Marginal Product of Labor - Relation Between MP_L and AP_L

Relation Between MP_L and AP_L

The average product of labor is the total product of labor divided by the number of units of labor employed or Q/L. The average product of labor is a common measure of labor productivity. The AP_L curve is shaped like an inverted “u”. At low production levels the AP_L tends to increases as additional labor is added. The primary reason for the increase is specialization and division of labor. At the point the AP_L reaches its maximum value AP_L equals the MP_L. Beyond this point the AP_L falls.

During the early stages of production MP_L is greater than AP_L. When the MP_L is above the AP_L the AP_L will increase. Eventually the MP_L reaches it maximum value at the point of diminishing returns. Beyond this point MP_L will decrease. However, at the point of diminishing returns the MP_L is still above the AP_L and AP_L will continue to increase until MP_L equals AP_L. When MP_L is below AP_L, AP_L will decrease.

Graphically the AP_L curve can be derived from the total product curve by drawing secants from the origin that intersect (cut) the total product curve. The slope of the secant line equals the average product of labor (Slope = dQ/dL). The slope of the curve at each intersection marks a point on the average product curve. The slope increases until the line reaches a point of tangency with the total product curve. This point marks the maximum average product of labor. It also marks the point where MP_L (which is the slope of the total product curve) equals the AP_L (the slope of the secant). Beyond this point the slope of the secants become progressively smaller as AP_L declines. The MP_L curve intersects the AP_L curve from above at the maximum point of the AP_L curve. Thereafter, the MP_L curve is below the AP_L curve.