Consider a variant of the model studied in Section 11.3 in which the technology in the consumption good sector is still given by (11.27), while the technology in the investment good sector is modified to
where β ∈ (α, 1). The labor market clearing condition now requires LC(t) + LI (t) ≤ L(t). The rest of the environment is unchanged.
(a) Define a competitive equilibrium.
(b) Characterize the steady-state equilibrium, and show that it does not involve sustained growth.
(c) Explain why the long-run growth implications of this model differ from those of Section 11.3.
(d) Analyze the steady-state income differences between two economies taxing capital at the rates τ and τ . What are the roles of the parameters α and β in determining these relative differences? Why do the implied magnitudes differ from those in the one-sector neoclassical growth model?