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.
Chapter1: Making Economics Decisions
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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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