chapter 8: production and cost in the short run mcgraw-hill/irwin copyright © 2011 by the...
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Chapter 8: Production and Cost in the Short Run
McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
8-2
Basic Concepts of Production Theory
• Production function• Maximum amount of output that can be produced
from any specified set of inputs, given existing technology
• Technical efficiency• Achieved when maximum amount of output is
produced with a given combination of inputs
• Economic efficiency• Achieved when firm is producing a given output
at the lowest possible total cost
8-3
• 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 changed quite
readily
• Fixed input• An input for which the level of usage cannot readily 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
8-4
• Short run• At least one input is fixed• All changes in output achieved by changing
usage of variable inputs
• Long run• All inputs are variable• Output changed by varying usage of all inputs
Basic Concepts of Production Theory
8-5
Sunk Costs
• Sunk cost• Payment for an input that, once made, cannot
be recovered should the firm no longer wish to employ that input
• Not part of the economic cost of production• Should be ignored for decision making
purposes
8-6
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
• Reflect the opportunity costs of resource use
8-7
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)
8-8
Production Function
8-8
8-9
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
8-10
Total, Average, & Marginal Products of Labor, K = 2 (Table 8.2)
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
104
-4
8-11
Total, Average, & Marginal Products K = 2 (Figure 8.1)
8-12
Panel A
Panel B
Total product
Average product
Marginal product
Q1
L1
L1
L2
Q2
L2
L0
Q0
L0
Total, Average, & Marginal Product Curves
8-13
Law of Diminishing Marginal Product (Returns)
• Only holds in the short-run
• As the quantity of the variable input (labor) increases, the capital to labor ratio declines
• Eventually an incremental increase in the variable input adds less to output than the previous incremental increase in the variable input
8-13
8-14
Change in Capital Stock
8-14
8-15
Change in Capital Stock
8-15
8-16
Short Run Production Costs
• Total variable cost (TVC)• Total amount paid for variable inputs• Increases as output increases
• Total fixed cost (TFC)• Total amount paid for fixed inputs• Does not vary with output
• Total cost (TC)
TC = TVC + TFC
8-17
Short-Run Total Cost Schedules (Table 8.4)
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
8-18
Total Cost Curves (Figure 8.3)
8-19
Average Costs
• Average variable cost (AVC)
• Average fixed cost (AFC)
• Average total cost (ATC)
TVCAVC
Q
TFCAFC
Q
TCATC AVC AFC
Q
8-20
Short Run Marginal Cost
• Short run marginal cost (SMC) measures rate of change in total cost (TC) as output varies
TC TVCSMC
Q Q
8-21
Average & Marginal Cost Schedules (Table 8.5)
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
3030
56.7
--
50
56
$100
6050
66.7
--
50
80
$40
2030
120
8-22
Average & Marginal Cost Curves (Figure 8.4)
8-23
Short Run Average & Marginal Cost Curves (Figure 8.5)
8-24
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
8-25
• 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
8-26
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
8-27
Marginal Cost and Marginal Product
LMPw
q
LwMC
q
Lw
q
wL
q
VCMC
q
CMC
1
)(
Marginal cost is inversely related to marginal product
8-28
Marginal Cost and Marginal Product
• W = $10
• MP = 10
• MC =$1
• MP = 5
• MC = $2
8-28
8-29
Average Variable Cost and Average Product
LAPw
q
LwAVC
q
wL
q
VCAVC
q
CAVC
1
Average variable cost is inversely related to average product
8-30
Short-Run Production and Total Cost
8-30
8-31
Short-Run Production and Marginal cost
8-31
8-32
Short-Run Production & Cost Relations (Figure 8.6)
8-33
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