Question

is there any relation between the consumer preferences and two variable input profuction model?

Answer 1

I guess the question really is whether there are any similarities between consumer preferences and two factor input production model.

The answer is yes.

Let's assume that a consumer has two goods that she consumes to derive utility and has a fixed amount of money using which she can buy these goods. Similarly, a firm would have a fixed budget using which to buy the two factors of production (say labour and capital) to employ in production process.

Hence the first point of similarity is a fixed amount of money that can be spent to generate utility or production.

The second point of similarity is that different combinations of goods yield different amounts of utility for the consumer, and different combinations of factors of production yield different amounts of production.

The third point of similarity is that as the amount (or proportion) of one good increases in the consumer's bundle its marginal utility starts to fall after a point. When the proportion of labour (or capital) increases in a production set up its marginal productivity goes down beyond a point.

Hence the objective the consumer has (as does a firm) is to maximise utility (or production) by consuming a combination of two goods (or employing a combination of two factors of production), subject to availability of a fixed amount of money to spend on them.