Question

You are the manager of a firm that produces apple pies. You are considering employing an additional worker, but you want to know what effect the new worker will have on production. Based on your knowledge of how your firm produces its apple pies you have the production function
q =K^1/2*L^1/2, where L represents the number of workers. Since you are contemplating making the hire very soon you know that your capital is fixed at 10. What effect will hiring an additional worker have on production?

Answer 1

F =K^1/2*L^1/2.

given the production function we multiply both factors of production by z

so zF= (zK)^1/2(zL)^1/2 => zKL.

so this means that we get constant returns to scale . so when we are given that K is 10 which is fixed , increasing the labour L would increase the labour to capital ratio ie for every labour less of capital would be available and so the productivity reduces per worker.

eg : when we take both K and L as 10 and find the Y/L ie output per worker it would be

Y/L =( K/L)^1/2 which would be 1

and when we increase L to 15 , then the ratio would be

Y/L= ( K/L)^1/2 =(10/15)^1/2= 0.816 which is less than 1

which implies that the productivity or output per worker would reduce when capital is fixed and labour increases