Optimum Use of One variable input | Managerial Economic

Optimum use of one variable input

In this article, we will discuss about an economic concept of employment of one variable input (i.e Labour)optimally. This article includes basic concept, its assumptions and clear explanation of figure related to this concept. So let's dive into the detail explanation of this theory.

Concept:

The theory of optimum use of one variabale input is short run production concept. In short run, there is only one input is variable i. e Labour while other inputs or factors of production are assumed to be remained constant. The objective of the firm is to maximize its profit, so it explains what units of labour should be used to meet its profit maximizing objective. The firm use an additional unit of labor as long as marginal revenue exceeds marginal cost. Marginal revenue is the revenue earned by selling the product produced by additional unit of labor and marginal cost is the cost for additional unit of labour or we can say the cost of hiring an additional unit of labour or wage rate.

Assumption:

This concept of optimum use of one variable input is based on the followings assumptions:

1.  The firm used only one variable input i.e Labour,

2. The firm produces only one product,

3. The firm has profit maximizing objective,

4. The market structure is perfect competition,

5. Price of the product is constant,

6. Technology remains constant

Equilibrium condition

The firm meets its objective or reaches in equilibrium position when demand of labour is equal to supply of labour.

i.e. DL=SL

Where

DL = Demand of labour

SL = Supply of Labour

Demand of Labour (DL)

Demand of labour equals to the marginal revenue productivity of labour (MRPL). MRPL is the total revenue earned from selling the output produced by an additional unit of labour.

MRPL(DL)= MPL×Px

Where,

MRPL= Marginal revenue productivity of labour

MPL=Marginal productivity of labour

Px= price of output

Supply of Labour(SL)

Supply of labour is equals to the marginal cost of labour(MCL). MCL is the additional cost for additional unit of labour or we can say the price of labour i.e wage rate 'w'. As wage rate is assumed to be constant, MCL is horizontal line parallel to x-axis.

The optimal use of one variable input is also explained by the help of following graph.

In the above figure x-axis represents units of labour and y-axis represents wage rate. MRPL represents marginal reveneu productivity of labour and MCL represents marginal cost of labour. At point E, MRPL intersects MCL where demand of labour is equals to demand of supply. So the point E is the equilibrium point. Hence the firm having profit maximizing objective hire the OL units of labour at the wage rate of OW.

If the firm hires OL1 units of labour, MRPL will be higer than wage rate. The firm will increase the unit of labour to increase the profit untill the wage rate equals MRPL. On the other hand, if firm hires OL2 units of labour, the marginal cost of labour or wage rate will be higher than the marginal revenue productivity of labour(MRPL) which represents the loss position. Therefore it deducts the unit of labour to OL units of labour where w= MRPL.

Hence, the optimum number of employees is OL at OW wage rate.