Principles of Economics (MindTap Course List)
8th Edition
ISBN: 9781305585126
Author: N. Gregory Mankiw
Publisher: Cengage Learning
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Chapter 18, Problem 9PA
Subpart (a):
To determine
To calculate: The output, wage, and labor share.
Subpart (b):
To determine
To calculate: The output, wage, and labor share.
Subpart (c):
To determine
To calculate: The output, wage, and labor share.
Subpart (d):
To determine
To calculate: The output, wage, and labor share.
Subpart (e):
To determine
To calculate: The output, wage, and labor share.
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Some economists believe that the US. economy as a whole
can be modeled with the following production function, called
the Cobb-Douglas production function: Y = AK¹/32/3
where Y is the amount of output K is the amount of capital, L is
the amount of labor, and A is a parameter that measures the
state of technology. For this production function, the marginal
product of labor is MPL = (2/3) A(K/L)¹/³. Suppose that the
price of output P is 2, A is 3, K is 1,000,000, and L is 1/100. The
labor market is competitive, so labor is paid the value of its
marginal product.
a. Calculate the amount of output produced Y and the dollar
value of output PY.
b. Calculate the wage W and the real wage W/P. (Note: The
wage is labor compensation measured in dollars, whereas the
real wage is labor compensation measured in units of output)
Q2.
1- Suppose that you are given the following production function:
Q = 100K0.6L0.4
Determine the marginal product of capital and the marginal product of labor when K =
25 and L= 100.
2- For each of the following production functions, determine whether returns to scale
are decreasing, constant, or increasing when capital and labor inputs are increased from
K= L = 1 to K = L = 2.
a. Q = 25K0.5L0.5
b. Q = 2K + 3L + 4KL
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
Chapter 18 Solutions
Principles of Economics (MindTap Course List)
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