Hence, I start by calculating a competitive equilibrium
for a greatly simplified version of the growth model.
Specifically, consider a discrete-time model of growth with two periods.
Let each of S identical consumers have a twice continuously
differentiable, strictly concave utility function U(Ci, C2), defined over
consumption of a single output good in periods 1 and 2. Let each
consumer be given an initial endowment of the output good in period
1. Suppose that production of consumption goods in period 2 is a
function of the state of knowledge, denoted by k, and a set of additional
factors such as physical capital, labor, and so forth, denoted by
a vector x.6 To restrict attention to a choice problem that is essentially