Consider the production function

(a) Determine the optimality conditions for the problem

with utility function

(b) Calculate the steady-state value of capital, production, and consumption.
Draw the phase diagram in the capital–consumption space. (The formal derivations can be limited to the region K

(c) To draw the phase diagram, one needs to keep in mind the role of parameters · and Ò. But what is the role of ‚?

(d) The production function does not have constant returns to scale. This is a problem (why?) if one wants to interpret the solution as a dynamic equilibrium of a market economy. Show that for a certain g (L) the production function

has constant returns to K and L in the relevant region. Also show that the solution characterized above corresponds to the dynamic equilibrium of an economy endowed with an amount L = 2 of a non-accumulated factor.

Y = F (K) = JaK - K 12 a if K < a, otherwise.