A.5. Project Evaluation
A.5. Project Evaluation
Imagine that, even though the government does not optimize the economy, it can bring about small changes to it by altering the existing resource allocation mechanism in minor ways. The perturbation in question could be small adjustments to the prevailing structure of taxes for a short while; it could be minor alterations to the existing set of property rights for a brief period; it could be a public investment—or whatever. Call any such perturbation a policy reform.^{14}
Consider an investment project. It can be viewed as a perturbation to the resource allocation mechanism α for a brief period (economists call it the ‘gestation period’ of the project), after which the mechanism reverts back to its earlier form. We consider projects that are small relative to the size of the economy. How should they be evaluated? In Chapter 10 the required evaluation criterion was developed in an informal manner. Here I offer a formal account.
The project involves small quantities of manufactured capital, labour, and natural resources to produce a small additional quantity of the all‐purpose commodity Y. Denote the project's output and inputs at t by the vector (Δ Y _{t}, Δ K _{t}, Δ L _{t}, Δ R _{t}).^{15}
The project's acceptance would perturb aggregate consumption and labour supply under α. Let the perturbation at t be $(\Delta {\stackrel{\sim}{C}}_{t}\text{,}\Delta {\stackrel{\sim}{L}}_{t})$. This would affect U _{t} by the amount $({U}_{C}\Delta {\stackrel{\sim}{C}}_{t}+{U}_{L}\Delta {\stackrel{\sim}{L}}_{t})$. It would be tiresome if the project evaluator were required to estimate $(\Delta {\stackrel{\sim}{C}}_{t}\text{,}\Delta {\stackrel{\sim}{L}}_{t})$ for every project that came up for consideration. Accounting prices of capital assets are useful because they enable the evaluator to estimate $(\Delta {\stackrel{\sim}{C}}_{t}\text{,}\Delta {\stackrel{\sim}{L}}_{t})$ indirectly.^{16}
Recall that U is the unit of account. So, δ is the accounting rate of interest on well‐being. Since the accounting price of manufactured capital is p _{t} (equation (A.10a)), the corresponding accounting rental rate is δ p _{t}. It is most unlikely that consumption and investment have the same accounting price in an imperfect economy. So we decompose Δ Y _{t} into two components: changes (p.245) in consumption, and changes in investments in manufactured capital. Denote them as Δ C _{t} and Δ (dK _{t}/dt), respectively.^{17}
Let w _{t} denote the accounting wage rate. How would we measure it? If we knew α, we would be able to estimate $\Delta {\stackrel{\sim}{L}}_{t}/\Delta {L}_{t}$. Now, ${w}_{t}=(\Delta {\stackrel{\sim}{L}}_{t}/\Delta {L}_{t}){U}_{L}$. So, w _{t} = −U _{L} if $\Delta {\stackrel{\sim}{L}}_{t}=\Delta {L}_{t}$, and w _{t} = 0 if $\Delta {\stackrel{\sim}{L}}_{t}=0$. In ‘labour‐surplus economies’ one would typically find 0 < −(w _{t}/U _{L}) < 1.
It follows that

Proposition 2: A project should be accepted if and only if the present discounted value of its social profits is positive.
How is project evaluation related to optimum planning? Imagine that at each date projects are evaluated as a tatônnement. The accounting prices used to evaluate projects along the tatônnement are those that would prevail if all acceptable projects in the queue to date had been accepted and all unacceptable ones rejected. This sequence of hypothetical choices is often called the ‘gradient process’ (also called the ‘hill‐climbing method’). Arrow and Hurwicz (1958) proved in the context of a finite‐dimensional economy that, provided the set of economic possibilities has a sufficiently strong convex structure, the gradient process converges to the optimum. Given that we are considering infinite‐dimensional economic programmes, a corresponding result for our model economy would be harder to prove. It is reasonable to conjecture that, despite this, a sequence of project selections in the form of a suitably defined gradient process would converge to an optimum economic programme if the economy had a strong convex structure.^{18} If the economy does not have a convex structure, the gradient method can at best be expected to lead to a local optimum.
Notes:
(14) Over the years, economic evaluation of policy reform in imperfect economies has been discussed by a number of economists (Meade, 1955; Dasgupta, Marglin, and Sen, 1972; Mäler, 1974; Starrett, 1988; Ahmad and Stern, 1990; Dreze and Stern, 1990; and Edwards and Keen, 1996, to name only a few). But they did not develop a formal account of intertemporal welfare economics in a reformist economy. This section of the Appendix is an attempt to fill that gap.
(15) If the project has been designed efficiently, we would have Δ Y _{t} = F _{K}Δ K _{t} + F _{L}Δ LT + F _{R}Δ R _{t}. The analysis that follows in the text doesn't require the project to have been designed efficiently.
(16) The arguments in the text develop the theory of social cost–benefit analysis in Dasgupta, Marglin, and Sen (1972).
(18) In referring to an optimum economic programme, I include ‘second‐best’ optima.