Chapter 14 - Partial Derivatives - 14.1 Functions of Several Variables - 14.1 Exercises - Page 939: 4

$2P(L,K)$

1)If the amounts of labor and capital are both doubled, we replace L,K in the function with 2L,2K. $P(2L,2K)$ $=1.01(2L)^{0.75}(2K)^{0.25}$ $=1.01(2)^{0.75}(2)^{0.25}L^{0.75} K^{0.25}$ $=(2)^{1}1.01L^{0.75} K^{0.25}$ $=2P(L,K)$ 2) It is also true for general case $2P(L,K)=bL^{a}K^{1-a}$ $=b(2)^{a}(2)^{1-a}L^{a} K^{1-a}$ $=2P(L,K)$