The name is absent

The public good is produced by a simple linear technology with labour as the only
input:

G=α.                               (2.4)

At the start of the period considered, each country in the world is endowed with
a fixed total capital stock k. All countries are assumed to be symmetric, with
identical labour forces, capital endowments, tastes and technologies.

2.2. The first-best allocation

For later reference it will be useful to characterize the first-best allocation of
resources in our simple world economy, assuming that the social planner in the
representative country wishes to maximise the utilitarian social welfare function

SW = α [u (C_g)+g (α)] + (1 - α)[u (C_p)+g (α)] .          (2.5)

One condition for global optimality is global production efficiency which requires
that capital’s marginal product be equalized across countries. With identical
countries this is achieved when investment in each country equals the country’s
fixed capital endowment. Hence optimality is attained when the social welfare
function (2.5) is maximised with respect to Cg, Cp, and α, subject to the resource
constraint

αCg + (1 - α) Cp = F (k, 1 - α^¢ .                  (2.6)

Denoting the marginal product of private sector labour input by F_L , the first-order
conditions for the solution to this problem can be shown to imply

u⁰(Cg)=u⁰(Cp)=⇒ Cg =Cp =C,             (2.7)

Ug_r(C) = FL (k^, 1 ^{- α}) .                                  (2.8)

Equation (2.7) states that private consumption levels must be equalized so as
to equalize the marginal utility of consumption across the two groups of workers.
This condition may be said to reflect policy concerns about equity. Equation (2.8)
is the Samuelson condition for the optimal supply of public goods, stating that
the sum of the marginal rates of substitution between private and public goods
should equal the marginal rate of transformation (recall that the total population

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