Question

1. An entrepreneur starts a small firm with one machine, and a small factory space and employs one person initially. With the aid of appropriate diagrams/table and theory, explain the process of production as he increases his output. Indicate clearly what law governs this process of production, the variable and the fixed factors used by this entrepreneur.

Answer 1

Let output be denoted by Q , Machine as capital by K and Labour by L.

As the entreprenuer starts with labour and 1 machine.

In short term, only labour can be increased due to limited budget so capital is a fixed factor and labour is variable factor. In short term, law of variable proportion is applicable to production process.

As per law of variable proportion taking other factors of production as fixed, with increase in variable factor, total output increases in an increasing rate then increases in a diminishing rate and finally decreases. This is because initially with increase in labour, work is sorted out and organised so there are efficiency gains. As more and more labour is added output increases but at decreasing rate due to diminishing marginal product of labor. Finally output decreases becuase excess labour causes overcrowding as fixed capital is now distributed among large workforce.

However in the long term as all factors of production become variable entreprenuer can choose or substitute between inputs. Also due to economies of scale cost advantages are  obtained. Also entreprenuer will choose combination of inputs such that costs are optimised. Let his production function be given by Cobb - Douglas production function as,

f(Q) = TKa Lb

where f(Q) is function of output as a combination of two inputs which is labour and capital. T is a any positive constant and a and b are elasticity coefficients of output for inputs.

The expansion path of the firm is given by a straight line starting from origin. If the sum of a and b is =1 then the firm is observing constant returns to scale, i.e. amount of output generated is equal to the amount of inputs.

Similarly, if a + b < 0 then decreasing returns to scale.

and a + b > 0 then increasing returns to scale.

To determine where production should be located in long term, entreprenuer has to choose combination of inputs that give same amount of output. These are called isoquants.
(Note output is determined by market requirements or market demand curve faced by the entreprenuer).

If successive isoquants are placed near to each other in the expansion path of the firm it means decreasing returns to scale are applicable. Also if succesive isoquants are distant from each other then there are increasing returns to scale.Therefore the business owner will choose that isoquant when total output is increasing or has attained maximum. At this point the isoquant is tangential to isocost curve and production is optimised.