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 = AK¹/3 L2/3 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
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 = AK¹/3 L2/3 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
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.9P
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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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0dcfc0a-e791-4eee-a49f-35fc9b627afe%2F6353e95c-bb51-43b0-85f3-83beaeb24a98%2Fqwc4c1e_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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)
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