Question

1List the properties of homothetic and linearly homogeneous production function

Answer 1

• Homothetic production functions have the property that $f(x)=f(y)$ implies $f(\lambda x)=f(\lambda y).$
• Homogeneous production functions have the property that $f(\lambda x)=\lambda^kf(x)$ for some value k.
• Homogeneity of degree one implies constant returns to scale.
• Homogeneous implies homothetic, but not conversely. For instance, $f(x_1,x_2)=x_1x_2+1$ is homothetic but not homogeneous.
• A function is homogeneous if it is homogeneous of degree $\alpha$ for some $\alpha$ $\epsilon$ R.
• A function, f is linearly homogeneous if it is homogeneous of degree 1. Along any ray from the origin, a homogeneous function defines a power function. If f is linearly homogeneous, then the function defined along any ray from the origin is a linear function.