A) q =3L + 2K

This function exhibits constant returns to scale. For example, if L is 2 and K is 2

then q is 10. If L is 4 and K is 4 then q is 20. When the inputs are doubled, output

will double.

B) q = (2L + 2K)^1/2

This function exhibits decreasing returns to scale. For example, if L is 2 and K is 2 then q is 2.8. If L is 4 and K is 4 then q is 4. When the inputs are doubled, output will less than double.

C) q = (3LK)^2

This function exhibits increasing returns to scale. For example, if L is 2 and K is 2

then q is 24. If L is 4 and K is 4 then q is 192. When the inputs are doubled, output

will more than double. Notice also that if we increase each input by the same factor

λ then we get the following:

q' = 3(λL)(λK)^2 = λ^3LK^2 = λ^3q

Since λ is raised to a power greater than 1, we have increasing returns to scale

D) q=4L^1/2 + 4K

This function exhibits decreasing returns to scale. For example, if L is 2 and K is 2

then q is 13.66. If L is 4 and K is 4 then q is 24. When the inputs are doubled,

output will less than double.

E) q = L^1/2 + K^1/2

This function exhibits constant returns to scale. For example, if L is 2 and K is 2 then q is 2. If L is 4 and K is 4 then q is 4. When the inputs are doubled, output will exactly double. Notice also that if we increase each input by the same factor λ then we get the following:

q' = (λL)^1/2(λK)^1/2 = λL^1/2K^1/2 = λq

Since λ is raised to the power 1, we have constant returns to scale. 11th EditionClaudia Bienias Gilbertson, Debra Gentene, Mark W Lehman1,012 solutions

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