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

question 112

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 $a = 1 / 3$ ?

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Definitions:

Integuments

Layers or coverings of an organism or organ, serving to protect or enclose, especially the outer layer of seeds or the skin of humans and animals.

Megasporangium

A plant structure that produces megaspores, which develop into female gametophytes in seed plants and certain ferns.

Ovules

Small structures within the ovary of seed plants that develop into seeds upon fertilization.

Over-The-Counter

Refers to drugs or medications that can be purchased without a prescription, available directly to consumers.