Does the production function:q=100L-20/kexhibit increasing, decreasing, or constant returns to scale?

the production function q exhibits decreasing returns to scale

Explanation:

to see if the function exhibits decreasing, increasing or constant returns of scale, let increase the input of the function

q=100L-20/k

then for N times units of Labor L and Capital K

qn = 100 (N*L) - 20 / (N*k) = N*[100*L - 20 / (N²*K) ]

since 20 / (N²*K) 1

qn = 100 (N*L) - 20 / (N*k) = N*[100*L - 20 / (N²*K) ] < N*[100*L - 20 / (K) ] = N*q (constant returns of scale)

thus qn < constant returns of scale

therefore q exhibits decreasing returns to scale