Microeconomics Theory- Production Function

Algebra Level 1

The Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs, particularly physical capital and labor, and the amount of output that can be produced by those inputs. Below are 4 functions. Identify the one/ones with increasing returns to scale .

  1. Q=2LK
  2. Q=L 0.8 ^{0.8} K 0.2 ^{0.2}
  3. Q=10L 0.6 ^{0.6} K 0.5 ^{0.5}
  4. Q=0.5L 0.6 ^{0.6} K 0.2 ^{0.2}
1 & 2 4 3 1 & 3

Venture Hi by Venture HI , 27, USA

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1 solution

Venture Hi
Apr 7, 2014

To check if the function exhibit an increasing return to scale ( or decreasing or constant), simply multiple each factor input with a constant, k. For example, take the first function Q=2LK. If we multiply k with both inputs like so, Q=2(kL)(kK )and simplify, we get Q=2LKk 2 ^{2} . Therefore, the k constant becomes k 2 ^{2} . We can conclude this function does exhibit an increase return to scale.

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