engineering economics "cost concepts
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Transcript of engineering economics "cost concepts
Cost concepts
A cost is incurred when a firm uses a resource for some purpose
Costs are assembled into meaningful groups called cost pools (e.g., by type of cost or source)
Any factor that has the effect of changing the level of total cost is called a cost driver
A cost object is any product, service, customer, activity, or organizational unit to which costs are assigned for some management purpose
Basic Definitions
Cost Function Cost is the function of output c=f(X) C=f(X, T, ,K)
WHEREC=TOTAL COSTX=outputT=technologyK=price of factors = FIXED FACTORS(S)
Determinants Of Cost(1) Rate of output (i.e., utilization of fixed plant) (2) Size of plant (3) Prices of input factors (materials and labour) (4) Technology (5) Stability of output (6) Efficiency (of management as well as labour)
Elements of cost
MATERIAL
LABOUR
EXPENSES
What Makes Cost Analysis Difficult?
Link Between Accounting and Economic Valuations Accounting and economic costs often
differ. Most of the cost are uncontrollable Demand varies
Fixed CostDoes not vary with the output
Average Fixed costAVC = TFC / No. of units (Fixed cost per Unit)
Variable CostCost that varies directly with the output
VC
Output
Cost
Average Variable Cost
AVC = TVC / No.of Units (Variable cost per unit)
Output
Cost
AVC
Total Cost
TC = TFC + TVC
TVC
Output
Cost
TC
TFC
Opportunity Cost Value foregone while choosing the next best
alternative The income that would have been received if
the input had been used in its most profitable alternative use
It denotes the real cost of using an input Economic concept of cost
Incremental, Marginal and Sunk Costs
Incremental Cost Incremental cost is the change in cost
tied to a managerial decision. Fixed cost and variable cost changes
Marginal cost Additional cost of producing one
additional unit of output Only the variable cost changes
Shut down & Abandonment Costs
Shutdown cost – Expenses of temporary closure
Abandonment cost – Expenses of permanent closure
Is an expenditure that cannot be recovered Sunk costs are irrelevant to present decisions.
Sunk Cost
Avoidable and Unavoidable cost
Cost that can be avoided by eliminating a product or department is avoidable and that which cannot be, is unavoidable.
Ex. – Rent of factory is unavoidable if a product is discontinued
Historical, Current and Replacement Cost
Historical Versus Current Costs Historical cost is the actual cash outlay. Current cost is the present cost of
previously acquired items. Replacement Cost
Cost of replacing productive capacity using current technology.
Short-run and Long-run Costs
How Is the Operating Period Defined? At least one input is fixed in the short
run. All inputs are variable in the long run.
Fixed and Variable Costs Fixed cost is a short-run concept. All costs are variable in the long run.
Cost Concepts Total Fixed Costs (TFC)
The summation of all fixed and sunk costs to production.
Total Variable Costs (TVC) The summation of all variable costs to
production. Total Costs (TC)
The summation of total fixed and total variable costs.
TC=TFC+TVC
Cost Concepts Average Fixed Costs (AFC)
The total fixed costs divided by output. Average Variable Costs (AVC)
The total variable costs divided by output. Average Total Costs (ATC)
The total costs divided by output. The summation of average fixed costs and
average variable costs, i.e., ATC=AFC+AVC.
Cost Concepts
Marginal Costs The change in total costs divided by the
change in output. TC/Y
The change in total variable costs divided by the change in output. TVC/Y
Marginal Cost
How can marginal cost equal both the change in total cost divided by the change in output and the change in total variable cost divided by the change in output when variable costs are not equal to total costs? Short answer: fixed costs do not change.
Marginal Cost Cont. We want to show that MC = TVC/Y when
TVC TC. We know that TC = TFC + TVC This implies that TC = (TFC + TVC) This implies that TC = TFC + TVC We know that TFC = 0 Hence, TC = TVC Divide the previous by Y, we obtain TC/Y = TVC/Y MC = TVC/Y
Marginal Cost
AVC = TVC / No.of Units (Variable cost per unit)
Output
Cost MC
Graphical Representation of Cost Concepts
$
Y
ATC
MC
AVC
AFC
Typical Average & Marginal Cost Curves
AFC is always declining at a decreasing rate.
ATC and AVC decline at first, reach a minimum, then increase at higher levels of output.
The difference between ATC and AVC is equal to AFC.
MC is generally increasing.
MC crosses ATC and AVC at their minimum point.
If MC is below the average value: Average value will be
decreasing. If MC is above the average
value: Average value will be
increasing.
MC will meet AVC and ATC from below at the corresponding minimum point of each. Why?
As output increases AFC goes to zero. As output increases, AVC and ATC get
closer to each other.
Long-Run cost curves
Nothing is fixed – everything is variable.
The long run average cost curve is called as the envelope curve
Example of Cost Concepts
O/p
TFC TVC TC AFC AVC ATC MC
10
30
48
65
81
96
108
116
120
117
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1600
2000
2200
2600
3200
4000
5000
6200
7600
2000
2600
3000
3200
3600
4200
5000
6000
7200
8600
100
33.33
20.83
15.38
12.35
10.42
9.26
8.62
8.33
8.55
100
53.33
41.67
33.85
32.10
33.33
37.04
43.10
51.67
64.96
200
86.67
62.50
49.23
45.45
43.75
46.30
51.72
60.00
73.51
30
22.22
11.76
25
40
66.67
125
300
-466.67
X
10
16
20
22
26
32
40
50
62
76
MATERIAL
Direct: traceable to one particular process, job or product – identified with each unit of product
Example: manufacturing an apparel Cloth, collar, buttons, cufflinks, thread Primary packing material (e.g., carton,
wrapping, cardboard, boxes, etc.) Fuel, lubricating oil etc for operating &
maintenance of machine Small tools Materials used for repairs & maintenance
LABOUR
Inspectors Supervisors Internal transport staff Storekeeper, maintenance staff
EXPENSES
Expenses leading to a job or contract Traveling expenses for negotiation Special pattern, design Special tools for executing the contract
Rent Insurance Canteen, hospital, power , lighting,
maintenance
Types of Costs Variable Costs
These costs exist only if production occurs. E.g., fuel for tractor, seed, etc.
Fixed Costs These cost exist whether production occurs or
not. In the long-run there are no fixed costs. Can be both cash and non-cash expenses. E.g., depreciation on tractors and buildings, etc.
Types of Costs Cont.
Sunk Costs Is an expenditure that cannot be
recovered. In essence, it becomes part of fixed
costs. E.g., pre-harvest costs.
Long-Run Average Costs The long run average cost (LRAC) curve is
the envelope of the short run average cost curves when the size of the operation is allowed to increase or decrease.
Note that a short run average cost curve exists for every possible farm size, as defined by the amount of fixed input available.
Long-Run Average Costs Cont.
In a competitive market, the long run optimal production will occur at the lowest point on the LRAC, i.e., economic profits are driven to zero.
Size in the Long-Run
A measure of size in the long run between output and costs as farm size increases (EOS) is the following: EOS = percent change in costs divided
by percent change in output value
Size in the Long-Run Cont. If this ratio of EOS is less than one, then
there are decreasing costs to expanding production, i.e., increasing returns to size.
If this ratio is equal to one, then there are constant costs to expanding production, i.e., constant returns to size.
If this ratio is greater than one, then there are increasing costs to expanding production, i.e., decreasing returns to size.
Economies of Size This exists when the LRAC is decreasing. Also known as increasing returns to size. Usually occurs because of full utilization of
capital (tractors and buildings) and labor. Also occurs because of discount pricing for
buying in bulk and selling price benefits for selling large quantities.
Diseconomies of Size This exists when the LRAC is increasing. Also known as decreasing returns to size. Usually occurs because a lack of
managerial skills. Also occurs because travel time increases
as farm increases. Livestock: disease control and manure disposal. Crops: geographical distance away from each
other.
Revenue Concepts Revenue (TR) is defined as the output
price (py) multiplied by the quantity (Y).
Average revenue (AR) equals total revenue divided by output (Y), i.e., TR/Y, which equals py.
Marginal Revenue is the change in total revenue divided by the change in output, i.e., TR/Y.
Short-Run Decision Making
In the short-run, there are many ways to choose how to produce. Maximize output. Utility maximization of the manager. Profit maximization.
Profit () is defined as total revenue minus total cost, i.e., = TR – TC.
Short-Run Decision Making Cont. When examining output, we want to
set our production level where MR = MC when MR > AVC in the short-run. If MR AVC, we would want to shut
down. Why?
If we can not set MR exactly equal to MC, we want to produce at a level where MR is as close as possible to MC, where MR > MC.
Intuition for Setting MR = MC
Suppose MR < MC. This implies that by producing more
output, you have a greater addition of cost than you do revenue. Hence you would not make the change.
Intuition for Setting MR = MC Suppose MR > MC. This implies that by producing
more output, you have a greater addition of revenue than you do cost. Hence you would make the change.
You would stop increasing output at the point where the trade-off in additional revenue is just equal to the trade-off in additional costs.
Why Shutdown WhenMR < AVC
If MR < AVC, this implies that you are not bringing in enough revenue from each unit produced to cover your variable costs.
Hence you could minimize your loss if you were to shutdown.
Why Produce When ATC > MR > AVC When MR < ATC, the company is making a
loss. Why would it produce?
Since the firm is making something above and beyond its variable cost, it can put some of that revenue towards fixed cost. This implies that it minimizes its loss by
producing.
Profit Scenario Graphically
$
Y
ATC
MC
AVC
AFC
MR = py
Profit
ATC
Yprofit
Loss Minimizing Graphically
$
Y
ATC
MC
AVC
AFC
Loss
ATC
Yloss
MR = py
Shutdown Decision Graphically
$
Y
ATC
MC
AVC
AFC
Loss = A + B
ATC
Yloss
MR = py
A
B
If we did not produce: loss = B
Production Rules for the Long-Run
To maximize profits, the farmer should produce when selling price is greater than ATC at the production level where MC = MR.
To minimize losses, the farmer should not produce when selling price is less than ATC, i.e., shutdown the business.
Note on Cost Concepts
The producer’s supply curve is the part of the MC curve that is above the shutdown point.
Short-Run & Long-Run “Time concepts” rather than fixed
periods. Short-run:
One or more production input is fixed: Increasing cropland?
One crop or livestock production cycle. Long-run:
The quantity of all necessary production inputs can be changed.
Expand or acquire additional inputs.
Fixed Costs Result from owning a fixed input or
resource. Incurred even if the resource isn’t
used. Don’t change as the level of
production changes (in the short run). Exist only in the short run. Not under the control of the manager
in the short run. The only way to avoid fixed costs is to
sell the item.
Fixed Costs(DIRTI – 5)
1. Depreciation2. Interest3. Rent4. Taxes
(property)5. Insurance
Cash
Noncash
Important Fixed Costs Total fixed cost (TFC):
All costs associated with the fixed input.
Average fixed cost per unit of output:
AFC = TFC Output
Variable Costs
Can be increased or decreased by the manager.
Variable costs will increase as production increases.
Total Variable cost (TVC) is the summation of the individual variable costs.
VC = (the quantity of the input) X (the input’s price).
Variable Costs Variable costs exist in the short-
run and long-run: In fact, all costs are considered to
be variable costs in the long run. Variable versus Fixed, some
examples: Fertilizer is a variable cost until it has
been purchased and applied. Labor and cash rent contracts have to
be considered fixed costs during the duration of the contract.
Irrigation water is generally variable, but can have a fixed component.
Important Variable Costs Total variable cost (TVC):
All costs associated with the variable input.
Average variable cost per unit of output:
AVC = TVC Output
Total Cost
The sum of total fixed costs and total variable costs:
TC = TFC + TVC
In the short run TC will only increase as TVC increases.
Average Total Cost Average total cost per unit of
output:
AFC + AVC
ATC = TC Output
Marginal Cost The additional cost incurred from
producing an additional unit of output:
MC = TC Output
MC = TVC Output
Typical Total Cost Curves
Typical Total Cost Curves(selected attributes)
TFC is constant and unaffected by output level.
TVC is always increasing: First at a decreasing rate. Then at an increasing rate.
TC is parallel to TVC: TC is higher than TVC by a distance
equal to TFC.
Typical Average & Marginal Cost Curves
Stocking Rate Problem
Production Rules for the Short-Run
If expected selling price > minimum ATC (which implies TR > TC): A profit can be made.
Maximize profit by producing where: MR = MC
Production Rules for the Short-Run
If expected selling price < minimum ATC but > minimum AVC: (which implies TR > TVC but < TC) A loss cannot be avoided. Minimize loss by producing where
MR = MC. The loss will be between 0 and TFC.
Production Rules for the Short-Run
If expected selling price < minimum AVC (which implies TR < TVC): A loss cannot be avoided. Minimize loss by not producing. The loss will be equal to TFC.
Short Run Production Decisions
Production Rules for the Long-Run
If selling price > ATC (or TR > TC): Continue to produce. Maximize profit by producing
where MR = MC.
Production Rules for the Long-Run
If selling price < ATC (or TR < TC): There will be a continual loss. Sell the fixed assets to eliminate
fixed costs. Reinvest money in a more
profitable alternative.
Farm Size in the Short-Run
Possible Size-Cost Relations
Economies of Size Increasing returns to size. LRAC curve is decreasing. Economies of size result from:
Full utilization of labor, machinery, buildings.
Ability to afford specialized labor and machinery and new technology.
Price discounts for volume purchasing of inputs.
Price advantages when selling large amounts of output.
Long-Run Average Cost Curve(Economies of Size)
Diseconomies of Size
Decreasing returns to size. LRAC curve begins to increase. Diseconomies of size result from:
Lack of sufficient managerial skill. Need to hire, train, supervise, and
coordinate larger labor force. Dispersion over a larger
geographical area. Disease control, waste disposal.
Long-Run Average Cost Curve(Diseconomies of size)