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McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 8Production and Cost in the Short Run
8-2
Learning Objectives
Explain general concepts of production and cost analysis
Examine the structure of short-run production based on the relation among total, average, and marginal products
Examine the structure of short-run costs using graphs of the total cost curves, average cost curves, and the short-run marginal cost curve
Relate short-run costs to the production function using the relations between (i) average variable cost and average product, and (ii) short-run marginal cost and marginal product
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Basic Concepts of Production Theory
Production function~ A schedule showing the maximum amount of
output that can be produced from any specified set of inputs, given existing technology
Variable proportions production~ Production in which a given level of output can be
produced with more than one combination of inputs
Fixed proportions production~ Production in which one, and only one, ratio of
inputs can be used to produce a good
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Basic Concepts of Production Theory
Technical efficiency~ Achieved when maximum amount of output is
produced with a given combination of inputs and technology
Economic efficiency~ Achieved when firm is producing a given
output at the lowest possible total cost
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Inputs are considered variable or fixed depending on how readily their usage can be changed
Variable input~ An input for which the level of usage may be varied to
increase or decrease output Fixed input
~ An input for which the level of usage cannot be changed and which must be paid even if no output is produced
Quasi-fixed input~ A “lumpy” or indivisible input for which a fixed amount must
be used for any positive level of output~ None is purchased when output is zero
Basic Concepts of Production Theory
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Short run~ Current time span during which at least one
input is a fixed input Long run
~ Time period far enough in the future to allow all fixed inputs to become variable inputs
Planning horizon~ Set of all possible short-run situations the firm
can face in the future
Basic Concepts of Production Theory
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Sunk Costs
Sunk cost~ Payment for an input that, once made, cannot
be recovered should the firm no longer wish to employ that input
~ Irrelevant for all future time periods; not part of the economic cost of production in future time periods
~ Should be ignored for decision making purposes
~ Fixed costs are sunk costs
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Avoidable Costs
Avoidable costs~ Input costs the firm can recover or avoid
paying should it no longer wish to employ that input
~ Matter in decision making and should not be ignored
~ Variable costs and quasi-fixed costs are avoidable costs
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Inputs in Production (Table 8.1)
Input Type Payment Relation to Output
Avoidable or Sunk?
Employed in SR or LR?
Variable Variable cost
Fixed Fixed costs
Quasi-fixed Quasi-fixed costs
Direct
Constant
Constant
Avoidable
Avoidable
Sunk
SR & LR
SR only
If required: SR & LR
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Short Run Production
In the short run, capital is fixed~ Only changes in the variable labor input can
change the level of output Short run production function
Q = f (L, K) = f (L)
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Average & Marginal Products
Average product of labor~ AP = Q/L
Marginal product of labor~ MP = Q/L
When AP is rising, MP is greater than AP When AP is falling, MP is less than AP When AP reaches it maximum, AP = MP Law of diminishing marginal product
~ As usage of a variable input increases, a point is reached beyond which its marginal product decreases
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Total, Average, & Marginal Products of Labor, K = 2 (Table 8.3)
Number of workers (L)
Total product (Q) Average product (AP=Q/L)
Marginal product (MP=Q/L)
0 0
1 52
2 112
3 170
4 220
5 258
6 286
7 304
8 314
9 318
10 314
--
55
51.6
52
56
56.7
47.7
43.4
39.3
35.3
31.4
--
50
38
52
60
58
28
18
10
4
-4
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Total, Average, & Marginal Products K = 2 (Figure 8.1)
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Short Run Production Costs
Total fixed cost (TFC)~ Total amount paid for fixed inputs~ Does not vary with output
Total variable cost (TVC)~ Total amount paid for variable inputs~ Increases as output increases
Total cost (TC)
TC = TFC + TVC
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Short-Run Total Cost Schedules (Table 8.5)
Output (Q) Total fixed cost (TFC)
Total variable cost (TVC)
Total Cost (TC=TFC+TVC)
0 $6,000
100 6,000
200 6,000
300 6,000
400 6,000
500 6,000
600 6,000
$ 0
14,000
22,000
4,000
6,000
9,000
34,000
$ 6,000
20,000
28,000
10,000
12,000
15,000
40,000
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Total Cost Curves (Figure 8.3)
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Average Costs
Average fixed cost (AFC)
Average variable cost (AVC)
Average total cost (ATC)
TFCAVC
Q
TVCAFC
Q
TCATC AFC AVC
Q
8-18
Short Run Marginal Cost
Short run marginal cost (SMC) measures rate of change in total cost (TC) as output varies
TVC TC
SMCQ Q
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Average & Marginal Cost Schedules (Table 8.6)
Output (Q)
Average fixed cost (AFC=TFC/Q)
Average variable cost (AVC=TVC/Q)
Average total cost (ATC=TC/Q= AFC+AVC)
Short-run marginal cost (SMC=TC/Q)
0
100
200
300
400
500
600
--
15
12
$60
30
20
10
--
35
44
$40
30
30
56.7
--
50
56
$100
60
50
66.7
--
50
80
$40
20
30
120
8-20
Average & Marginal Cost Curves (Figure 8.4)
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Short Run Average & Marginal Cost Curves (Figure 8.5)
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Short Run Cost Curve Relations
AFC decreases continuously as output increases~ Equal to vertical distance between ATC &
AVC AVC is U-shaped
~ Equals SMC at AVC’s minimum
ATC is U-shaped~ Equals SMC at ATC’s minimum
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SMC is U-shaped~ Intersects AVC & ATC at their minimum
points
~ Lies below AVC & ATC when AVC & ATC are falling
~ Lies above AVC & ATC when AVC & ATC are rising
Short Run Cost Curve Relations
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Relations Between Short-Run Costs & Production
In the case of a single variable input, short-run costs are related to the production function by two relations
and w w
AVC SMCAP MP
Where w is the price of the variable input
TC = wL + rK
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Short-Run Production & Cost Relations (Figure 8.6)
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Relations Between Short-Run Costs & Production
When marginal product (average product) is increasing, marginal cost (average cost) is decreasing
When marginal product (average product) is decreasing, marginal cost (average variable cost) is increasing
When marginal product = average product at maximum AP, marginal cost = average variable cost at minimum AVC
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Summary
Technical efficiency occurs when a firm produces maximum output for a given input combination and technology; economic efficiency is achieved when the firm produces a given output at the lowest total cost~ Production inputs can be variable, fixed, or quasi-fixed inputs
Short run refers to the current time span during which one or more inputs are fixed; Long run refers to the period far enough in the future that all fixed inputs become variable inputs
Sunk costs are irrelevant for future decisions and are not part of economic cost of production in future time periods; avoidable costs are payments a firm can recover or avoid, thus they do matter in decisions
8-28
Summary The total product curve gives the economically efficient
amount of labor for any output level when capital is fixed in the short run
Average product of labor is the total product divided by the number of workers: AP = Q/L
Marginal product of labor is the additional output attributable to using one additional worker with the use of capital fixed: MP = ∆Q/∆L
The law of diminishing marginal product states that as the number of units of the variable input increases, other inputs held constant, a point will be reached beyond which the marginal product of the variable input declines
8-29
Summary Short-run total cost, TC, is the sum of total variable
cost, TVC, and total fixed cost, TFC: TC = TVC + TFC Average fixed cost, AFC, is TFC divided by output:
AFC = TFC/Q; average variable cost, AVC, is TVC divided by output: AVC = TVC/Q; average total cost (ATC) is TC divided by output: ATC = TC/Q
Short-run marginal cost, SMC, is the change in either TVC or TC per unit change in output Q
The link between product curves and cost curves in the short run when one input is variable is reflected in the relations, AVC = w/AP and SMC = w/MP, where w is the price of the variable input
