This document discusses the Cobb-Douglas production function and its application to estimating production at a lumber company. It begins by defining the Cobb-Douglas production function and its typical form. It then presents the specific production function estimated for Washington-Pacific Lumber, which models lumber output (Q) as a function of labor hours (L), machine hours (K), and energy input (BTUs) (E). It provides the estimated coefficients and standard errors from regressing data. The rest of the document works through examples calculating the effect on output from changes in inputs and determining the returns to scale for this production system based on summing the exponent coefficients.
Production function describes the technological relationship between inputs and output in physical terms. Study of production function is directed towards establishing the maximum output which can be achieved with given set of factors of production.
Production function describes the technological relationship between inputs and output in physical terms. Study of production function is directed towards establishing the maximum output which can be achieved with given set of factors of production.
Models of Oligopoly
Cournot’s duopoly model
Sweezy’s kinked demand curve model
Price leadership models
Collusive models :The Cartel Arrangement
The Game Theory
Prisoner’s Dilemma
Price leadership Model
Collusive models The Cartel Arrangement
Models of Oligopoly
Cournot’s duopoly model
Sweezy’s kinked demand curve model
Price leadership models
Collusive models :The Cartel Arrangement
The Game Theory
Prisoner’s Dilemma
Price leadership Model
Collusive models The Cartel Arrangement
We explore the application of optimal control techniques in agent-based macroeconomics. We specifically discussed the Ramsey-Cass-Koopman (savings), Barro (public finance), and Ellis-Fender (corruption) models. Model discussions lifted from Sala-i-Martin's lecture notes on economic growth. Some formulations were taken from lectures of Prof. Emmanuel de Dios and Prof. Rolando Danao of UP School of Economics. All errors mine.
VUCA Stands for Volatility, Uncertainty, Complexity and Ambiguity and often used to describe the new normal of today's business environment. The CPA Vision Project in 1998 identified many of these changes - this presentation talks about "now what"?
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The derivative of a composition of functions is the product of the derivatives of those functions. This rule is important because compositions are so powerful.
Part of Lecture series on EE646, Fuzzy Theory & Applications delivered by me during First Semester of M.Tech. Instrumentation & Control, 2012
Z H College of Engg. & Technology, Aligarh Muslim University, Aligarh
Reference Books:
1. T. J. Ross, "Fuzzy Logic with Engineering Applications", 2/e, John Wiley & Sons,England, 2004.
2. Lee, K. H., "First Course on Fuzzy Theory & Applications", Springer-Verlag,Berlin, Heidelberg, 2005.
3. D. Driankov, H. Hellendoorn, M. Reinfrank, "An Introduction to Fuzzy Control", Narosa, 2012.
Please comment and feel free to ask anything related. Thanks!
Question bank on digital electronics. Total 194 questions. Covering questions on basics of digital electronics, number systems, digital gates, logic families, the sum of product, the product of sum, boolean theorem, karnaugh map, coders, etc.
Production decline analysis is a traditional means of identifying well production problems and predicting well performance and life based on real production data. It uses empirical decline models that have little fundamental justifications. These models include
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Exponential decline (constant fractional decline)
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Harmonic decline, and
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Hyperbolic decline.
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2. What is Cobb-Douglas Production
Function?
During 1900–1947, Charles Cobb and Paul
Douglas formulated and tested the Cobb–
Douglas production function through various
statistical evidence.
Q = b0 X Y
b1
b2
The Cobb–Douglas functional form of
production functions is widely used to represent
the relationship of an output and two inputs.
3. Question 7.2
Production Function Estimation. WashingtonPacific, Inc., manufactures and sells lumber,
plywood, veneer, particle board, medium-density
fiber board, and laminated beams. The company
has estimated the following multiplicative
production function for basic lumber products in
the Pacific Northwest market:
Q = b0 L K E
b1
b2
b3
Q = output,
L = labor input in worker hours,
K = capital input in machine hours and
E = energy input in BTUs (British Thermal Unit)
4. Each of the parameters of this model
was estimated by regression analysis
using monthly data over a 3-years
period. Coefficient estimation results
were as follows:
ˆ
ˆ
ˆ
ˆ
b0 = 0.9; b1 = 0.4; b2 = 0.4; b3 = 0.2
The standard error estimates for each
coefficient are
σ b 0 = 0.6; σ b1 = 0.1; σ b 2 = 0.2; σ b 3 = 0.1
5. Question 1. Estimate the effect on
output of a 1% decline in worker hours
(holding K and E constant)
Given,
Q = b0 L K E
b1
b2
b3
Take the first derivation with respect to
worker hours (L)
Q = 0L K
b
b1
b2
E
b3
6. ∂
Q
1
=b0b1 Lb1 − K b2 E b3
∂
L
∂
Q
1
=b1b0 Lb1 K b2 E b3 L−
∂
L
∂
Q
1
=b1QL−
∂
L
∂
Q
Q
∂
Q
∂
L
=b1
=b1 *
Q
L
∂
L
L
∂
Q
∂
Q L
= 0.4( − .01)
0
*
=b1
Q
∂
L Q
∂
Q
= − .004 = − .4%
0
0
∂
Q ∂
L
Q
b1 =
÷
Q
L
7. Question 2 . Estimate the effect on output
of a 5% reduction in machine hours
availability accompanied by a 5% decline in
energy input (holding L constant)
Solution: From part A it is clear that,
∂Q
= b2 (∆K / K ) + b3 (∆E / E )
Q
∂Q
= 0.4(−0.05) + 0.2(−0.05)
Q
∂Q
= −0.03 = −3%
Q
ˆ
b0 = 0.9
ˆ
b = 0 .4
1
ˆ
b2 = 0.4
ˆ
b3 = 0.2
8. Question 3. Estimate the returns to scale for
this production system.
Solution:
In case of Cobb Douglas production function,
the returns to scale are determined by
summing up exponents because:
Q =b0 L K
b1
b2
E
b3
hQ =b0 ( kL) ( kK )
b1
b2
hQ =k
b1 + 2 + 3
b
b
b0 L K
hQ =k
b1 + 2 + 3
b
b
Q
b1
( kE )
b2
E
b3
b3
9. Thus, summing up the value of the
exponents, we get,
b1 + b2 + b3 = 0.4 + 0.4 + 0.2 = 1
hQ = k Q
1
h=k
1
This indicates constant returns to
scale estimation.
11. Conclusion
Returns
to Scale is the quantitative change
in output of a firm or industry resulting from
a proportionate increase in all inputs.
Adding
the value of the exponents, we can
determine the returns to scale of a
production function.