1.5 Output and Costs
** This note is summarized by Hui Wang.
Important reference Study Guides of Stalla Review for CFA Exams
Learning Outcomes
The candidate should be able to:
a. differentiate between short-term and long-term decision time frames;
b. describe and explain the relations among total product of labor, marginal product
of labor, and average product of labor, and describe increasing and decreasing
marginal returns;
c. distinguish among total cost (including both fixed cost and variable cost),
marginal cost, and average cost, and explain the relations among the various cost
curves;
d. explain the firm’s production function, its properties of diminishing returns and
diminishing marginal product of capital, the relation between short-run and longrun costs, and how economies and diseconomies of scale affect long-run costs.
Production decision time frame
Short run is the time span between one where the quantity of no input is variable
and one where the quantities of all inputs are variable. Simply put, at least one
input is fixed.
Long run is a time frame in which the quantities of all inputs can be changed. Put
another way, there is no fixed input in the long run.
Sunk cost
We use the concept of sunk cost to describe such investment- the cost already
incurred which cannot be recovered regardless of future events. When a firm
makes production decisions, it should ignore sunk cost. The only relevant costs
that influence its decisions are the short-run cost of changing variable inputs and
the long-run cost of changing its plant.
Short-run production
The production function is a table, a graph, or an equation showing the maximum
product output achieved from any specified set of inputs. The function
summarizes the characteristics of existing technology at a given time.
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Average product (AP) is the ratio of total product to the total quantity of an input
used to produce the product. For example, the average product of labor is
AP =
, holding K constant
Marginal product (MP) is the change in output that results from one additional
unit of a factor of production, all other factors remaining constant. For example,
the marginal product of labor is
MP =
or MP =
, holding K constant
The general relation between marginal product and average product is:
MP < AP
AP declines
MP > AP
AP rises
MP = AP
AP is maximized
This average-marginal relation for production is closely tied to the law of
diminishing marginal returns, which refers to how the marginal product of an
input usually decreases as more of the input is used.
Isoquants
An isoquant is a graph of all possible combinations of inputs that result in the
production of a given level of output. Isoquants have several properties: 1) the
farther the isoquant is from the origin, the greater the output it represents; 2)
isoquants are always downward-sloping and convex to the origin; 3) two different
isoquants can never cross; 4) any combination of inputs above or to the right of an
isoquant results in more output than any point on the isoquant.
If the distance between isoquants increases as output increases, the firm’s
production function is exhibiting decreasing returns to scale; if the distance is
decreasing as output increases, the firm is experiencing increasing returns to scale.
Short-run cost
We need to analyze three cost concepts: fixed, variable, and total. Total fixed cost
(TFC) is the cost of production that does not change with changes in the quantity
of output produced by a firm in the short run. Total variable cost (TVC) is the cost
of production that varies directly in proportion to the number of units produced.
Variable cost often includes labor expenses and raw material cost. Total cost (TC)
is the sum of total fixed and total variable costs.
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Total fixed cost can be represented by a horizontal line. Variable costs start at
original point, increase with output at a decreasing rate and then increase with
output at an increasing rate. The total cost curve is the vertical summation of the
fixed cost curve and the total variable cost curve.
Average fixed cost (AFC) is the total fixed costs divided by the quantity (Q) of
units produced. Average fixed cost is a per-unit measure of fixed costs. Average
variable cost (AVC) is a firm’s variable costs divided by the quantity (Q) of total
units of output. Initially, average variable cost decreases as output increases.
However, as output increases, at some point of increased production, average
variable cost rises,
AVC=
=
Where L is the number of variable inputs used in the production, and w is per unit
cost of L. We defined average product as:
AP=
Therefore AP is the inverse of L/Q. Now we can rewrite AVC as
AVC= W*
So we can think AVC as the inverse of average product times the cost per unit of
input. Since average product initially increases with output, reaches a maximum,
and then begins to decline. Given the inverse relationship between AVC and AP,
AVC mirrors the behavior of AP- when AP increase, AVC decreases; when AP
decreases, AVC increases. So we expect AVC to initially decrease, hit a minimum,
and then increase.
Average total (ATC) is total cost divided by output. ATC can also be derived by
the sum of AVC and AFC,
ATC=
=
=
+
= AFC+AVC
The marginal cost (MC) of an additional unit of output is the cost of the additional
inputs needed to produce that output. Mathematically, the marginal cost is the
derivative of total production costs with respect to the level of output.
If ΔTVC is the change in total variable costs resulting from a change in output of
ΔQ and if ΔTFC is the change in total fixed costs resulting from a change in output
of ΔQ then,
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MC=
But TFC is constant in the short-run, which means that ΔTFC is zero; therefore
MC=
= w*
Recall that we defined MP as
MP=
Therefore we can rewrite MC as
MC= w*
Average total cost and average variable cost initially decreases, reach a minimum,
and then increase as output increases. The average total cost curve is the vertical
summation of the average fixed cost and the average variable cost curves. Marginal
cost intersects with both average total cost and average variable cost at their
minimum level. Moreover, when marginal cost is below the average cost, average
cost falls and when marginal cost is above the average cost, average cost rises.
Average total cost achieves its minimum at a higher output rate than average
variable cost because the increases in average variable cost are, up to a point, more
than offset by decreases in average fixed cost.
Further discussion in cost curves
There are two reasons for the U shape of the average total cost curve,
(1) As output increases, the total fixed cost is spread over a larger quantity of
output and thus the average fixed cost declines.
(2) The production will eventually enter the phase of diminishing returns.
The position of a firm’s short-run cost curves may vary with the following two
factors:
(1) Technology.
(2) Prices of inputs.
Cost curves and product curves
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AP and MP
AP
MP
0
Variable input
Cost
MC
0
Phase A
Phase B
AVC
Output
Phase C
Phase A: rising MP and falling MC; rising AP and falling AVC
Phase B: falling MP and rising MC; rising AP and falling AVC
Phase C: falling MP and rising MC; falling AP and rising AVC
A firm that seeks to maximize its profit will choose to organize production at
Phase B.
Long-run cost
In the long-run all inputs are variable, and firms have options to build plants of
different size. The long-run average cost function (LAC) shows the minimum cost
per unit of all output levels when any desired size plant is built. Any point on the
long-run average cost curve is the lower-cost point of the corresponding short-run
cost function for the given output level.
The long-run total cost function represents the relationship between long-run total
cost and output. The long-run total cost of a given output level equals the long-run
average cost times output. The long-run total cost curve pass through the origin.
The long-run marginal cost function represents the change in the long-run total
cost of producing a good or service resulting from a change in the quantity of
output produced.
Economies of scale and diseconomies of scale
Economies of scale: the increase in efficiency of production as the number of
goods being produced increases. With given factor prices, if the percentage
increase in output exceeds the percentage increase in all factors of production, the
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firm is experiencing economies of scale. Economies of scale arise from greater
specialization of both labor and capital.
Diseconomies of scale: a firm may grow beyond the scale of production that
minimizes long-run average cost and produce goods or services at increased perunit costs. Diseconomies of scale arise from the difficulty of managing a very large
firm: there will be greater challenge of organizing the firm and greater cost of
communicating information.
Constant returns to scale: a production function exhibits constant returns to scale if
changing all inputs by a positive proportional factor has the effect of increasing
output by that factor.
The general case is that: a new start-up firm will first experience decreasing
average cost as it expands its production, then the firm will reach its minimum
Scale economies and returns to scale generally produce the U-shaped long-run
marginal cost curve.
Term
Total Fixed cost
Total Variable cost
Total cost
Symbol
TFC
TVC
TC
Equation
Marginal cost
MC
MC =
Average fixed cost
AFC
AFC =
Average variable cost
AVC
AVC =
Average total cost
ATC
ATC = AFC + AVC
TC = TFC + TVC
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Exercise Problems: (provided by Stalla PassMaster for CFA Exams.)
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EXPLANATION
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