Integrated Assessment Models of Economics of Climate Change. Economics 331b Spring 2009. Slightly Simplified Equations of DICE-2007 Model: Revised. Note: For complete listing, see Question of Balance, pp. 205-209. How do we solve IA models numerically?.
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Note: For complete listing, see Question of Balance, pp. 205-209.
We take discrete version of model, simplified as follows.
We solve using various mathematical optimization techniques.
Start with an initial feasible solution, which is equal reductions in all periods.
Then maximize PV output
Subject to the constraint that:
the sum of emissions
< target sum of emissions
Note that the emissions controls are generally “backloaded” because of the positive discounting (productivity of capital) and because damages are in future.
Remember that in a constrained optimization (Lagrangean), the multipliers have the interpretation of d[Objective Function]/dX.
So, in this problem, interpretation is MC of emissions reduction.
Optimization programs (particularly LP) will generate the shadow prices of carbon emissions in the optimal path.
For example, in the problem we just did, we have the following shadow prices:
With a little work, you can show that the rate of growth of prices = interest rate for this case.
Major applications of IA Models:
For these, I will illustrate using the DICE-2007 model:
2. Optimal policy. Emissions and carbon prices set for economic optimum.
3. Climatic constraints with CO2 concentration constraints. Concentrations limited to 550 ppm
4. Climatic constraints with temperature constraints. Temperature limited to 2½ °C
5. Kyoto Protocol. Kyoto Protocol without the U.S.
6. Strengthened Kyoto Protocol. Roughly, the Obama/EU policy proposals.
7. Geoengineering. Implements a geoengineering option that offsets radiative forcing at low cost.
Illustrative Policies for DICE-2007
Two major policy variables are
- emissions control rate
- carbon tax
We want to examine the economic efficiency of each of the scenarios.
- PV of abatement, damages, and total
- PV as percent of PV of total consumption
- Consumption annuity equivalent:
Increase, price of energy, US
Kyoto: global average
30.7%What do carbon prices mean in practice?
The impact of efficient/climate target carbon taxes is relatively modest:
Why is the debate so strident? Why are some people so opposed?