# Isn't the parameter A denoting technological progress from Cobb-Douglas already included in alpha and beta?

Does it not follow that if capital is better performing than labor it would be used more frequently? What exactly does parameter A actually mean, then?

• In crude terms $A$ in $Y=AL^\alpha K^\beta$ captures impact of quality whereas $\alpha, \beta$ will capture impact of quantity. Two different production units with same $\alpha, \beta$ and same quantity of $L, K$ employed can have different output if, say, the workers in one factory are more skilled (or the machines/tools are more advanced) - i.e., higher $A$.. – Dayne Dec 16 '20 at 13:23
• A being a general parameter of quality is then the average of the parameters of quality for both L and K? Still, do alpha & beta not capture the ideas sufficiently (since their sum is equal to 1, the addend that is more efficient will be greater than 0.5) @Dayne – asdfghjkl Dec 16 '20 at 13:31
• $\alpha>\beta$ simply means that an extra unit of labor contributes more than an extra unit of capital. So in relative terms $L$ is better than $K$ but $A$ allows you to compare capture improvement within one (or both) factor(s). – Dayne Dec 16 '20 at 13:35
• Why is it so that α>β means that an extra unit of labor contributes more than an extra unit of capital? Why would an economy use more of a factor that is less efficient? – asdfghjkl Dec 16 '20 at 13:40
• because of the declining marginal product for both factors. – Dayne Dec 16 '20 at 14:20

However, in macroeconomics it is often equated to the $$A$$ parameter (see Romer Advanced Macroeconomics chapter 1 where technology growth and growth of $$A$$ for Cobb-Douglass function is used interchangeably throughout the chapter and also elsewhere in the book).
In the macroeconomic sense they are not technology and the technology would be solely captured by $$A$$. In macro sense the $$L^{\alpha}K^{\beta}$$ would be some sort of ‘vanilla’ production which is then augmented by technology parameter $$A$$ (which could by the way also enter in a way that would augment only labor ($$(AL)^{\alpha}K^{\beta}$$) or only capital ($$L^{\alpha}(AK)^{\beta}$$) or also both ($$AL^{\alpha}K^{\beta}$$)).