Post on 03-Jun-2018
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Production
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Production
an activity that creates value
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Inputs for Production
raw materials, labor, land, capital, &entrepreneurial or managerial talent.
Capital includes tools, machinery,equipment, & physical facilities.
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Production Function
Q = f(X 1,X2,X3,X4,,X n)where Q is the quantity of output that can
be produced with amounts of inputs,X1,X2,X3,X4,,X n.
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Long run
time period long enough for all inputs to bechanged
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Fixed input
an input whose quantity can not be changedin the short run
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Variable input
an input whose quantity can be changed in a
short period of timeExamples: labor, raw materials
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We can look at the productivity of a variableinput given a fixed level of fixed input.
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Graphical Interpretation of MP
The continuous MP is the slope ofthe total product curve at aparticular point.
The discrete MP is the slope of theline segment connecting 2 points onthe total product curve.
Q = TP
X
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Example: Q = 21X + 9X 2 X3
X Q = TP
0 0
1 292 70
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Example: Q = 21X + 9X 2 X3
AP = Q / X = (21X + 9X 2 X3) / X
= 21 + 9X X2
X = 1: AP = 29
X = 2: AP = 35
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In this graph, we see that initially, AP is increasing
X
Q = TP
0
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Total Product,Marginal Product, & Average Product
Curves
Q = TP
XMP
AP
X
AP
MP
incr margreturns
pt of dim
marg returns
Diminishing marginal
returns set in whenMP starts to fall (butis still positive).
The TP curve gets
flatter as the slope ofTP falls.
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Q = TP
XMP
AP
X
AP
MP
pt of dimavg returns
Diminishing averagereturns set in when
AP starts to fall.(Remember that APis the slope of theline from the origin tothe point on the TPcurve.)
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Q = TP
XMP
AP
X
AP
MP
marginal returnsbecome negative
dim totalreturns
Diminishing totalreturns set in when
the TP curve turnsdownward and MPbecomes negative.
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Isoquant
a curve showing all possible efficientcombinations of input that are capable of
producing a certain quantity of output
(Note: iso means same, so isoquant meanssame quantity)
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Isoquants for different output levels
50
100
125
Quantity of capitalused per unit of time
Quantity of laborused per unit of time
As you move in a northeasterlydirection, the amount of outputproduced increases, along withthe amount of inputs used.
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If you move out from the origin along a ray withconstant slope, the input combinations have a
constant capital-labor ratio.
50100
125
Quantity of capitalused per unit of time
Quantity of labor used per unit of time
140
15 24 36 45
15
12
8
5
Each of the indicated pointsuses one-third as muchcapital as labor.
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It is possible for an isoquant to havepositively sloped sections.
Quantity of capitalused per unit of time
Quantity of labor used per unit of time
In these sections, youreincreasing the amounts ofboth inputs, but output isnot increasing, because
the marginal product ofone the inputs is negative.
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The lines connecting the points where the isoquantsbegin to slope upward are called ridge lines.
Quantity of capitalused per unit of time
Quantity of labor used per unit of time
ridge lines
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No profit-maximizing firm will operate at a pointoutside the ridge lines, since it can produce the
same output with less of both outputs.
Quantity of labor usedper unit of time
Quantity ofcapital used perunit of time
L1 L2
K2
K1
Notice, for example, thatsince points A & B are onthe same isoquant, theyproduce the sameamount of output.However, point B is amore expensive way toproduce since it usesmore capital & morelabor.
B A
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Marginal rate of technical substitution(MRTS)
The slope of the isoquantThe rate at which you can trade off inputsand still produce the same amount of output.For example, if you can decrease theamount of capital by 1 unit while increasingthe amount of labor by 3 units, & stillproduce the same amount of output, themarginal rate of technical substitution is 1/3.
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What is the MRTS or slope of the isoquant?
Q 2
Quantity of capital
used per unit oftime
Quantity of laborused per unit of time
K A
KB
L A LB
A
B
Q 1
C
Consider 2 points A & B on the same isoquant.
Lets divide the movement between A & B into 2 parts, from A to C, & from C to B.Moving from A to C, Q = ( Q/ K) K .Moving from C to B, Q = ( Q/ L) L .Moving from A to B, Q = ( Q/ K) K + ( Q/ L) L
= MPK K + MP
L L .
Since A & B are on the same isoquant, Q = 0.So, MP K K + MP L L = 0 .
MP K K = - MP L L .
K/ L = - MP L/MP K
slope ofisoquant
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How does output respond to changes in
scale in the long run?
Three possibilities:
1. Constant returns to scale2. Increasing returns to scale3. Decreasing returns to scale
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Constant returns to scale
Doubling inputs results in double the output.
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Increasing returns to scaleDoubling inputs results in more than doublethe output.One reason this may occur is that a firmmay be able to use production techniquesthat it could not use in a smaller operation.
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Decreasing returns to scale
Doubling inputs results in less than doublethe output.One reason this may occur is the difficultyin coordinating large organizations (morepaper work, red tape, etc.)
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Graphs of Constant, Increasing, &Decreasing Returns to Scale
Cons tan t Returns toScale : isoquants foroutput levels 50, 100,150, etc. are evenly
spaced.
Capital
Labor
150
100
50
150
Capital
Labor
50100
150
Capital
Labor
10050
Increas ing Returns toScale : isoquants foroutput levels 50, 100,150, etc. get closer &
closer together.
Decreas ing Return sto Scale : isoquantsfor output levels 50,100, 150, etc. become
more widely spaced.
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Methods of estimating production functions
1. using statistical analysis of time series orcross-sectional data.
2. based on experimentation or experiencewith day-to-day operations.
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