1. Fossil fuel stock Fossil fuel extraction Production Utility Welfare Pollution flows Consumption Pollution stocks Clean-up or defensive expenditure Environmental pressure Capital stock Figure 16.1 The structure of the aggregate stock pollution model

2. The following slides show the steps building up to Figure 16.2, then Figure 16.2 itself.

3. time, t units of utility PtPt Net Price 

4. time, t units of utility PtPt Net Price  P t +  R Marginal extraction cost

5. time, t units of utility PtPt  P t +  R Utility flow damage P t +  R +U E E R

6. time, t units of utility PtPt  P t +  R Pollution flow damage P t +  R -U E E R P t +  R +U E E R -  Q E E R

7. time, t units of utility PtPt  P t +  R Stock damage P t +  R -U E E R P t +  R -U E E R -  Q E E R P t +  R -U E E R -  Q E E R - M R Figure 16.2 Optimal time paths for the variables of the pollution model.

8. time, t PtPt  Gross Price Stock damage tax Figure 16.3 Optimal ‘three part’ pollution taxes. Pollution flow damage tax Utility damage tax units of utility

9. utility units M MM*M* Optimal tax M*M* MC MC (Social) MB MB =  Q R MC (Private) QRQR Notes: MC = MC (social) = P +  R – U E E R -  Q E E R - M R MC (private) = P +  R Optimal tax = – U E E R -  Q E E R - M R MB =  Q R Figure 16.4 Optimal taxes and the wedge between private and social costs.

10. a c d b Figure 16.5 Steady state solution and dynamics of the waste accumulation and disposal model.