Question

What is production function? and what is the importance of cobb duglas production function?

Answer 1

Production function shows how much of inputs (Labour or Capital) you are using while producing. Production itself is the function of n-number of inputs: Q=(x1,x2,...,Xn) where Q is quantity produced and X1, X2,...,Xn are the numbers (types) of inputs used.

Answer 2

Cobb Duglas production function measures how much each input contributes to the total amount of quantity produced:
\[Q=AL ^{\alpha}C ^{\alpha-1}\]

Answer 3

Where beta is alpha minus 1

Answer 4

Cobb Duglas is used to measure the relationship between two inputs (factors) used and its contribution to the total production.

Answer 5

A production function is a mathematical expression that describes how large the production will be if one uses different combinations of the input factors. Usually labor (L) and capital (K) are variables in the production function.

Here is an example of a production function
Q=f(K,L)
where Q is the total production for given imputs K,L

As for cobb-Douglas production function, it is widely used becouse it has very attractive mathematical characteristicssuch as diminishing marginal returns ( http://en.wikipedia.org/wiki/Diminishing_returns) to either factor of production and some other very convenient characteristics that enables analytical solutions.
However some say that cobb-Douglas production function lacks microfoundations but unfortunatelly i cant tell you if it is valid or not.

I hope i helped have fun.