d What do we mean by returns to scale Give examples of CobbD

(d) What do we mean by returns to scale? Give examples of Cobb-Douglas production functions exhibiting increasing decreasing and constant returns to scale. [A Cobb-Douglas production function takes the following form: Q- AK\'L®, A > 0, > 0,>0.]

Solution

Returns to scale is the term which relates the rate of increase in output (in the long run) to the associated increase in inputs. There are said to be increasing returns to scale when output more than doubles on doubling of inputs, there are decreasing returns to scale when output less than doubles on doubling of inputs and constant returns to scale are said to exist when output just doubles on doubling of inputs.

Cobb Douglas function:

Q = AK^aL^b

On Doubling of inputs:

Q\' = A(2K)^a(2L)^b = 2^a+bAK^aL^b

Q\' = 2^a+b.Q

Therefore, constant returns to scale would exist when a + b = 1 , there would be increasing returns when a + b >1 and decreasing returns when a + b < 1

Increasing returns: Q = AK¹L¹

Decreasing returns: Q = AK^0.25L^0.5

Constant returns: Q = AK^0.5L^0.5