Question

What are returns to scale? Under what conditions (that is, for what values of the parameters a and b) does the Cobb-Douglas production function,q = K^aL^b, exhibit constant and increasing returns to scale? (Hint: See Solved Problem 6.3.)

Answer 1

Ans A)

Returns to scale is the parameter to measure the efficiency of production function relative to inputs. It provides the relationship between factor of production and outputs

If we increase the inputs used in production then output increases even in higher rate therefore such production function seems to be exhibiting increasing return to scale. For example if we double the inputs then output increases 3 times

If rate of increase in inputs used in production gives same rate of increase in output then such production function exhibits constant return to scale

If we increase the inputs used in production gives even lower rate of increment in production therefore such production function exhibits decrease return to scale.

Ans B)

F(K,L)=K^a*L^b

If we increase the inputs with some positive factor "@" then new production function will be

F(@K,@L)=(@K)^a*(@L)^b=@^(a+b)*(K^a*L^b)=@^(a+b)*F(K,L)

Therefore if a+b>1 then our Cobb Douglas production function is Increasing return to scale

If a+b=1 then our function exhibits Constant return to scale

If a+b<1 then function exhibits Decreasing return to scale