Answer to Question #228431 in Microeconomics for Dam

Question

If a firm producing in long run using capital and labour inputs,how the least cost combination of the input will be determined? show it mathematically and graphically

Answer 1

Basic Principle of Least Cost Combination: It states that a rational firm tends to combine different factors of production in a strategic way to ensure least input but highest or maximum outputs with very least cost possible. This combination is called “Least Cost Combination”.

 

Various assumptions are made under this principle: 1) factors of production are labor and capital, 2) Units of these factors of production are homogenous, 3) prices of these factors of production are constant, 4) the company aims at profit maximization.

Mathematically, the least cost combination in the presented scenario can be represented as follows:

1.     Marginal Rates of Substitution= {Number of unit replaced resources (X2)/ Number of unit added resource (X1)}

MRS=X2/X1

2.     Price Ratio (PR)=

Cost per unit of added resource (Price of X1)/ Cost per unit of replaced resource (Price of X2)

PR= Price of X1/ Price of X2

Assuming the company in question is producing computers and utilizing programmers as labor, then we can capture this least cost combination as follows:

 

Graphically Least Cost Combination is shown as captured below: