The Aggregate Production Function

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The Aggregate Production Function
Our objective is todescribe the
(short-run)technical relationshipbetween real
output (GDP)and total employment
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What do you mean by the short-run?

• In the context of the theory of the firm, the
  short-run means a situation in which there is at
  least one fixed productive factor.
• In the macroeconomic context, the short-run means
  that period in which productive capacity is taken
  as given within narrows--that is, a period not
  sufficient to allow for a substantial
  augmentation of the capital stock, meaningful
  technical change, or the discovery of new natural
  resources.

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Definitions

• Q Potential output (GDP)
• Y Actual output (GDP)
• N The economys labor force
• N Actual employment
• H Standard hours worked per year
• R Economys stock of know and useful natural
  resources
• K Economys capital stock
• T Technological state-of-the-art
• Pa Average output per worker per hour
• PR Average output per worker per year

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Short-run defined more precisely
Thus in the short-run N,H, K, R, and T do
notchange
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Deriving the function
Q f(N, H,K, RT) 1
Labor is thevariable inputin the short-run
We can also say that
Q (N ? H ? Pa) 2
Let PR H? Pa 3
Substituting 3 into 2 to obtain Q N ? PR

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Thus, in the short-run Y f(N, R, K T)
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Actual output (Y)is given by actual employment
(N) timesave. productivity (PR)
Y N ? PR
Y

• Notice the function exhibits diminishing returns.
• In the short-run we move ALONG the function

Ya
?
Y2
?
Y1
0
N
N1
N2
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Shifts of the function
Y N ? PR
Y

• Augmentation of the capital stock.
• Discovery of hitherto unknown resources.
• Improvements in the quality of human resources.
• Technical change

Yb
Ya
?
?
Y2
Y1
?
0
N
N1
N2