Consider the Cobb-Douglas Production Function $Y _ { t } = A _ { t } K _ { t } ^ { a } L _ { t } ^ { 1 - a }$

Essay

Consider the Cobb-Douglas production function $Y _ { t } = A _ { t } K _ { t } ^ { a } L _ { t } ^ { 1 - a }$
.
(a) Write this in growth-rate terms.
(b) Next, define this in terms of per capita growth and identify the contributions of the components of per capita growth.
(c) If the growth rate of capital per worker is 1.3 percent, the labor composition growth rate is 0.4 percent, TFP growth is 1.2 percent, and $a = 1 / 2$ , what is the growth rate of output per worker? If $a = 1 / 3$ ?