Basic micro doubts - help!

[Homer Simpson]

Identify if production function and respective marginal products has CRS, IRS or DRS-

1) x1 + (x2)^(0.5)

2) (x1 + 1)^(0.5) x (x1)^(0.5)

How to solve this? Scaling up is not working in the usual way!

[kangkan]

hey,can you expand the terms?

[Dreyfus]

@tsuki....for 1st I m solving...2nd u can do it with this method
Let this function be homogenous of degree n,
x*t + y½*t½ = tⁿ(x + y½)
Now this eq holds for all values of t, x & y
Let t=4
4x + 2y½ = 4ⁿ(x + y½)
Let x=0, y=1
2=4ⁿ........eq1
Now let x=1 y=0
4=4ⁿ....eq 2
Since eq 1 and eq2 aren't consistent, therefore function is not homogeneous

[Homer Simpson]

here are the questions again. Vaibhav, i am still not clear with this method...the function is different from the one you have written for second part?

[Dreyfus]

Tsuki I hv solved for the first function with x1 and  x2 being x and y respectively!

[Homer Simpson]

acha, i get it now! so these functions wont have any particular returns to scale?

[Dreyfus]

They don't... As returns to scale is used just in replace of three different cases of homogeneity of function!

[Homer Simpson]

ok i got it now, thank you!

[Dreyfus]

@tsuki....actually function is not homogenous but it posses decreasing  returns to scale.....sry for that

[Homer Simpson]

Ok, how do i find out if it has DRS in this case?

[Dreyfus]

Tsuki...because here F(tx,try) < t*F(x,y) ie  x*t + t½*y½ < t(x + y½) so its drs