Special Production Functions:
Linear Production Function (Perfect Substitutes, σ = ∞)
Q = cL + dK , c and d are positive constants.
Example: natural gas or fuel oil in manufacturing process.
Company data storage between high-capacity and low-capacity computers.
Fixed-proportions Production Function (Perfect Complements, σ = 0, Leontief Function)
Q = min(aL,bK), a and b are positive constants.
Example: fixed portions of oxygen and hydrogen atoms to make water molecules one frame with two tires for bicycle one chassis with four tires for a car.
Cobb-Douglas Production Function:
Q = ALα Kβ, A, α, β are positive constants.
Homogeneous Function of degree r:
y = f (x, z)
If we k-fold all the independent variables x and z, f (kx, kz) ≡ kr f (x, z) = kr y
If r = 1, the function is also known as linear homogeneous function.
Example: Identify the following functions.
a) y = 3x2 + xz − 2z2b) y= (x/3z) + 5c) y = xa z1−a
Returns to scale for a Cobb-Douglas Production Function:
Let L1 and K1denote the initial quantities of labor and capital, and let Q1 denote the initial output, so Q1 AL1α K1β . Now let’s increase all input quantities by the same proportional amount λ , where λ > 1, and let Q2 denote the resulting volume of output:
Q2 A (λ L1)α (λ K1)β = λα+β AL1α K1β = λα +β Q1. From this, we can see that if:
a) α + β > 1, then λα +β > λ , and so Q2 > λ Q1 (increasing returns to scale IRS)b) α + β = 1 , then λα+β = λ , and so Q2 = λ Q1 (constant returns to scale CRS)c) α + β < 1, then λα+β < λ , and so Q2 < λQ1 (decreasing returns to scale DRS)
Constant Elasticity of Substitution (CES) Production Function:
σ is independent of MRTSL,K or input ratio (K/L) or even output Q
Q = A[aL-p + (1− a)K-p]-r/p, where A > 0, 0 < a < 1, ρ ≥ −1.
r is the degree of homogeneity. σ = (1/p)
a) If ρ = −1 (σ = ∞) , Q = A[aL + (1− a)K]r (isoquant is a straight-line).
b) If ρ = 0 (σ = 1), we need a trick because we can’t define 1∞
Taking log on both sides, we can get logQ = log A – (r/p) log[aL-p + (1− a)K-p]
But the second term of r.h.s. is indeterminate because of 0/0. The best way to solve this problem is to use L’Hospital rule.
(You can check out why Cobb-Douglas has σ = 1)
c) If ρ →∞ (σ = 0 ). Leontief Production Function Q = min[aL, bK]
Returns to Scale: revisited
f (kL, kK) = kf (L, K) : CRSf (kL, kK) > kf (L, K) : IRSf (kL, kK) < kf (L, K) : DRS
Latest technology based Microeconomics Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Microeconomics help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Microeconomics, project ideas and tutorials. We provide email based Microeconomics help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Microeconomics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Microeconomics Homework help and assignment help services. They use their experience, as they have solved thousands of the Microeconomics assignments, which may help you to solve your complex issues of Microeconomics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
tutorsglobe.com market according to area assignment help-homework help by online classification of markets tutors
tutorsglobe.com dominant epistasis assignment help-homework help by online types of epistasis tutors
it is significant to take great care throughout the bearing removal to make sure that the bearing, shaft and housing are not broken. bearing removal is best accomplished through using a bearing puller for standard outer and inner rings.
Ratios can be collected into categories, with each category relating to a specific aspect of financial performance or position.
Theory and lecture notes of Fiscal Policy-Automatic Stabilizers all along with the key concepts of Rules vs. Authorities, Competence and Objectives, Political Business Cycle , Central Bank Independence. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Fiscal Policy-Automatic Stabilizers.
Habitat Studies tutorial all along with the key concepts of Animal Sampling Methods, Short vegetation and litters, Tall vegetation or grasses, Plant Sampling Methods and Soil Sampling Methods
basic concept of statistical mechanics tutorial all along with the key concepts of elementary probability theory, entropy and probability, concept of statistical mechanic, statistical ensembles, distribution function
Theory and lecture notes of Calculating Real GDP all along with the key concepts of calculating real gdp, Real GDP, Inventories and Imputations. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Calculating Real GDP.
Preventive maintenance is the maintenance that has to be performed to the equipment, in a pre designed way before severe breakdown occurs.
to learn the two inputs of the arithmetic circuits of half adder, full adder and flip flops using ics.
tutorsglobe.com greek art assignment help-homework help by online humanities tutors
tutorsglobe.com acquired immunity assignment help-homework help by online immunology tutors
www.tutorsglobe.com offers theoretical physics homework help, theoretical physics assignment help, online tutoring assistance, online theoretical physics solutions by online qualified and experienced tutors help.
tutorsglobe.com lysogenic cycle assignment help-homework help by online life cycle of a phage tutors
www.tutorsglobe.com offers literature review, annotated bibliography writing service, writing literature review homework help, assignment help by online literature review writers help.
1960148
Questions Asked
3689
Tutors
1441278
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!