Price Demand Relationship

We have analysed the effect of changes in the MRP of a firm on its demand for a variable input. Now let us analyse what happens when the price of the variable input changes while its MRP remains unchanged. We begin from a position of equilibrium, P = MRP; and when labour is the variable factor under discussion, this equilibrium is defined by the equation

W = MRP.

Now, if the wage rate falls while MRP remains unchanged, then the equation becomes
W < MRP

That it costs less to a firm to employ an additional unit of labour than the addition made to firm’s revenue by employing this unit. Therefore the firm’s profits would increase if this extra unit or all the extra units of labour are employed till MRP falls to become equal to the reduced wage rate. Thus the new equilibrium of W = MRP would be reached by employing extra units of labour. The firm’s demand for labour would thus increase when wage rate becomes lower. Thus the quantity demanded of a variable input increases with a fall in price of that input. Conversely when wage rate goes up, the equation becomes
W > MRP.

This means the cost to the firm of last unit of labour employed is more that what it adds to firm’s revenue. Clearly there is a loss here, which can be avoided by removing this worker and other similar units of lobour whose MRP is lower than wages and reach the equilibrium position of W = MRP.
Thus with the price of a variable input while its MRP remains unchanged, the quantity employed or demand for that input will decrease. The demand curve for a variable input is thus negatively sloped. The underlying factor behind this negative slope of short – run demand curve is the operation of law of variable proportions (diminishing returns) due to which MRP falls with additional employment and Chrystal, “in the short run, with only variable input, the firm’s demand for its variable input is negatively sloped as a result of the operation of the law of diminishing returns.”

Diagrammatic derivation of a firm’s demand curve for a variable input (labour).

Units of the variable factor labour are n\measured on the X – axis and marginal revenue product of labour is measured on the Y – axis. MRP is the marginal revenue product curve of labour, which is downward sloping showing the law of diminishing marginal productivity or the law of diminishing returns. The price per unit of the factor (wage rate) is also measured on the Y – axis.

Profit maximizing employment levels of a firm at various wage rates. At the wage rate W₀, a profit maximizing firm will employ ON₀ quantity of labour as the point of intersection E₀ shows that with employment of ON₀ units of lobour MRP = W (which is W₀ in this case). No further employment is profitable because beyond E₀, MRP becomes less than the wage rate. However, when wages fall to lower level W₁, equilibrium point (where wages are equal to MRP and profits are maximized) shifts to E₁ and employment increase to ON₁. A further fall in wage rate to W₂ pushes up employment to ON₂. Thus given the marginal revenue productivity of labour, more units of labour are employed when wage rate is lower while employments become lower when wage rate is higher.

Plotting the various quantities of lobour employed at different wage rates. We get a downward sloping demand curve for lobour. Thus, quantity of labour demanded increases from ON0 to ON1 when wage rate falls from W₀ to W₁. Conversely a rise in wages from W₂ to W₁ reduces demand from ON2 to ON₁.