unit v production costs (chapter 12). in this chapter, look for the answers to these questions: ...
TRANSCRIPT
Unit V
Production Costs (Chapter 12)
In this chapter, look for the answers to these questions:
What is a production function? What is marginal product? How are they related?
What are the various costs, and how are they related to each other and to output?
How are costs different in the short run vs. the long run?
What are “economies of scale”?
Short Run and Long run
• The Short Run: Fixed Plant– The short run is a time frame in which the
quantities of some resources are fixed. – In the short run, a firm can usually change the
quantity of labor it uses but not the quantity of capital.
• The Long Run: Variable Plant– The long run is a time frame in which the
quantities of all resources can be changed.– A sunk cost is irrelevant to the firm’s decisions.
Short Run Production
• To increase output with a fixed plant, a firm must increase the quantity of labor it uses.
• We describe the relationship between output and the quantity of labor by using three related concepts:
– Total product
– Marginal product
– Average product
The Production Function
• A production function shows the relationship between the quantity of inputs used to produce a good, and the quantity of output of that good.
• It can be represented by a table, equation, or graph.
• Example:– Farmer Jack grows wheat. – He has 5 acres of land. – He can hire as many workers as he wants.
The Production Function
• Total Product
– Total product (TP) is the total quantity of a good produced in a given period.
– Total product is an output rate—the number of units produced per unit of time.
– Total product increases as the quantity of labor employed increases.
The Production Function• The figure shows
the total product and the total product curve.
• Points A through H on the curve correspond to the columns of the table.
• The TP curve is like the PPF: It separates attainable points and unattainable points.
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5
No. of workers
Qu
anti
ty o
f o
utp
ut
EXAMPLE: Farmer Jack’s Production Function
30005
28004
24003
18002
10001
00
Q (bushels
of wheat)
L
(no. of workers)
Marginal Product• Marginal product is the change in total product
that results from a one-unit increase in the quantity of labor employed. – Marginal product tells us the contribution to total product
of adding one more worker. – E.g., if Farmer Jack hires one more worker,
his output rises by the marginal product of labor. – Notation:
∆ (delta) = “change in…”– Examples:
∆Q = change in output, ∆L = change in labor – Marginal product of labor (MPL) = ∆Q
∆L
Marginal Product
• The figure shows total product and marginal product.
• We can illustrate marginal productas the orange bars that form steps along the total product curve.
• The height of each step represents marginal product.
Marginal Product
• The table calculates marginal product and the orange bars in part (b) illustrate it.
• Notice that the steeper the slope of the TP curve, the greater is marginal product.
Marginal Product• The total product
and marginal product curves in this figure incorporate a feature of all production processes:– Increasing
marginal returns initially
– Decreasing marginal returns eventually
– Negative marginal returns
30005
28004
24003
18002
10001
00
Q
(bushels of wheat)
L
(no. of workers)
EXAMPLE: Total & Marginal Product
200
400
600
800
1000
MPL
∆Q = 1000∆L = 1
∆Q = 800∆L = 1
∆Q = 600∆L = 1
∆Q = 400∆L = 1
∆Q = 200∆L = 1
MPL equals the slope of the production function.
Notice that MPL diminishes as L increases.
This explains why the production function gets flatter as L increases.
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5
No. of workers
Qu
anti
ty o
f o
utp
ut
EXAMPLE: MPL = Slope of Prod Function
30005200
28004400
24003600
18002800
100011000
00
MPL
Q
(bushels of wheat)
L
(no. of workers)
Why MPL Is Important• Rational people think at the margin.• When Farmer Jack hires an extra worker,
– his costs rise by the wage he pays the worker– his output rises by MPL
• Comparing them helps Jack decide whether he would benefit from hiring the worker.
Increasing Marginal Returns
• Increasing marginal returns occur when the marginal product of an additional worker exceeds the marginal product of the previous worker.
• Increasing marginal returns occur when a small number of workers are employed and arise from increased specialization and division of labor in the production process.
Why MPL Diminishes• Decreasing marginal returns occur when
the marginal product of an additional worker is less than the marginal product of the previous worker.
– E.g., Farmer Jack’s output rises by a smaller and smaller amount for each additional worker. Why?
– If Jack increases workers but not land, the average worker has less land to work with, so will be less productive.
• In general, MPL diminishes as L rises whether the fixed input is land or capital (equipment, machines, etc.).
Why MPL Diminishes• Decreasing marginal returns are so pervasive that
they qualify for the status of a law:• The law of decreasing returns states that:
As a firm uses more of a variable input, with a given
quantity of fixed inputs, the marginal product of the
variable input eventually decreases.
SHORT-RUN PRODUCTION
The figure graphs the average product against the quantity of labor employed.
The average product curve is AP.
When marginal product exceeds average product, average product is increasing.
SHORT-RUN PRODUCTION
When marginal product is less than average product, average product is decreasing.
When marginal product equals average product, average product is at its maximum.
SHORT-RUN COST
• To produce more output in the short run, a firm employs more labor, which means the firm must increase its costs.
• We describe the relationship between output and cost using three cost concepts: – Total cost– Marginal cost– Average cost
SHORT-RUN COST
• Total Cost
– A firm’s total cost (TC) is the cost of all the factors of production the firm uses.
• Total Cost divides into two parts:– Fixed cost (FC) is the cost of a firm’s fixed
factors of production used by a firm—the cost of land, capital, and entrepreneurship. o Fixed costs don’t change as output changes.
SHORT-RUN COST
– Variable cost (VC) is the cost of the variable factor of production used by a firm—the cost of labor. o To change its output in the short run, a firm must
change the quantity of labor it employs, so total variable cost changes as output changes.
o Total cost is the sum of total fixed cost and total variable cost. That is,
TC = FC + VC
SHORT-RUN COST
Fixed cost (FC) is constant—it graphs as a horizontal line.
Total cost (TC) also increases as output increases.
Variable cost (VC) increases as output increases.
SHORT-RUN COST
The vertical distance between the total cost curve and the total variable cost curve is total fixed cost, as illustrated by the two arrows.
Marginal Cost
• Marginal Cost (MC) is the increase in Total Cost from producing one more unit:
∆TC∆Q
MC =
Marginal cost tells us how total cost changes as total product changes.
Recall, Marginal Cost (MC) is the change in total cost from producing one more unit:
Usually, MC rises as Q rises, due to diminishing marginal product.
Sometimes (as here), MC falls before rising.
(In other examples, MC may be constant.)
EXAMPLE: Marginal Cost
6207
4806
3805
3104
2603
2202
1701
$1000
MCTCQ
140
100
70
50
40
50
$70
∆TC∆Q
MC =
SHORT-RUN COST
• Average Cost– There are three average cost concepts:– Average fixed cost (AFC) is total fixed
cost per unit of output. – Average variable cost (AVC) is total
variable cost per unit of output. – Average total cost (ATC) is total cost per
unit of output.
SHORT-RUN COST
•The average cost concepts are calculated from the total cost concepts as follows:
TC = TFC + TVC
•Divide each total cost term by the quantity produced, Q, to give
ATC = AFC + AVC
Q Q QTC = TFC + TVC
or,
A C T I V E L E A R N I N G 1: Costs Fill in the blank spaces of
this table.
210
150
100
30
10
VC
43.33358.332606
305
37.5012.501504
36.672016.673
802
$60.00$101
n.a.n.a.n.a.$500
MCATCAVCAFCTCQ
60
30
$10
Use AFC = FC/QUse AVC = VC/QUse relationship between MC and TCUse ATC = TC/Q
First, deduce FC = $50 and use FC + VC = TC.
A C T I V E L E A R N I N G 1: Answers
210
150
100
60
30
10
$0
VC
43.33358.332606
40.003010.002005
37.502512.501504
36.672016.671103
40.001525.00802
$60.00$10$50.00601
n.a.n.a.n.a.$500
MCATCAVCAFCTCQ
60
50
40
30
20
$10
EXAMPLE: Average Fixed Cost
1007
1006
1005
1004
1003
1002
1001
14.29
16.67
20
25
33.33
50
$100
n.a.$1000
AFCFCQ Average fixed cost (AFC) is fixed cost divided by the quantity of output:
AFC = FC/Q
Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units.
EXAMPLE: Average Variable Cost
5207
3806
2805
2104
1603
1202
701
74.29
63.33
56.00
52.50
53.33
60
$70
n.a.$00
AVCVCQ Average variable cost (AVC) is variable cost divided by the quantity of output:
AVC = VC/Q
As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises.
EXAMPLE: Average Total Cost
88.57
80
76
77.50
86.67
110
$170
n.a.
ATC
6207
4806
3805
3104
2603
2202
1701
$1000
74.2914.29
63.3316.67
56.0020
52.5025
53.3333.33
6050
$70$100
n.a.n.a.
AVCAFCTCQ Average total cost (ATC) equals total cost divided by the quantity of output:
ATC = TC/Q
Also,
ATC = AFC + AVC
Usually, as in this example, the ATC curve is U-shaped.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
EXAMPLE: Average Total Cost
88.57
80
76
77.50
86.67
110
$170
n.a.
ATC
6207
4806
3805
3104
2603
2202
1701
$1000
TCQ
EXAMPLE: The Various Cost Curves Together
AFCAVCATC
MC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
SHORT-RUN COST
REMEMBER -- The marginal cost curve (MC) intersects the average variable cost curve and the average total cost curve at their minimum points.
The vertical distance between these two curves is equal to average fixed cost, as illustrated by the two arrows.
SHORT-RUN COST
• Why the Average Total Cost Curve Is U-Shaped
– Average total cost, ATC, is the sum of average fixed cost, AFC, and average variable cost, AVC. –The shape of the ATC curve combines the shapes of the AFC and AVC curves. –The U shape of the average total cost curve arises from the influence of two opposing forces:
o Spreading total fixed cost over a larger outputo Decreasing marginal returns
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
EXAMPLE: Why ATC Is Usually U-shaped
As Q rises:
Initially, falling AFC pulls ATC down.
Eventually, rising AVC pulls ATC up.
EXAMPLE: ATC and MC
ATCMC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
When MC < ATC,
ATC is falling.
When MC > ATC,
ATC is rising.
The MC curve crosses the ATC curve at the ATC curve’s minimum.
SHORT-RUN COST
• Cost Curves and Product Curves– The technology that a firm uses determines its
costs.– At low levels of employment and output, as the
firm hires more labor, marginal product and average product rise, and marginal cost and average variable cost fall.
– Then, at the point of maximum marginal product, marginal cost is a minimum.
– As the firm hires more labor, marginal product decreases and marginal cost increases.
SHORT-RUN COST
– But average product continues to rises, and average variable cost continues to fall.
– Then, at the point of maximum average product, average variable cost is a minimum.
– As the firm hires even more labor, average product decreases and average variable cost increases.
SHORT-RUN COST
This figure illustrates the relationship between the product curves and cost curves.
A firm’s marginal cost curve is linked to its marginal product curve.If marginal product rises, marginal cost falls.
If marginal product is a maximum, marginal cost is a minimum.
SHORT-RUN COST
A firm’s average variable cost curve is linked to its average product curve.
If average product rises, average variable cost falls.
If average product is a maximum, average variable cost is a minimum.
SHORT-RUN COST
At small outputs, MP and AP rise and MC and AVC fall.
At intermediate outputs,MP falls and MC rises andAP rises and AVC falls.
At large outputs,MP and AP fall andMC and AVC rise.
SHORT-RUN COST
• Shifts in Cost CurvesTechnology– A technological change that increases
productivity shifts the total product curve upward. It also shifts the marginal product curve and the average product curve upward.
– With a better technology, the same inputs can produce more output, so an advance in technology lowers the average and marginal costs and shifts the short-run cost curves downward.
SHORT-RUN COST
Prices of Factors of Production–An increase in the price of a factor of production
increases costs and shifts the cost curves.–But how the curves shift depends on which
resource price changes.An increase in rent or another component of fixed cost
–Shifts the fixed cost curves (TFC and AFC) upward.–Shifts the total cost curve (TC) upward.–Leaves the variable cost curves (AVC and TVC)
and the marginal cost curve (MC) unchanged.
SHORT-RUN COST
• An increase in the wage rate or another component of variable cost – Shifts the variable curves (TVC and AVC)
upward.– Shifts the marginal cost curve (MC) upward.– Leaves the fixed cost curves (AFC and TFC)
unchanged.
• Plant Size and Cost– When a firm changes its plant size, its cost of
producing a given output changes.– Will the average total cost of producing a
gallon of smoothie fall, rise, or remain the same?
– Each of these three outcomes arise because when a firm changes the size of its plant, it might experience:o Economies of scaleo Diseconomies of scaleo Constant returns to scale
LONG-RUN COST
• Economies of scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by a larger percentage and average total cost decreases.– The main source of economies of scale is
greater specialization of both labor and capital.
Economies of Scale
• Diseconomies of scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by a smaller percentage and average total cost increases.– Diseconomies of scale arise from the difficulty
of coordinating and controlling a large enterprise.
– Eventually, management complexity brings rising average total cost.
Diseconomies of Scale
• Constant returns to scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by the same percentage and average total cost remains constant.– Constant returns to scale occur when a firm is
able to replicate its existing production facility including its management system.
Constant Returns to Scale
•The Long-Run Average Cost Curve–The long-run average cost curve shows
the lowest average cost at which it is
possible to produce each output when the
firm has had sufficient time to change both
its plant size and labor employed.
LONG-RUN COST
EXAMPLE: LRATC with 3 Factory Sizes
ATCS ATCM ATCL
Q
AvgTotalCost
Firm can choose from 3 factory sizes: S, M, L.
Each size has its own SRATC curve.
The firm can change to a different factory size in the long run, but not in the short run.
EXAMPLE: LRATC with 3 Factory Sizes
ATCSATCM ATCL
Q
AvgTotalCost
QA QB
LRATC
To produce less than QA, firm will
choose size S in the long run.
To produce between QA
and QB, firm will
choose size M in the long run.
To produce more than QB, firm will
choose size L in the long run.
A Typical LRATC Curve
Q
ATCIn the real world, factories come in many sizes, each with its own SRATC curve.
So a typical LRATC curve looks like this:
LRATC
How ATC Changes as the Scale of Production ChangesEconomies of scale: ATC falls as Q increases.
Constant returns to scale: ATC stays the same as Q increases.
Diseconomies of scale: ATC rises as Q increases.
LRATC
Q
ATC
CONCLUSION
• Costs are critically important to many business decisions, including production, pricing, and hiring.
• This chapter has introduced the various cost concepts.
• The following chapters will show how firms use these concepts to maximize profits in various market structures.
CHAPTER SUMMARY Implicit costs do not involve a cash outlay,
yet are just as important as explicit costs to firms’ decisions.
The production function shows the relationship between output and inputs.
The marginal product of labor is the increase in output from a one-unit increase in labor, holding other inputs constant. The marginal products of other inputs are defined similarly.
Marginal product usually diminishes as the input increases. Thus, as output rises, the production function becomes flatter, and the total cost curve becomes steeper.
CHAPTER SUMMARY Variable costs vary with output; fixed costs do
not. Marginal cost is the increase in total cost from an
extra unit of production. The MC curve is usually upward-sloping.
Average variable cost is variable cost divided by output.
Average fixed cost is fixed cost divided by output. AFC always falls as output increases.
Average total cost (sometimes called “cost per unit”) is total cost divided by the quantity of output. The ATC curve is usually U-shaped.
CHAPTER SUMMARY The MC curve intersects the ATC curve
at minimum average total cost. When MC < ATC, ATC falls as Q rises. When MC > ATC, ATC rises as Q rises.
In the long run, all costs are variable.
Economies of scale: ATC falls as Q rises. Diseconomies of scale: ATC rises as Q rises. Constant returns to scale: ATC remains constant as Q rises.