Graphical Comparison of Marginal and Average Product
The conceptual distinction between marginal and average product is visualized on the production function graph through two different slope measures. The marginal product at a given point is represented by the slope of the tangent to the production function at that point, mathematically denoted by the first derivative, . The average product of labor (APL) at that same point is represented by the slope of a ray drawn from the origin to the point on the function, calculated as .
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Graphical Comparison of Marginal and Average Product
Example Calculation of Average Product of Labor at Point P
A firm's production process is represented by a curve on a graph where the horizontal axis is labor input and the vertical axis is total output. The curve starts at the origin (0,0), rises, and then flattens. Four points (A, B, C, and D) are marked along the curve in order of increasing labor input. A straight line (a ray) is drawn from the origin to each of these points. The ray to point B is the steepest among the four. The ray to point A is less steep than B. The rays to points C and D are progressively flatter than the ray to point B. At which point is the average output per unit of labor maximized?
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Interpreting Production Efficiency
Consider a production process represented by a curve on a graph where the horizontal axis measures labor input and the vertical axis measures total output. True or False: If Point X on the curve represents a lower quantity of labor input than Point Y, then the average output per unit of labor must be lower at Point X than at Point Y.
A production process is described by a function where total output depends on the amount of labor input. At 10 hours of labor, the total output is 50 units. At 20 hours of labor, the total output is 120 units. At 30 hours of labor, the total output is 150 units. Based on this information, how does the average product of labor change as labor input increases from 10 to 20 hours, and then from 20 to 30 hours?
On a standard production function graph with labor input on the horizontal axis and total output on the vertical axis, match each graphical feature to the economic concept it represents.
Analyzing Study Productivity
A firm's production is represented on a graph where the horizontal axis measures hours of labor and the vertical axis measures total units of output. Point A on the graph represents 10 hours of labor producing 100 units of output. Point B on the graph represents 20 hours of labor producing 150 units of output. Which statement correctly compares the average product of labor at these two points?
A manager is analyzing a production graph where the horizontal axis represents the number of workers and the vertical axis represents total units produced. The company is currently operating at Point A. The manager proposes hiring more workers to move to Point B, which would increase the total units produced. However, a straight line drawn from the origin (0,0) to Point B is noticeably flatter than a straight line drawn from the origin to Point A. If the manager's primary goal is to maximize the average output per worker, what is the best evaluation of this proposal?
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Graphical Comparison of Marginal and Average Product
A farm manager is deciding whether to hire one additional farmhand to help with the harvest. The farm currently employs 10 farmhands who collectively harvest 500 bushels of apples per day. To make the most profitable decision about hiring an 11th worker, which of the following pieces of information is most crucial for the manager to determine?
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A company's management notes that the average output per employee for the entire year was higher than the previous year's average. From this single piece of information, they can confidently conclude that the last employee hired during the year produced more output than the company's new yearly average.
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Match each scenario with the productivity concept it best illustrates.
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A factory employs 5 workers. The output produced by the 5th worker alone is 20 units. If the average output per worker for all 5 workers is 25 units, it must be true that the average output per worker for the first 4 workers was greater than 25 units.
If the output generated by one additional worker is greater than the average output of the existing workforce, what will happen to the average output per worker once this new worker is included in the calculation?
Learn After
Marginal Product of Labour
The Condition for a Diminishing Average Product
Graphical Evidence of MP < AP on a Concave Function
Consider a standard production function graphed with the quantity of an input on the horizontal axis and the quantity of output on the vertical axis. At a specific point 'P' on this function's curve, a straight line (Line 1) is drawn tangent to the curve at that point. A second straight line (Line 2) is drawn from the origin (0,0) directly to point 'P'. Based on the geometric properties of this graph, what do the slopes of these two lines represent?
On a graph of a production function, with input quantity on the horizontal axis and output quantity on the vertical axis, consider a specific point on the curve. If the line tangent to the curve at this point is steeper than the line drawn from the origin (0,0) to this same point, it implies that the addition of one more unit of input will cause the average output per unit of input to increase.
On a standard production function graph, which plots total output (vertical axis) against the quantity of a single variable input (horizontal axis), match each graphical feature with the economic concept it represents.
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Analyzing the Relationship Between Marginal and Average Productivity
A firm is operating at a point on its production function where the output gained from adding one more unit of a variable input is less than the current average output per unit of that input. On a standard graph of this production function (with input on the horizontal axis and output on the vertical axis), what must be true about the geometry at this specific point of operation?
On a graph of a production function where total output is plotted against the quantity of a single variable input, the point where the average output per unit of input is at its maximum occurs where the slope of the line tangent to the curve is equal to the slope of the line drawn from the origin to that same point.
Evolution of Productivity on a Production Curve
A firm's production process is represented by a typical production function graph (with input on the horizontal axis and output on the vertical axis) that is initially convex and then becomes concave. Consider the progression of production as the quantity of the variable input increases. Arrange the following statements, which describe the geometric relationship between the tangent line and the ray from the origin at a point on the curve, into the correct sequence that reflects this progression.