# Why are production functions linear in technology?

Economists often assume a production function of the form $$Y = A f(K, L)$$, where $$Y$$ is output, $$K$$ is capital, $$L$$ is labour and $$A$$ is technology. This form of production function can describe both nation-wide production or firm-wide production.

Now, my question is, why is the production function assumed to be linear in the technology $$A$$? For example, can't we have a production function of the form

$$Y = \sum_{i = 1}^n A^{\alpha_i} K^{\beta_i} L^{1-\beta_i} \quad$$

where $$\alpha_1, \beta_1, \alpha_2, \beta_2, \dots \alpha_n, \beta_n$$ are exogenous parameters?

$$F=AK^{\alpha}L^{1-\alpha}$$