The golden-rule level of education. Consider the model of Section 4.1 with the assumption that G(E) takes the form G(E) = e φE .

(a) Find an expression that characterizes the value of E that maximizes the level of output per person on the balanced growth path. Are there cases where this value equals 0? Are there cases where it equals T?

(b) Assuming an interior solution, describe how, if at all, the golden-rule level of E (that is, the level of E you characterized in part (a )) is affected by each of the following changes:

(i) A rise in T.

(ii) A fall in n.