Question

A firm has a production technology given by: y = x^0.35z^0.65 , where x is labour input, z is the amount of physical capital. Initial input prices are given by w =1 and r = 1. Suppose now that both capital and labour are variable inputs.

Find returns to scale for given technology.

Answer 1

Answer

A function exhibits constant returns to scale if f(tx,tz) = t*f(x,z) for all t > 1

A function exhibits increasing returns to scale if f(tx,tz) > t*f(x,z) for all t > 1

A function exhibits decreasing returns to scale if f(tx,tz) < t*f(x,z) for all t > 1

Now, Production function is given by :

y = f(x,z) = x^0.35z^0.65

=> f(tx,tz) = (tx)^0.35(tz)^0.65 = t^0.35+0.65(x^0.35z^0.65) = t*x^0.35z^0.65 = t*f(x,z)

So, f(tx,tz) = t*f(x,z) for all t > 1 and thus this function exhibit Constant returns to scale.

Hence, For this technology we have Constant returns to scale.