returms to scale..plz help/ Amit Sir

[Target MA]

Of the production functions, which one of the following represents decreasing
returns to scale?
a) Q = 2K + 3L +KL
b) Q = 20K^0.6L^0.5
c) Q = 100 + 3K +2L
d) Both a) and c) above

in option b it is increasing returns to scale but how to find the returns to scale for option a and c ??

[MI]

I think only c is decreasing return to scale.

[Target MA]

could you explain how and how do you find returns to scale for such a function?

[Target MA]

could you explain how and how do you find returns to scale for such a function?

[Amit Goyal]

For (a), let f(K, L) = 2K + 3L +KL
Consider t > 1,
and let K > 0, and L > 0:
f(tK, tL) = 2tK + 3tL + (tK)(tL) = t(2K) + t(3L) + (t^2)(KL) > t(2K) + t(3L) + (t)(KL) = tf(K, L)
Thus, it does not satisfy decreasing returns to scale.

For (c), let h(K, L) = 100 + 3K +2L  
Consider t > 1,
h(tK, tL) = 2tK + 3tL + 100 = t(2K) + t(3L) + 100 < t(2K) + t(3L) + 100t = th(K, L)
Thus, it satisfy decreasing returns to scale.

[Target MA]

thankyou so much sir..