# Lecture 2 Cost - Benefit Analysis. Intertemporal welfare economics An allocation of resources is efficient, if it is impossible to make one individual.

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Lecture 2 Cost - Benefit Analysis

Intertemporal welfare economics An allocation of resources is efficient, if it is impossible to make one individual better off without making the other individual worth off. Consider two individuals (A, B), two time periods (0,1) with utility function U and who want to maximise consumption C

Intertemporal welfare economics Allocation question: how is total consumption divided between two individuals in each period? Assuming a single efficiently produced commodity that can be either consumed or added to the stock of capital for future production. Efficiency requires: 1. Equality of A and B’s consumption discount rate; 2. Equality of rates of return to investment across firms; 3. Equality of the consumption discount rate with the rate of return to investment.

UAUA UAUA C OA C 1A (a) C OB C 1B UBUB UBUB (b) Figure 11.1 Equality of consumption discount rates (Perman et al.: page 353) An allocation is intertemporally efficient if the marginal rates of utility substitution are the same for A and B: Consumption discount rate: => r A = r B = r

Figure 11.2 Shifting consumption over time (Perman et al.: page 354) COCO C1C1 C 1 max C 1b C 1a C1C1 A C 0b C 0a C0C0

C 11 C 12 C 01a C 01b C 01 C 02b C 02a C 02 Figure 11.3 Equality of rates of return (Perman et al.: page 355) An allocation is intertemporally efficient if the marginal rates of returns to investment are the same for all firms:

Figure 11.4 Equality of rate of return and discount rate (Perman et al.: page 355) COCO C1C1 C 1* C 0* a b c An allocation is intertemporally efficient if the marginal rates of returns to investment equals the consumption rate of discount:  = r.

C1C1 C 1max C 1* C 0* C 0max C0C0 U U Figure 11.5 Intertemporal optimum for an individual (Perman et al.: page 357)

C1C1 C0C0 U U Figure 11.6 Present value maximisation (Perman et al.: page 357) b a A C 1* C1C1 R B C 0* C0C0 S

C1C1 C0C0 U U Figure 11.6 (2) Present value maximisation b a A C 1* C1C1 R B C 0* C0C0 S

Intertemporal welfare economics For any given set of data, resource endowment, production function, preferences and the like => several intertemporally efficient allocations. => Choosing among the set of intertemporally efficient allocations requires a social welfare function.

Cost - Benefit Analysis Project appraisal: private: social: utility based consumption based a) b)

Environmental Cost - Benefit Analysis Project appraisal: social: (Krutilla - Fisher model)

Environmental Cost - Benefit Analysis Objections to ECBA: individuals may be inadequately informed individuals may be insufficiently deliberative in assessing consequences of alternatives individuals lack self-knowledge individuals’ preferences may not reflect their true interests due to preference shaping from socialisation processes

Environmental Cost - Benefit Analysis Alternatives to ECBA: impact assessment cost-effectiveness analysis multi-criteria analysis deliberative polling citizens’ juries

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