, the estimate of the expected value of the cost will rise.
(I keep wanting to make the mistake of just calling “the estimate of the expected value of the cost” the cost. It’s important to know it’s not. The cost is the thing we are trying to predict– but we know our predictions are uncertain. )
Paul_K
We covered both in engineering econ I. But I thought for the purpose of this post it wasn’t worth saying more. I didn’t take engineering econ II. In engineering econ I, someone asked how we figure out what the discount rate should be. The answer was that was covered later on. 🙂
Yes. That’s why I wrote “one” in:
There are lots of reasons costs are discounted. Because people do argue about the proper discount rate, I wanted to show that we can describe at least one reason for it rather easily. (Cost of money could have been added into the example by having the student faced with the question “I only have $700. Should I borrow money so I can buy the refrigerator and also lend my friend money?” And so on.)
To further this point about distinctions, I would think in the case of AGW where tort law were applicable and in an idealized case (see Murray Rothbard here http://mises.org/daily/2120 on Law, Property Rights and Air Pollution) if it could be shown that the effects of AGW were doing damage to my person and/or property or a group of which I am part, we could collect damages from those parties shown to be responsible or we even might obtain a cease and desist order or a way to mitigation.
This is to see the effects of AGW in a whole other light of the effect it might have on an individual or group of individuals and further of having to prove or show these effects are damaging or that future effects with near certainty will have damaging effects. Making economic calculations on these matters outside the damage to individuals seems to preclude individual property rights and is more in tune with a collectivist approach. Most of these calculations never take into consideration the very nature of a government project and all the history we have that shows weaknesses and failures associated with, amongst a host of items, the politicalization of it, the almost always occurring cost overruns and resistance to changing direction or admitting failure.
Kenneth Fritsch (Comment #103223)-I can see property rights as working as a “solution” if certain conditions are met, but I’m not sure they can be in this case:
The first condition applies to “tort” solutions in general: it is pretty much necessary that we have unbiased courts that are able to judge underlying scientific issues. If someone is dumping nuclear waste in my backyard, the issue is sufficiently clear cut that this is probably not absolutely necessary to either have a lack of bias or good judgement. But in this case it seem like it would be necessary, and also impossible.
The second condition is that one can take the commons and break it into private property. Um, obviously you can’t do that with the atmosphere…I suppose you could sue someone for the damage caused to your property and self by the effect someone had on the commons. But who do you sue, exactly? No single person or comporation or whatever is singularly responsible even in theory for any “damage” from climate change. Is it going to be like reverse class action? Every individual suing everyone else for their share of the damages? Including the individual themselves, since they are, however minisculely, partially responsible?
On the plus side, many such suits would probably get laughed out of court for being patently ridiculous. Oh wait…
thanks for the comments, Carrick and Lucia….but do you have reasonable grounds to think Moore’s “Law” is about to get busted?
sorry – I should add that my thoughts are conditioned by reading Tobis and Halpern et al…they seem to think that technological progress is at an end – my interpretation of their doomsday talk. I tend to believe that future generations will continue to innovate so, instinctively, I do not see a rising cost curve. And, because i do not apply a randomly-derived mathematical function to the curve I envisage, unlike Annan and co, I have zero understanding. Zap me.
diogenese–
The arguments for why the costs due to a 5C change are larger than a 3 C change have little to do with innovation. Assume innovation will happen. It will happen whether the temperature rises 5C; it will happen if temperature rise 3C.
Meanwhile if temperature rise 5C, we end up forced to innovate to continue to grow crops in some places that get too hot. We might have to abandon fields on place and plant in new places. The replacement might be just fine, but moving costs something. Some developed land previously above water might now be in a flood plain or under water. We have to build something. Even if we can innovate, building new stuff costs relate to being able to continue using what you were using before.
So, the cost of 5 C rise will be higher than the cost of a 3 C rise. (There are some arguments about an optimum. It might be that a 1C rise doesn’t cost more than no rise. But it’s pretty well accepted that the cost function will be rising as we go to larger changes.
But this has little to do with innovation. Where innovation comes into play is figuring out what discount range we should use, and deciding which strategies will let us adapt or mitigate at the lowest cost (or greatest benefit.)
The idealized solution would take a major change in the way we think about these issues and problems. I would agree that tort law as it is currently adjudicated is a captive of some trial lawyers merely looking for deep pockets and too many judges and jurors willing to go along. If we were to make a major change in our thinking I do not see the issues you raise as limiting, but obviously that change is not just over the horizon.
Laws should be used to protect individuals and their properties from others initiating force against them wherever that force may come. The more we lose sight of that proposition the more our politicians and governments will attempt mitigation for something like AGW by way of crony capitalism, special interest favoritism, phony measures of progress/success, inability to admit failure or change course and using the problem, real or manufactured, to further an unrelated political agenda.
Most economists and planners never factor these inherent weaknesses of government, as most are currently structured, into their plans and policies and that is why I personally see a high probability of mitigation for AGW making the situation worse.
“Assume innovation will happen. It will happen whether the temperature rises 5C; it will happen if temperature rise 3C.”
Lucia, I do not follow you here. Innovation, and a particular innovation, surely can be motivated by need.
“Meanwhile if temperature rise 5C, we end up forced to innovate to continue to grow crops in some places that get too hot. We might have to abandon fields on place and plant in new places. The replacement might be just fine, but moving costs something. Some developed land previously above water might now be in a flood plain or under water. We have to build something. Even if we can innovate, building new stuff costs relate to being able to continue using what you were using before.”
Obviously a lot depends on how fast we would get a 5 degree C rise in average temperature, but my observations on agriculture in the US is that under a gradual warming, heat and drought resistance can be breed (or through direct genetic manipulation) into crops. Is there a limit? I do not think we know. Also while a southerly located crop may suffer some yield decrease with a rapidly warming world that crop already grown in a more northerly location would be expected to have increased yields in general.
Changing crops on an individual farm is not all that difficult these days. Most machinery required is adaptable to various crops. Most crops currently suffer more from drought than temperatures although temperatures work both ways with much damage coming from late and early frost. What amazes me is the yields one can obtain from crops like corn in many different locations in the US if you irrigate.