Alter the Solow growth model so that the production technology is given by Y = zK, where Y is output, K is capital, and z is total factor productivity. Thus, output is produced only with capital.

(a) Show that it is possible for income per person to grow indefinitely.

(b) Also show that an increase in the savings rate increases the growth rate in per capita income.

(c) From parts (a) and (b), what are the differences between this model and the basic Solow growth model? Account for these differences and discuss.