1. Show that the two-input Cobb-Douglas production function used in this lecture has DRS, CRS or IRS depending on whether a + az is smaller than, equal, or larger than one.
1. Show that the two-input Cobb-Douglas production function used in this lecture has DRS, CRS or IRS depending on whether a + az is smaller than, equal, or larger than one.
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.9P
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Q1
and ignore lecture info,,...
you do it
![1. Show that the two-input Cobb-Douglas production function used in this lecture has
DRS, CRS or IRS depending on whether an + az is smaller than, equal, or larger
than one.
2. Show that the two-input CES production function used in this lecture has DRS, CRS
or IRS depending on whether 3 is smaller than, equal, or larger than one.
3. Show that, for the two-input CES production function used in this lecture,
4. Verify that a homogenous function has IRS, CRS or DRS depending on whether the
degree of the function satisfies y > 1, y = 1, or y < 1.
5. Verify that a homogenous function is necessarily homothetic.
6. A general version of the Cobb-Douglas production function can be written as
сan
f(r1,..., In) = x'r ...
where a > 0 for k = 1,...,n. Similarly, a general version of the CES production
function can be written as
f(#1,... , In) = A(Eapr9/°,
where E ar = 1. For each of the two production functions, find the TRS between
two inputs, k and k'.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe71589-55eb-49b1-8991-b6a0b3ca4044%2F9fe77f98-b20b-434f-bf96-800d6ac63b73%2F9qo5rv9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Show that the two-input Cobb-Douglas production function used in this lecture has
DRS, CRS or IRS depending on whether an + az is smaller than, equal, or larger
than one.
2. Show that the two-input CES production function used in this lecture has DRS, CRS
or IRS depending on whether 3 is smaller than, equal, or larger than one.
3. Show that, for the two-input CES production function used in this lecture,
4. Verify that a homogenous function has IRS, CRS or DRS depending on whether the
degree of the function satisfies y > 1, y = 1, or y < 1.
5. Verify that a homogenous function is necessarily homothetic.
6. A general version of the Cobb-Douglas production function can be written as
сan
f(r1,..., In) = x'r ...
where a > 0 for k = 1,...,n. Similarly, a general version of the CES production
function can be written as
f(#1,... , In) = A(Eapr9/°,
where E ar = 1. For each of the two production functions, find the TRS between
two inputs, k and k'.
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