Homogeneous of degree Note: 1st derivatives a function homogeneous of degree k are homogeneous of degree (k 1) – Implication: For linearly homogeneous production functions (i.e. CRTS), the marginal products MPi = are homogeneous of degree 0. fi Homogeneity of degree 0 implies: , so that increasing all inputs proportionally does not change the function. In terms of marginal products, this implies that proportionally increasing all inputs does not change the MP of the inputs because the MP are proportional functions of input ratios. Because the MP do not change with proportional increase, the MRTS (-f1/f2) will not change along a ray, so isoclines are rays from the origin.
Homogeneous of degree Note: 1st derivatives a function homogeneous of degree k are homogeneous of degree (k – 1) Implication: For linearly homogeneous production functions (i.e. CRTS), the marginal products MPi = fi are homogeneous of degree 0. Homogeneity of degree 0 implies: , so that increasing all inputs proportionally does not change the function. In terms of marginal products, this implies that proportionally increasing all inputs does not change the MP of the inputs because the MP are proportional functions of input ratios. Because the MP do not change with proportional increase, the MRTS (-f1/f2) will not change along a ray, so isoclines are rays from the origin.
Technical%20Aspects%20of%20Production.docx