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10.6.1 Optimal inflation and unemployment

Given assumption N4, the social welfare function (W) of the policy makers

will be the discounted value of the aggregate voting function. In the absence

of political constraints a social planner will seek to maximize the welfare

function given by equation (10.6) subject to the macroeconomic constraints

given by equations (10.2)–(10.5):

W g Ut Pt e dt

= rt ∫∞ − 0

( , ˙ ) (10.6)

Figure 10.3 The Nordhaus political business cycle model

There are several possible outcomes depending on the policy makers’ choice

of discount rate (r). Where future generations are given the same weight as

the current generation (r = 0), the outcome is indicated by G in Figure 10.3.

Here the LRPC is at a tangent to the aggregate voting function (V2) and this

represents the best sustainable combination of inflation and unemployment.

Nordhaus calls this outcome the ‘golden rule’ policy solution, which involves

inflation = ˙PG and unemployment = UG. Where the policy makers care only

about the current generation (infinite discount rates are applied) a ‘purely

myopic’ policy results in an outcome indicated in Figure 10.3 by point M,

where SM is at a tangent to V4. In other words, ‘myopic’ policies which ignore

the welfare of future generations lead to higher inflation (P˙M ) and lower

unemployment (UM) than golden rule policies (Nordhaus, 1975). Where the

policy maker cares about both generations (∞ > r > 0), an outcome Nordhaus

refers to as the ‘general welfare optimum’ (W) results. In this case U = UW

and P˙ = P˙W .