A homogeneous production function (HPF) of degree k implies that all factors of production are increased in a given proportion t, outputs are also increased in the proportion t

Q (tx

k = 1 Constant

k > 1 Increasing

k < 1 Decreasing

1. Partial derivatives of homogeneous function of degree k are homogeneous of degree k-1.

2. Isoquants of HPF possess the similar properties of indifference curves of utility function.

3. Expansion path of HPF is also the straight line through the origin, as RTS = f

Linear Homogeneous Production Function (LHPF) of 1st degree implies that if all factor of production are increased in a given proportion, outputs are also increased in same proportion i.e.

Q (tx

A function which is homogenous of degree one is said to be linearly homogeneous. This does not imply that the production function is linear.

^{k}Q (tx

_{1},tx_{2}) = t^{k}Q (x_{1},x_{2}) .__Value of k____Return to Scale__k = 1 Constant

k > 1 Increasing

k < 1 Decreasing

**Properties of HPF:**1. Partial derivatives of homogeneous function of degree k are homogeneous of degree k-1.

2. Isoquants of HPF possess the similar properties of indifference curves of utility function.

3. Expansion path of HPF is also the straight line through the origin, as RTS = f

_{1}/f_{2}depends on the ratio in which inputs are used.**Linear Homogeneous Production Function:**Linear Homogeneous Production Function (LHPF) of 1st degree implies that if all factor of production are increased in a given proportion, outputs are also increased in same proportion i.e.

Q (tx

_{1},tx_{2}) = t. Q (x_{1}, x_{2})A function which is homogenous of degree one is said to be linearly homogeneous. This does not imply that the production function is linear.

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