In economics and econometrics, the Cobb-Douglas production function is a particular functional form of e production function, widely used to represent the technological relationship between the amounts of two : more inputs (particularly physical capital and labor) and the amount of output that can be produced by nose inputs. The function they used to model production is defined by, P(L, K) = 6LªK1-a where P is the total production (the monetary value of all goods produced in a year), L is the amount labor (the total number of person-hours worked in a year), and K is the amount of capital invested (the onetary worth of all machinery, equipment, and buildings). Its domain is {(L, k)|L > 0, K > 0} because L nd K represent labor and capital and are therefore never negative. Show that the Cobb-Douglas production function can be written as P = In b +a ln K L P(L, K) = ¿LªK!-a → In K
In economics and econometrics, the Cobb-Douglas production function is a particular functional form of e production function, widely used to represent the technological relationship between the amounts of two : more inputs (particularly physical capital and labor) and the amount of output that can be produced by nose inputs. The function they used to model production is defined by, P(L, K) = 6LªK1-a where P is the total production (the monetary value of all goods produced in a year), L is the amount labor (the total number of person-hours worked in a year), and K is the amount of capital invested (the onetary worth of all machinery, equipment, and buildings). Its domain is {(L, k)|L > 0, K > 0} because L nd K represent labor and capital and are therefore never negative. Show that the Cobb-Douglas production function can be written as P = In b +a ln K L P(L, K) = ¿LªK!-a → In K
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.2P
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![In economics and econometrics, the Cobb-Douglas production function is a particular functional form of
ne production function, widely used to represent the technological relationship between the amounts of two
r more inputs (particularly physical capital and labor) and the amount of output that can be produced by
nose inputs. The function they used to model production is defined by,
P(L, K) = 6LªK!-a
where P is the total production (the monetary value of all goods produced in a year), L is the amount
f labor (the total number of person-hours worked in a year), and K is the amount of capital invested (the
onetary worth of all machinery, equipment, and buildings). Its domain is {(L, k)|L > 0, K > 0} because L
nd K represent labor and capital and are therefore never negative.
Show that the Cobb-Douglas production function can be written as
P
P(L, K) = 6LªK1-a → In
K
L
In b+ a ln
K](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40588187-81d1-497b-9f13-c3fe35682ff3%2Ff2cd73c2-1160-4f17-b30d-5d26c492d17b%2Fs2po0td_processed.png&w=3840&q=75)
Transcribed Image Text:In economics and econometrics, the Cobb-Douglas production function is a particular functional form of
ne production function, widely used to represent the technological relationship between the amounts of two
r more inputs (particularly physical capital and labor) and the amount of output that can be produced by
nose inputs. The function they used to model production is defined by,
P(L, K) = 6LªK!-a
where P is the total production (the monetary value of all goods produced in a year), L is the amount
f labor (the total number of person-hours worked in a year), and K is the amount of capital invested (the
onetary worth of all machinery, equipment, and buildings). Its domain is {(L, k)|L > 0, K > 0} because L
nd K represent labor and capital and are therefore never negative.
Show that the Cobb-Douglas production function can be written as
P
P(L, K) = 6LªK1-a → In
K
L
In b+ a ln
K
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