Question

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

Answer 1

Answer:

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) < 20/K for N>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