marginal revenue product (MRP) theory: definition and calculation of marginal revenue product

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Marginal Revenue Product (MRP) Theory

This section explores the Marginal Revenue Product (MRP) theory, a key concept in understanding labour demand. It explains how firms determine the quantity of labour to employ based on the additional revenue generated by each additional unit of labour.

Definition of Marginal Revenue Product (MRP)

Marginal Revenue Product (MRP) is the additional revenue generated by employing one more unit of labour. It is calculated by multiplying the marginal product of labour (MPL) by the marginal revenue (MR).

Mathematically, MRP is represented as:

$$MRP = MPL \times MR$$

Understanding the Components

  • Marginal Product of Labour (MPL): This is the additional output produced by employing one more unit of labour, holding other inputs constant.
  • Marginal Revenue (MR): This is the additional revenue generated from selling one more unit of output.

Calculating Marginal Revenue Product (MRP)

To calculate MRP, you need to determine both the MPL and the MR. The calculation involves the following steps:

  1. Calculate the Total Product (TP): This is the total quantity of output produced.
  2. Calculate the Marginal Product (MP): This is the change in TP resulting from a one-unit increase in labour. $$MP = \Delta TP / \Delta L$$
  3. Calculate the Marginal Revenue (MR): This is the change in total revenue resulting from a one-unit increase in output. $$MR = \Delta TR / \Delta Q$$
  4. Calculate the Marginal Revenue Product (MRP): Multiply the MPL by the MR. $$MRP = MPL \times MR$$

Example Calculation

Consider a firm that employs 10 workers. The following data is available:

Number of Workers (L) Total Product (TP) Marginal Product (MP) Marginal Revenue (MR)
0 0 - -
1 5 5 20
2 12 7 40
3 20 8 60
4 25 5 70
5 28 3 75
6 30 2 77
7 30 0 76
8 28 -2 73
9 22 -6 68
10 15 -7 62

In this example, the MRP is calculated as follows:

  • L = 1: MPL = 5, MR = 20, MRP = 5 x 20 = 100
  • L = 2: MPL = 7, MR = 40, MRP = 7 x 40 = 280
  • L = 3: MPL = 8, MR = 60, MRP = 8 x 60 = 480
  • L = 4: MPL = 5, MR = 70, MRP = 5 x 70 = 350
  • L = 5: MPL = 3, MR = 75, MRP = 3 x 75 = 225
  • L = 6: MPL = 2, MR = 77, MRP = 2 x 77 = 154
  • L = 7: MPL = 0, MR = 76, MRP = 0 x 76 = 0
  • L = 8: MPL = -2, MR = 73, MRP = -2 x 73 = -146

The MRP is positive up to a certain point, where it then becomes negative. This indicates that the firm is employing too many workers, as the additional revenue generated by each additional worker is less than the cost of employing them.

The MRP Curve

The MRP curve typically has an inverted U-shape. It initially rises as more labour is employed (due to increasing marginal productivity), reaches a peak, and then falls as marginal productivity declines.

Suggested diagram: MRP Curve showing an inverted U-shape. The vertical axis represents MRP and the horizontal axis represents the quantity of labour.

Implications for Labour Demand

The MRP theory suggests that firms will continue to hire labour as long as the MRP is greater than or equal to the wage rate. If the wage rate is below the MRP, the firm will hire more workers. If the wage rate is above the MRP, the firm will hire fewer workers.