A
Simple
Growth
Model
Set up a production function, which relates inputs to outputs.
We try to
imagine the economy as a factory:
Y = f(K,L).
Output, Y, depends on
combinations of inputs of capital and labor, K and L.
Particular functions, as
Mankiw points out, allow us to transform the original model to a per worker
representation, Y/L =
f(K/L,1):
this says that output per worker (or GDP per
worker) depends on capital per worker.
Simplify the notation to Y/L
≡
y and K/L
≡
k and draw a graph of the relationship:
capital per worker
output
per worker
y = f(k)
Next, take the simple national income model of a closed economy without a
government sector, that is,
Y = C + I.
Here, GDP is just consumption and
investment. Put it on a per worker basis as well, to get y = c + i, where
Y/L
≡
y,
or GDP per worker,
C/L
≡
c, or consumption per worker, and I/L
≡
i, or
investment per worker.
We need to define a consumption function, which relates workers’
consumption to their income, as c = (1  s) y.
This says that workers’
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 Spring '08
 NORMMILLER
 Economics, Macroeconomics, Stock and flow, worker, Outpu t

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