What is q 1 2 nv2

LHS ~ RHS

zQ[L;K] ~ Q[zL;zK]

z>1

IF zQ[L;K]>Q[zL;zK] then Q[L;K]→decreasing returns to scale

IF zQ[L;K]=Q[zL;zK] then Q[L;K]→constant returns to scale

IF zQ[L;K]<Q[zL;zK] then Q[L;K]→increasing returns to scale

a)

Q=3L+2K

z(3L+2K) ~ 3zL+2zK

z(3L+2K) ~ z(3L+2K)

1 ~ 1

zQ[L;K] = Q[zL;zK] → constant returns to scale

b)

Q=(2L+2K)^½

z(2L+2K)^½ ~ (2zL+2zK)^½

z(2L+2K)^½ ~ √z (2L+2K)^½

z ~ √z

√z ~ 1

√z > 1

zQ[L;K] > Q[zL;zK] → decreasing returns to scale

c)

Q=3LK²

z(3LK²) ~ 3(zL)(zK)²

z(3LK²) ~ z³(3LK²)

z ~ z³

1 ~ z²

1 < z²

zQ[L;K] < Q[zL;zK] → increasing returns to scale

d)

Q=√(LK)

z√(LK) ~ √((zL)(zK))

z√(LK) ~ z√(LK)

z ~ z

1 = 1

zQ[L;K] = Q[zL;zK] → constant returns to scale

e)

Q=4√L + 4K

z(4√L + 4K) ~ (4√zL + 4zK)

4z√L + 4zK ~ 4√zL + 4zK

4z√L ~ 4√zL

z ~ √z

√z ~ 1

√z > 1

zQ[L;K] > Q[zL;zK] → decreasing returns to scale