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Production Function Analysis, Assignments of Economics

Carleton UniversityEconomics

A detailed analysis of production functions, including the concepts of average product, marginal product, and marginal rate of technical substitution. It covers various production function scenarios, such as when capital is fixed, when labor and capital are perfect substitutes, and when there are increasing, decreasing, or constant returns to scale. The document also includes specific examples of production functions for different firms and the calculation of their respective marginal products and marginal rates of technical substitution. Overall, this document offers a comprehensive understanding of production function theory and its practical applications in economic analysis.

Typology: Assignments

2023/2024

Uploaded on 05/25/2024

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Chanitatallapudi
ECON
202013
Fall
2022
Student
D:
101241001
Assignment
31
Production
Function
:
q
=
[
◦
'
75
k
0.25
a)
The
average
product
,
when
capital
is
fixed
at
E
.
AP
,
=
¥
=
[
◦
'
75
1<-0.25
c-
=
2-
◦
'
25
¢-0.25
=
]
◦
'
25
b)
The
Marginal
Product
of
labour
is
,
MP
,
=
dd&
=d(ik
=
3-
¥1025
pf3
pf4
pf5
pf8
pf9

Partial preview of the text

Download Production Function Analysis and more Assignments Economics in PDF only on Docsity!

Chanitatallapudi

ECON (^202013) Fall 2022 Student^ D: 101241001 Assignment

Production (^) Function : q

= [

◦ ' 75

k

a) The^ average product , when^ capital is^ fixed at^ E^. AP,^ = ¥ = [ ◦ ' 75 1<-0.

c-

◦ ' 25

= ] ◦ ' 25 b) The Marginal Product of^ labour^ is (^) , MP,^ = dd& =d(ik = 3-¥ 1025

c) At^ I^ =^16.

AR =

#]^ ° " = (^2) L

  • (^) O - 25 0- MP.^ -^ - 1- (E) = g3- ✗ (^2) (^ 0-

1<=2 (^) ; ( →

varry

a) q =^ 10L^ +^ K

Since (^) , the firm fixed (^) capital at (^) 1<=2 (^) , the Marginal

Product of

labor . MR

=gdq- is constant 10 even (^) though the labor varrys .

Hence ,

at (^) the (^) production function (^) ,

q

= 10L + K and 1<=2 , the firm

does not (^) experience any diminishing returns of^ labor^.

4.1£ a) Will 's^ production function^. Gw =^ 2.5^ AO^

  • Ro - Therefore.

Will 's^ MPR =

dˢ

d(25g°ˢᵗR"

= / • 6 ( A

◦ ' 36 R

  • 036 ) = 1-61,1%7-1=1.61* ""
  • ①

David's Production function ,

GD =^ 2.5A^ ◦ ' 25120-

Therefore ,

David's MPR =

ddG#

d(25Ag°;5R°' = / • 875 ( AO (^) -2512 -025 ) = 1-8751%9%-1=1-87511-1%

  • ②

b) The^

Marginal Rate of^ Technical Substitution^ (^ MRTS) tells (^) us how

many

units of^ capital the firm^ can replace with an extra^ unit of^ labour

while (^) holding output constant - To (^) calculate (^) Will 's MRTS (^) = MμPp÷

  • ③

MPa

=daaGw_

d(25aAn°ˢ°Rʳ = 0.9 A -0-64120. = (^) a .%%:÷ (^) ] = 0-91* "" _ ⑥

will 's MRTS =

Mμ;- Substituting ⑥ and^ ① in (^) ③ =%¥¥É " = :*

c) Consider the (^) following production functions

Gw =^ 1.5^ A

◦ '

2512075 ; G,^ =^ 3A

" 2512075 Will 's^ MPA =^0375 [ ]^ ◦ (^) " 5

Davids MPa =^075

[Raif ◦ ' * Will 's^ MPR = 1.1251¥]^ ""

David's^ MPR =

2.251,2-- "° Calculate (^) MRTS for will and David (^).

Will 's^ MRTS =

[÷]^ ° "

David 's^ MRTS =

13-[1*2] ◦ ° Thus, the functions^ have^ different^ marginal products^

but the

same MRTS^.

51 Marginal Property^

: It is

change

in (^) output (^) resulting from^ employing one or more unit^ of^ particular input. The Cobb^ Douglas production function is (^). q

= Ala Kb Mc = f (L , K , M )

Here.

L →^ labor K →^ Capital

M → Material

q

→ (^) output for (^) Increasing Returns to scale at btc >^1

for Decreasing Returns to Scale

at b^ +^ c^ <^1 for (^) Constant Returns to Scale at btc^ =^ / A =^0 -23 (^) , D= 0-10 (^) , C = 0. A t^ b^ t^ C =^ 0-23^ +^ 0-10^ +^ 0. = (^) 0. I (^1)

Since , atbtc ≈^1. the

production function (^) has nearly

constant

returns to scale^.