ECON 4910 Environmental Economics 
                   Summary of first five lectures  
                   Private and public goods/bads 
                   Two goods (or one good and one bad):  
                   eg=   ()yor  yf= ()e 
                    f ′ < 0if e is a good 
                    f ′ > 0 if e is a bad 
                    
                   Two consumers:  
                    yy=+y 
                        12
                   ee=+eif e is a private good/bad 
                        12
                    
                   Preferences:  
                   uy(,e)if eis a private good/bad 
                     iii
                   uy,e if eis a public good/bad 
                      ()
                     ii
                    
                   u >0 if eis a good 
                     ie
                   u <0 if eis a bad 
                     ie
                    
                   Pareto efficiency:  
                    
                           e is a private good:  
                           uu
                            12ee′ 
                               ==−f
                           uu
                            12yy
                           
                           e is a public good:  
                           uu
                            12ee′ 
                              +=−f
                           uu
                            12yy
                    
                   Competitive equilibrium gives Pareto efficiency when e is a private good/bad.  
                    
                   If e is a private good/bad and  f ′′ < 0, any Pareto efficient outcome can be achieved 
                   through a competitive market.  
                    
                   Public (non-rival) good may be excludable or non-excludable.  
                    
                   Markets may provide excludable public goods, but typically not in an efficient manner.  
                    
                   Pollution is a non-excludable bad, and cannot be handled efficiently by markets.  
                                                             - 1 -
                       Money measure of environmental damage 
                                De()
                       Define          by  
                       uy+=De,(e uy,0) 
                                  ()
                         ()
                          ′      −ue       
                        De()=>0
                                  uy
                          ′′
                        De()≥0 if preferences are convex (i.e. if u is a quasiconcave function) 
                       Efficient negotiations and property rights 
                       Income (producer):  f (e) 
                       Environmental cost (consumer): De( ) 
                       Social welfare:  f eD−          e 
                                             () ()
                        
                       e∗maximizes social welfare, and is achieved through negotiations if no transaction costs 
                       or other obstacles. Negotiated level of pollution independent of property rights, but 
                       property rights matter for the distribution of net benefits between the producer and the 
                       consumer. In reality several obstacles: 
                       -   transaction costs 
                       -   free riding 
                       -   unstable conditions 
                       More on  f e  
                                       ()
                        f  e = reduced form income function, defined by  
                          ()
                        f ()eF=−max       (vq)    vG(v)=e 
                                     v {                       }
                       where v is an input vector and q is the associated price vector.  
                        
                                                                    0        00
                       Unconstrained maximization gives v  and  yf=                  e.  
                                                                                    (   )
                       Constrained maximization:  
                                    ′
                                  Fq−
                          ′        kk
                        fe=                 (same for all k ) 
                          ()           ′
                                    G
                                      k
                          ′  0                ′
                        fe()=0 since Fq=              at unconstrained optimum.  
                                              kk
                       Optimal pollution 
                        De()=∑hD()e = aggregate environmental cost 
                                       h
                        
                       Social welfare =          f (eD) −   (e) where ee=           
                                            ∑i ii                            ∑i
                        
                       Optimum (for interior solution):  
                             ∗∗∗
                          ′′
                                                    ′
                                == =  
                        f ()ef...         ()eD()e
                         11              nn
                                                                          - 2 -
                             
                            First n−1 equations are conditions for cost-effectiveness, which also may be defined by 
                             f  ef==max                (e)        ee 
                               ()             {                           }
                                               ∑∑
                                                      ii i
                                                   ii
                            It follows from the first order conditions and the envelope theorem that 
                               ′          ′′
                                                                     
                             f (ef) ==(e)          ... =f(e)
                                         11                nn
                            Environmental regulation 
                            Types of regulation:  
                                 (a) direct regulation of emissions 
                                 (b) emission tax 
                                 (c) tradable quotas 
                                 (d) subsidies to abatement 
                                 (e) direct regulation of the producers` input choices 
                             
                            (a) direct regulation of emissions 
                                                    ∗∗
                                                  ee,...,
                            -    to achieve                     the regulator must know all functions  f (e ) 
                                                 ()
                                                    1       n                                                            ii
                            -    optimal emissions will generally vary across firms, such regulation may be 
                                 considered unfair 
                             
                            (b) emission tax 
                             Producer j:  
                                                               gives  f ′ et=  
                                       max f (et)− e                        (    )
                                                jj j                      jj
                                                                                              ′  ∗        ′   ∗       ∗       ′  ∗
                                      so cost-effectiveness achieved, also  f (eD) =                       (e)if (tD=           e) 
                                       
                            (c) tradable quotas 
                                      Producer j:  
                                       max f (eq)−−(ee)  i.e. max f (eq)−+eqe 
                                                jj jj                                   jj j j
                                       gives  f ′()eq=           (where q is quota price) 
                                                   jj
                                       
                            (d) abatement subsidy 
                                      Producer j:  
                                                              0                                            0
                                       max f (es)+−(ee)i.e. max f (es)−+ese 
                                                jj jj                                 jj j j
                                      gives  f ′()es=           (where s is subsidy rate) 
                                                  jj
                            Note similarity with emission tax and in particular with free tradable quotas  
                             
                            (e) direct regulation of vj .  
                                                        i
                                      - income =  f ()ef<               ()e 
                                                           j   jjj
                                         i
                                      -  f j not equalized across firms 
                             
                            Note: Incentives for new firms to enter market differ between the alternative regulations! 
                                                                                         - 3 -
                          
                         Complications: 
                         -    non-convex technologies 
                         -    asymmetric information 
                               
                         Non-convex technologies 
                         Simple example: 
                         Producer(s) can choose between y=f(e) with same properties as before or zero-emissions 
                                                                                      0
                         technology giving income Y where f(0)