Consider the baseline endogenous technological change model with expanding machine varieties in Section 13.1. Suppose that x now denotes machines that do not immediately depreciate. In contrast, once produced, these machines depreciate at an exponential rate δ. Preferences and the rest of the production structure remain unchanged.
(a) Define the equilibrium in BGP allocations.
(b) Formulate the maximization problem of producers of machines.
(c) Characterize the equilibrium in this economy, and show that all the results are identical to those in Section 13.1.