is normalised to unity, so the left-hand side of (2.8) is the sum of the marginal
rates of substitution). Clearly, (2.8) captures policy concerns about efficiency.
We will now study whether the market-based allocation will differ from this
first-best optimum.
2.3. The market economy
Competitive profit-maximising firms invest up to the point where capital’s mar-
ginal product equals the cost of capital, implying
f0(k)=r+τ, (2.9)
where r is the after-tax interest rate and τ is a source-based unit tax on capital.
From (2.9) it follows that capital intensity is given by
k = k(r+τ),k0 =1/f00 < 0. (2.10)
Moreover, (2.9) and the linear homogeneity of the production function imply that
the private sector real wage (w) is
w (r + τ)=f (k (r + τ)) - (r + τ) k (r + τ) ,w0 = -k. (2.11)
Capital is perfectly mobile across countries. With source-based capital tax-
ation, this means that all the n countries in the world face the same after-tax
interest rate r. A global capital market equilibrium is attained when
(1 — α) k (r + τ) + (n — 1) (1 — b) b (r + b) = nk, (2.12)
where (1 - α) k (r + τ) is capital demand in the domestic country under consider-
ation, and (1 — αb) kb (r + τb) is capital demand in each of the n — 1 identical foreign
countries. Thus the left-hand side of (2.12) measures the global demand for capital
which must equal the fixed global capital supply, nk. By implicit differentiation
of (2.12) we may find the isolated effects of domestic tax and spending policies on