Econ 100B:
Macroeconomic Analysis
Fall 2008
Problem Set #9 ANSWERS
(Due September 29 - 30, 2008)
A.
Solow Growth Model:
1.
Clearly and accurately draw and label a diagram of the Solow Growth Model.
2.
Provide an economic explanation of the shape of the curve(s) in your diagram in #1.
The per-worker production function shows a positive relationship
between income-per-
worker, Y/N, and the capital-to-labor ratio, K/N, for a given level of productivity, A.
The per-worker production function slopes upward because there are increasing returns to a
higher capital-to-labor ratio
, i.e., as the capital-to-labor ratio increases, income-per-worker
also increases.
The slope of the per-worker production function decreases as the capital-to-labor ratio
increases because of the diminishing marginal product of capital
, i.e., as the capital-to-labor
ratio increases, income-per-worker also increase but by progressively smaller and smaller
amounts.
The per-worker saving function also shows a positive relationship
between saving-per-
worker, S/N, and the capital-to-labor ratio, K/N. Because of the assumption of a constant
saving rate, the per-worker saving function is simply proportional to the per-worker
production function, the proportion dependent on the saving rate.
K/N
K/N
Y/N, S/N, Ib/N
Y/N
S/N, Ib/N
Y/N = A
0 *
f(K/N)
Ib/N = (n + d) * K/N
S/N = s * Y/N
“A”

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