Consider the lab-equipment model of Section 13.1, but modify the innovation possibilities frontier to be
where φ > 0.
(a) Define an equilibrium and characterize the market clearing factor prices and determine the free-entry condition.
(b) Show that without population growth, there will be no sustained growth in this economy.
(c) Now consider population growth at the exponential rate n, and show that this model generates sustained equilibrium growth, as in the model analyzed in Section 13.3.