Exercise 11.14. Consider a variant of the model studied in Section 11.3, where the technology in the consumption-good sector is still given by (11.27), while the technology in the investment-good sector is modified to I (t) = A (KI (t))β (LI (t))1−β , where β ∈ (α, 1). The labor market clearing condition requires LC (t) + LI (t) ≤ L(t). The rest of the environment is unchanged. (1) Define a competitive equilibrium. (2) Characterize the steady-state equilibrium and show that it does not involve sustained growth. (3) Explain why the long-run growth implications of this model differ from those of Section 11.3. (4) Analyze the steady-state income differences between two economies taxing capital at the rates τ and τ 0 . 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?