4.3 Cobb Douglas production function.

Model:

$$y = A \times x_1^{\alpha_1} \times x_2^{\alpha_2} \times x_3^{\alpha_3},$$

where

• y is the output
• A denotes the state of technical knowledge
• x_i denotes the quantity of input i
• $\alpha_i$ is the parameter to be estimated (like an elasticity of output with respect to input i)

Note: the response is output. Another multiplicative model.

Define returns to scale as $r = \sum\alpha_i.$