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Unformatted text preview: apital on Output With these two assumptions, our first relation between
output and capital per worker, from the production side,
can be written as Yt
N f Kt
N In words, higher capital per worker leads to
higher output per worker. the first relation 37 111 INTERACTIONS BETWEEN OUTPUT AND
CAPITAL
The Effects of Output on Capital Accumulation To derive the second relation, between output and
capital accumulation, we proceed in two steps:
1. We derive the relation between output and
investment. 2. We derive the relation between investment
and capital accumulation. 38 111 INTERACTIONS BETWEEN OUTPUT AND
CAPITAL
The Effects of Output on Capital Accumulation
Output and Investment We make three assumptions to derive the relation
between output and investment:
We assume the economy is closed.
I S (T G) We assume public saving, T – G, is equal to zero.
I S We assume that private saving is proportional to
income, so
S sY
Combining these two relations gives: It s Yt
39 of 39 Macroeconomics by Yao Li 111 INTERACTIONS BETWEEN OUTPUT AND
CAPITAL
The Effects of Output on Capital Accumulation
Investment and Capital Accumulation
The evolution of the capital stock is given by: Kt 1 (1 )Kt It denotes the rate of depreciation
Combining the relation from output to investment,
I t sY t , and the relation from investment to capital
accumulation, we obtain the second important relation
we want to express, from output to capital accumulation:
Kt
N 1 (1 ) Kt
N s Yt
N 40 111 Interactions between Output and Capital
The Effects of Output on Capital Accumulation
Investment and Capital Accumulation
Output and Capital per Worker: Kt 1 N (1 ) Kt
N s Yt
N Rearranging terms in the equation above, we can
articulate the change in capital per worker over time:
Kt
N 1 Kt
N s Yt Kt N N In words, the change in the capital stock per worker (left side)
is equal to saving per worker minus depreciation (right side).
the 2nd relation 41...
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This note was uploaded on 03/05/2014 for the course ECON 2123 taught by Professor Yanyu during the Fall '13 term at HKUST.
 Fall '13
 YANYU

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