Consider a firm that has a Cobb-Douglas technology. The firm wishes to minimize the cost of producing y units of output and has access to perfectly competitive factor markets. The firm's cost minimization problem is given by: min wl +rk {k,l} s.t. k°18 = Y Let μ denote the Lagrange multiplier on the output constraint.
Consider a firm that has a Cobb-Douglas technology. The firm wishes to minimize the cost of producing y units of output and has access to perfectly competitive factor markets. The firm's cost minimization problem is given by: min wl +rk {k,l} s.t. k°18 = Y Let μ denote the Lagrange multiplier on the output constraint.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Please answer in detail according to the picture.
Show that the cost function is homogeneous of degree 1/(α+β) in output.
How do the returns to scale (degree of homogeneity of the production function) relate to the properties
of the cost function? Does this make sense to you? Explain clearly why.
![Consider a firm that has a Cobb-Douglas technology. The firm wishes to minimize the cost of producing y
units of output and has access to perfectly competitive factor markets. The firm's cost minimization problem
is given by:
min wl +rk
{k,l}
s.t. k°18
= Y
Let μ denote the Lagrange multiplier on the output constraint.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf58e778-209d-4051-b758-0c57e3f8187c%2Fda19c632-2feb-4a85-845a-9974b21408d8%2Fj8ya1o_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a firm that has a Cobb-Douglas technology. The firm wishes to minimize the cost of producing y
units of output and has access to perfectly competitive factor markets. The firm's cost minimization problem
is given by:
min wl +rk
{k,l}
s.t. k°18
= Y
Let μ denote the Lagrange multiplier on the output constraint.
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