1) Consider the following function, where A>0 and 0<α<1.Y=ALαThe function isa.strictly negative and concaveb.strictly negative and convexc.strictly positive and convexd.strictly positive and concave
Question
- Consider the following function, where A>0 and 0<α<1.Y=ALαThe function isa.strictly negative and concaveb.strictly negative and convexc.strictly positive and convexd.strictly positive and concave
Solution
The function Y=AL^α is strictly positive and concave.
Here's why:
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The function is strictly positive because both A and L are positive. Any positive number raised to any power is always positive. Therefore, Y is always positive.
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The function is concave because 0<α<1. In the context of production functions like this one, α represents the elasticity of output with respect to the input L. When 0<α<1, it means that output increases at a decreasing rate as L increases, which is the definition of a concave function.
So, the correct answer is d. strictly positive and concave.
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