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whatis the differences between cobb-Douglass and leontief production technology

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What do you mean by "what is the difference"? Please clarify. These are just different production functions.

Suppose there are two different inputs $A$ and $B$.

The Cobb-Douglas production function is given by $$A^\alpha B^\beta.$$ You may think of $A$ and $B$ as capital and labor.

The Leontief production function is given by $$\min \{ A, B\}.$$ You may think of $A$ and $B$ as number of left and right shoes. If you have 7 left shoes and 3 right shoes, you have 3 pairs of shoes. Or let $A$ be "number of wheels divided by four and rounded down" and let $B$ be "number of car bodies" such that you can produce 5 cars with 7 car bodies and 21 wheels.

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    $\begingroup$ Well, clearly the difference in this case must be $A^\alpha B^\beta - \min \{ A, B \}$. $\endgroup$ Commented Jan 5, 2017 at 20:39
  • $\begingroup$ I briefly thought about making such a comment myself, but found it too cheeky - hat tip to you :) $\endgroup$
    – Bayesian
    Commented Jan 5, 2017 at 20:44
  • $\begingroup$ As a unifying perspective, one could mention that both are limiting cases of the C.E.S. production function, see for example economics.stackexchange.com/a/399/61 $\endgroup$ Commented Jan 6, 2017 at 17:25

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