A Growth Theoretical Approach
- New Horizons in Environmental Economics series
2. Our workhorse: the Brock model Let us now introduce, in an intuitive manner, the mathematical results which underlie the core of the subsequent analysis. We also introduce the particular dynamic growth model that will be our workhorse in the chapters to follow. Many features of welfare measurement in an imperfect market economy are more general when contrasted with the corresponding analysis in a perfect market economy. Weitzman’s classical result, that the Hamiltonian of a typical Ramsey growth model is directly proportional to future welfare, rests on a property of the optimal control problem. This property typically refers to the system as being not ‘fundamentally’ non-autonomous. This implies that the time dimension enters the problem solely through the state and control variables, and a constant utility discount rate. When externalities, distortionary taxation, unemployment, imperfect competition and distributional considerations are introduced into the economy, the model turns out to be ‘fundamentally time dependent’ or non-autonomous. As we explain below, in order to convert the market economy into a non-autonomous system, it is sufficient to introduce one of the market imperfections just mentioned. Each imperfection is a special case of a fundamental complication when measuring welfare in a non-autonomous dynamic growth model. In other words, as soon as first best principles are left behind, Weitzman’s fundamental theorem of welfare measurement breaks down, although it does so in a very systematic way. Even if it is not problematical to generalize his result in what then becomes a non-autonomous environment, the new situation introduces...
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