Let y = f(x1, x2)=x11/2 + x1x2 be a firm’s production function, where x1≥0, x2≥0.   Write down the firm’s production possibility set, and its input requirement set. Is this production function concave, quasi-concave? Is this production function homogenous? Find its returns to scale when x1=1, and x2=1.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.10P
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  1. Let y = f(x1, x2)=x11/2 + x1x2 be a firm’s production function, where x1≥0, x2≥0.

 

    1. Write down the firm’s production possibility set, and its input requirement set.
    2. Is this production function concave, quasi-concave?
    3. Is this production function homogenous?
    4. Find its returns to scale when x1=1, and x2=1.
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