Question 5. The Cobb-Douglas production function is widely used in economic and empirical analysis because it possesses several useful mothematical properties. The general form of the Cobb-Douglas production is given as: O = AkaU where A is a positive constant and 0
Question 5. The Cobb-Douglas production function is widely used in economic and empirical analysis because it possesses several useful mothematical properties. The general form of the Cobb-Douglas production is given as: O = AkaU where A is a positive constant and 0
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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![Question 5. The Cobb-Douglas production firnction is widely used in economic and empirical
analysis because it possesses several useful mathematical properties. The general form of the
Cobb-Douglas production is given as: Q = AkaL where A is a positive constant and 0< a<1,
0<B<1
(a The law of diminishing marginal product states that as units of a variable input are added
to a fixed input, output will increase at a decreasing rate. Suppose that capital (K) is the
fixed input, and that labour (L) is the variable input. Demonstrate the law of diminishing
marginal product using the Cobb-Douglas production function.
b. Assuming that capital is the constant factor of production, what is the proportional change
in output resulting from a proportional change in labour input?
Consider the following Cobb-Douglas production function Q 25k0.$L0.5, verify that this
expression exhibits the law of diminishing marginal product with respect to capital.
d. Suppose that an individual consumes three goods, Q1, Q2 and Q3. Suppose further that
the respective proportions of total income devoted to the consumption of these goods are
Eighty, Twenty and Twenty percent. The income elasticities for Qi and Q2 are 0.5 and
1.5. How would you.classify these goods?
Cunon contional data from PDO's](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F237376bc-3885-4a48-a3e3-6ce53540f723%2F50c1656c-178b-4b1f-8f19-27b64c6b7b09%2Falzdqa9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 5. The Cobb-Douglas production firnction is widely used in economic and empirical
analysis because it possesses several useful mathematical properties. The general form of the
Cobb-Douglas production is given as: Q = AkaL where A is a positive constant and 0< a<1,
0<B<1
(a The law of diminishing marginal product states that as units of a variable input are added
to a fixed input, output will increase at a decreasing rate. Suppose that capital (K) is the
fixed input, and that labour (L) is the variable input. Demonstrate the law of diminishing
marginal product using the Cobb-Douglas production function.
b. Assuming that capital is the constant factor of production, what is the proportional change
in output resulting from a proportional change in labour input?
Consider the following Cobb-Douglas production function Q 25k0.$L0.5, verify that this
expression exhibits the law of diminishing marginal product with respect to capital.
d. Suppose that an individual consumes three goods, Q1, Q2 and Q3. Suppose further that
the respective proportions of total income devoted to the consumption of these goods are
Eighty, Twenty and Twenty percent. The income elasticities for Qi and Q2 are 0.5 and
1.5. How would you.classify these goods?
Cunon contional data from PDO's
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