Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb a. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or or y' or dy/dk ? c. Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why?
Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb a. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or or y' or dy/dk ? c. Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why?
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.2P
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Question
Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb
a. |
Find output per labor; capital per labor (y=Y/ L and k= K/L ). |
b. |
Briefly define what is derivative of y with respect to k or or y' or dy/dk ? |
c. |
Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why? |
d. |
Briefly explain why y'' ≤ 0 . |
e. |
Find the elasticity of substitution between K and L. What does expansion path look like? |
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