Transcript Chapter 11A Essentials of Economics Paul Gregory 6 Lecture Notes

APPENDIX CHAPTER 11
FUNCTIONS AND GROWTH RATES
Y = F (K,L,T)
This chapter uses mathematical notations to
describe the relationship between output
(Y) and labor (L) and capital (K) inputs:
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Y = F (K,L,T)
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(1)
The amount of output the economy
produces (Y) depends on
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how much capital (K) and labor (L) the economy
has at its disposal and on the state of its
technology (T).
Y = F (K,L,T) – cont.
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If we have more L and K, we expect
more output; if technology improves,
output will increase.
The chapter uses dots above variables
to denote annual rates of growth.
A growth rate measures the rate at
which something changes.
Y = ƒ(K,L,T)
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Production function Y = F (K,L,T) in
terms of growth rate:
Y = ƒ(K,L,T)
Use this equation to calculate sources
of economic growth.
Y = ƒ(K,L,T) - cont
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We can measure K and L but we cannot
directly measure Ṫ, but we can
calculate it as a residual.
We use L’s share of income a 67
percent and K’s share of income as 33
percent.
Express the growth rate equation as:
Y = 0.67L + 0.33K +T.
(2)
Y - L = 0.67L + 0.33K +T - L
= 0.33(K – L) + T
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Growth per capita output, where per capita
output is Y/P, P stands for population.
In the long run, P and L grow at about the
same rate = calculate it as the growth of
Y/L.
The growth rate of Y/L equals the growth
rate of Y(Y) minus the growth rate of L(L).
Y - L = 0.67L + 0.33K +T - L
= 0.33(K – L) + T - cont
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If Y and L grow at the same rate, then Y/L
will not change, if Y grows faster than L will
Y/L grow.
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Calculate the growth rate of Y/L by subtracting L
from each side of (2):
Y - L = 0.67L + 0.33K +T - L = 0.33(K – L) + T
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This is the equation for calculating the
sources of per capita GDP growth.