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B Y
M I K E F L A D L I E N
M U S C A T I N E H I G H S C H O O L
Variable Costs
Review of Production Function
A mathematical relation between the production of a good or service and the inputs used. A production function captures the general relation between total production and one or more inputs. The standard production function includes labor and capital as the inputs. However, a production function is general enough that any number of inputs can be included.
I like to say that the production function increases at a decreasing rate or that more and more provide less and less.
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Total and Marginal Product
MARGINAL PRODUCT: The change in the quantity of total product resulting from a unit change in a variable input, keeping all other inputs unchanged. Marginal product, usually abbreviated MP, is found by dividing the change in total product by the change in the variable input. Marginal product lies at the very foundation of the analysis of short-run production and the subsequent explanation of the law of supply and the upward-sloping supply curve, using the law of diminishing marginal returns.
Total Product Marginal Product
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Marginal Product Curve
MARGINAL PRODUCT CURVE: A curve that graphically illustrates the relation between marginal product and the quantity of the variable input, holding all other inputs fixed. This curve indicates the incremental change in output at each level of the variable input. The marginal product curve is one of three related curves used in the analysis of the short-run production of a firm. The other two are total product curve and average product curve. The marginal product curve plays in key role in the economic analysis of short-run production by a firm in large part because economists are generally obsessed with marginal changes in production.
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Marginal and Average Product
VERAGE PRODUCT: The quantity of total output produced per unit of a variable input, holding all other inputs fixed. It is found by dividing total product by the quantity of the variable input. Average product, abbreviated AP also goes by the alias of average physical product (APP), so don't be confused by the extra term (physical). Compare this term with marginal product and average revenue product when you have a chance. If you haven't yet come across the term, then you really should spend some time with the law of diminishing marginal returns. The average-marginal rule is also worth a look.
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Average Variable Cost
Each unit of labor is paid $10
AVERAGE VARIABLE COST: Total variable cost per unit of output, found by dividing total variable cost by the quantity of output. Average variable cost, abbreviated AVC, decreases with additional production at relatively small quantities of output, then eventually increases with relatively larger quantities of output. This pattern is illustrated by a U-shaped average variable cost curve. The logic behind this decrease-increase U-shaped pattern can be found with a closer examination of the law of diminishing marginal returns, average product, and the average-marginal rule. You should also check out marginal cost.
Quantityof Labor
Wage is $10
Total Product
Average Variable
Cost
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Graph of Average variable Cost
AVERAGE VARIABLE COST CURVE: A curve that graphically represents the relation between average variable cost incurred by a firm in the short-run production of a good or service and the quantity produced. This curve is constructed to capture the relation between average variable cost and the level of output, holding other variables, like technology and resource prices, constant. The average variable cost curve is one the three average curves. The other two are average total cost curve and average fixed cost curve.
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Marginal cost
MARGINAL COST: The change in total cost (or total variable cost) resulting from a change in the quantity of output produced by a firm in the short run. Marginal cost indicates how much total cost changes for a give change in the quantity of output. Because changes in total cost are matched by changes in total variable cost in the short run (remember total fixed cost is fixed), marginal cost is the change in either total cost or total variable cost. Marginal cost, usually abbreviated MC, is found by dividing the change in total cost (or total variable cost) by the change in output.
Wage Marginal Product
Marginal Cost
10 4 2.5
10 8 1.25
10 6 1.67
10 4 2.5
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Graph of Marginal Cost
The marginal cost curve resembles a Nike swoosh. In this case, MC equals W/MP. This is shorthand for, dVC/dQ or dTC/dQwhere d means “delta” or change in.
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Marginal Cost and Average Variable Cost
Note how the marginal cost intersects the average variable cost curve at the lowest point.
It should be obvious that the marginal product curve and the marginal cost curves are mirror images of each other. Likewise, so are average product and average variable cost.
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Marginal Cost
Average Variable Cost
Variable Cost curve
AVERAGE VARIABLE COST CURVE: A curve that graphically represents the relation between average variable cost incurred by a firm in the short-run production of a good or service and the quantity produced. This curve is constructed to capture the relation between average variable cost and the level of output, holding other variables, like technology and resource prices, constant. The average variable cost curve is one the three average curves. The other two are average total cost curve and average fixed cost curve.
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