production. an activity that creates value inputs for production raw materials, labor, land,...
Post on 20-Dec-2015
228 views
TRANSCRIPT
![Page 1: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/1.jpg)
Production
![Page 2: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/2.jpg)
Production
an activity that creates value
![Page 3: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/3.jpg)
Inputs for Production
raw materials, labor, land, capital, & entrepreneurial or managerial talent.
Capital includes tools, machinery, equipment, & physical facilities.
![Page 4: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/4.jpg)
Production Function
Q = f(X1,X2,X3,X4,…,Xn)
where Q is the quantity of output that can
be produced with amounts of inputs,
X1,X2,X3,X4,…,Xn.
![Page 5: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/5.jpg)
Short run
time period so short that the amounts of some inputs can not be changed
For example, the quantity of plant & heavy equipment can not be changed in a short time period.
![Page 6: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/6.jpg)
Long run
time period long enough for all inputs to be changed
![Page 7: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/7.jpg)
Fixed input
an input whose quantity can not be changed in the short run
![Page 8: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/8.jpg)
Variable input
an input whose quantity can be changed in a short period of time
Examples: labor, raw materials
![Page 9: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/9.jpg)
The scale of a firm’s operation is determined by its fixed inputs.
![Page 10: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/10.jpg)
We can look at the productivity of a variable input given a fixed level of fixed input.
![Page 11: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/11.jpg)
Marginal Product (MP) of the variable input X
Discrete MP = ΔQ/ ΔX = ΔTP/ ΔX
Change in output resulting from a one-unit change in the quantity of input
Continuous MP = dQ/dX = dTP/dX
Rate of change in total output as the usage of the variable input increases by very small amounts.
![Page 12: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/12.jpg)
Graphical Interpretation of MP
The continuous MP is the slope of the total product curve at a particular point.
The discrete MP is the slope of the line segment connecting 2 points on the total product curve.
Q = TP
X
![Page 13: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/13.jpg)
Example: Q = 21X + 9X2 – X3
X Q = TP
0 0
1 29
2 70
![Page 14: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/14.jpg)
Example: Q = 21X + 9X2 – X3
X Q = TPDiscrete MP
ΔQ/ΔX
0 0 –
1 29 29
2 70 41
![Page 15: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/15.jpg)
Example: Q = 21X + 9X2 – X3
X Q = TPDiscrete MP
ΔQ/ΔXContinuous MP
dQ/dX =21+ 18 X – 3X2
0 0 – –
1 29 29 36
2 70 41 45
![Page 16: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/16.jpg)
Average Product (AP)
AP = Q / X = TP / X
Amount of product per unit of input
Can be calculated for variable or fixed inputs
![Page 17: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/17.jpg)
Example: Q = 21X + 9X2 – X3
AP = Q / X = (21X + 9X2 – X3) / X
= 21 + 9X – X2
X = 1: AP = 29
X = 2: AP = 35
![Page 18: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/18.jpg)
Graphical Interpretation of AP = Q / X
X
The AP of a particular value of X1 can be interpreted as the slope of the line from the origin to the corresponding point on the curve.
Q = TP
X1 →
Q1
0
![Page 19: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/19.jpg)
In this graph, we see that initially, AP is increasing
X
Q = TP
0
![Page 20: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/20.jpg)
and then decreasing
X
Q = TP
0
![Page 21: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/21.jpg)
Principle of Diminishing Marginal Returns
As the amount of a variable input is increased and combined with a specified amount of fixed inputs, a point is eventually reached where the resulting increases in the quantity of output get smaller & smaller.
In other words, as the amount of variable input increases, eventually the MP of the variable input falls.
![Page 22: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/22.jpg)
Total Product, Marginal Product, &
Average Product Curves
Q = TP
XMP AP
X
AP
MP
incr marg returns
pt of dim marg returns
Diminishing marginal returns set in when MP starts to fall (but is still positive).
The TP curve gets flatter as the slope of TP falls.
![Page 23: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/23.jpg)
Q = TP
XMP AP
X
AP
MP
pt of dim avg returns
Diminishing average returns set in when AP starts to fall. (Remember that AP is the slope of the line from the origin to the point on the TP curve.)
![Page 24: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/24.jpg)
Q = TP
XMP AP
X
AP
MP
marginal returns become negative
dim total returns
Diminishing total returns set in when the TP curve turns downward and MP becomes negative.
![Page 25: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/25.jpg)
Isoquant
a curve showing all possible efficient combinations of input that are capable of producing a certain quantity of output
(Note: iso means same, so isoquant means same quantity)
![Page 26: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/26.jpg)
Isoquant for 100 units of output
100
Quantity of capital used per unit of time
Quantity of labor used per unit of time
K1
K2
K3
K4
L1 L2 L3 L4
100 units of output can be produced in many different ways including L1 units of labor & K1 units of capital, L2 units of labor & K2 units of capital, L3 units of labor & K3 units of capital, & L4 units of labor & K4 units of capital.
![Page 27: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/27.jpg)
Isoquants for different output levels
50
100
125
Quantity of capital used per unit of time
Quantity of labor used per unit of time
As you move in a northeasterly direction, the amount of output produced increases, along with the amount of inputs used.
![Page 28: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/28.jpg)
If you move out from the origin along a ray with constant slope, the input combinations have a
constant capital-labor ratio.
50100
125
Quantity of capital used 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 points uses one-third as much capital as labor.
![Page 29: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/29.jpg)
It is possible for an isoquant to have positively sloped sections.
Quantity of capital used per unit of time
Quantity of labor used per unit of time
In these sections, you’re increasing the amounts of both inputs, but output is not increasing, because the marginal product of one the inputs is negative.
![Page 30: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/30.jpg)
The lines connecting the points where the isoquants begin to slope upward are called ridge lines.
Quantity of capital used per unit of time
Quantity of labor used per unit of time
ridge lines
![Page 31: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/31.jpg)
No profit-maximizing firm will operate at a point outside the ridge lines, since it can produce the
same output with less of both outputs.
Quantity of labor used per unit of time
Quantity of capital used per unit of time
L1 L2
K2
K1
Notice, for example, that since points A & B are on the same isoquant, they produce the same amount of output.
However, point B is a more expensive way to produce since it uses more capital & more labor.
B
A
![Page 32: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/32.jpg)
Marginal rate of technical substitution (MRTS)
The slope of the isoquant
The rate at which you can trade off inputs and still produce the same amount of output.
For example, if you can decrease the amount of capital by 1 unit while increasing the amount of labor by 3 units, & still produce the same amount of output, the marginal rate of technical substitution is 1/3.
![Page 33: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/33.jpg)
What is the MRTS or slope of the isoquant?
Q2
Quantity of capital used per unit of time
Quantity of labor used per unit of time
KA
KB
LA LB
A
B
Q1
C
Consider 2 points A & B on the same isoquant.
Let’s divide the movement between A & B into 2 parts, from A to C, & from C to B.Moving from A to C, ΔQ = (ΔQ/ΔK) ΔK .Moving from C to B, ΔQ = (ΔQ/ΔL) ΔL .Moving from A to B, ΔQ = (ΔQ/ΔK) ΔK + (ΔQ/ΔL) ΔL
= MPK ΔK + MPL ΔL .
Since A & B are on the same isoquant, ΔQ = 0.
So, MPK ΔK + MPL ΔL = 0 .
MPK ΔK = - MPL ΔL .
ΔK/ΔL = - MPL/MPK
slope of isoquant
![Page 34: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/34.jpg)
Marginal Rate of Technical Substitution (MRTS)
or slope of an isoquant
ΔK/ΔL = - MPL/MPK
the negative of the ratio of the marginal products of the inputs, with the input on the
horizontal axis in the numerator.
![Page 35: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/35.jpg)
How does output respond to changes in scale in the long run?
Three possibilities:
1. Constant returns to scale
2. Increasing returns to scale
3. Decreasing returns to scale
![Page 36: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/36.jpg)
Constant returns to scale
Doubling inputs results in double the output.
![Page 37: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/37.jpg)
Increasing returns to scale
Doubling inputs results in more than double the output.One reason this may occur is that a firm may be able to use production techniques that it could not use in a smaller operation.
![Page 38: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/38.jpg)
Decreasing returns to scale
Doubling inputs results in less than double the output.One reason this may occur is the difficulty in coordinating large organizations (more paper work, red tape, etc.)
![Page 39: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/39.jpg)
Graphs of Constant, Increasing, & Decreasing Returns to Scale
Constant Returns to Scale: isoquants for output levels 50, 100, 150, etc. are evenly spaced.
Capital
Labor
150
100
50
150
Capital
Labor
50100
150
Capital
Labor
10050
Increasing Returns to Scale: isoquants for output levels 50, 100, 150, etc. get closer & closer together.
Decreasing Returns to Scale: isoquants for output levels 50, 100, 150, etc. become more widely spaced.
![Page 40: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/40.jpg)
Methods of estimating production functions
1. using statistical analysis of time series or cross-sectional data.
2. based on experimentation or experience with day-to-day operations.
![Page 41: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/41.jpg)
A commonly used production function is the Cobb-Douglas function
Q = AL1 K2 M3
where K is the quantity of capital, L is the quantity of labor, & M is the quantity of raw materials. A, 1, 2, & 3 are parameters that depend on the specific case. Also, 1, 2, & 3 are between 0 & 1.
If 1+ 2 + 3 = 1, we have constant returns to scale.
If 1+ 2 + 3 > 1, we have increasing returns to scale.
If 1+ 2 + 3 < 1, we have decreasing returns to scale.
![Page 42: Production. an activity that creates value Inputs for Production raw materials, labor, land, capital, & entrepreneurial or managerial talent. Capital](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649d4b5503460f94a289cd/html5/thumbnails/42.jpg)
Suppose Q = AL.5 K.2 M.5
Show that with 1+ 2 + 3 = .5 + .2 + .5 = 1.2 > 1, this production function does have increasing returns to scale, by showing that
doubling inputs results in more than double the output.
Let Q’ be the output resulting from doubling the inputs. Then Q’ = (A)(2L).5 (2K).2 (2M).5 = (A) (2.5 L.5) (2.2 K.2) (2.5 M.5) = (A) (2.5) (2.2) (2.5)(L.5 K.2 M.5) = (A) (2 .5 + .2 + .5)(L.5 K.2 M.5) = 21.2 (A L.5 K.2 M.5) > 2 (A L.5 K.2 M.5) 2QSo doubling the inputs more than doubles the output.