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1. Under what conditions will each of the following production functions exhibit (i) increasing returns to scale, (ii) decreasing returns to scale, and (iii) constant returns to scale? Notes: your answer should be in the form of inequalities involving a and/or b. For some production functions it may not be possible to exhibit each type of returns to scale. (a) ƒ (L, K) = LªK" (assume that 0 < a < 1 and 0 < b < 1) (b) ƒ (L, K) = a ( K® + L') (assume that a > 0, b > 0) (c) f (L, K) = (aK + bL)î (assume a > 0 and b > 0) (d) ƒ (L, K) = aK L' (assume a > 0) %3D

1. Under what conditions will each of the following production functions exhibit (i) increasing returns to scale, (ii) decreasing returns to scale, and (iii) constant returns to scale? Notes: your answer should be in the form of inequalities involving a and/or b. For some production functions it may not be possible to exhibit each type of returns to scale. (a) ƒ (L, K) = LªK" (assume that 0 < a < 1 and 0 < b < 1) (b) ƒ (L, K) = a ( K® + L') (assume that a > 0, b > 0) (c) f (L, K) = (aK + bL)î (assume a > 0 and b > 0) (d) ƒ (L, K) = aK L' (assume a > 0) %3D

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. Under what conditions will each of the following production functions exhibit (i) increasing returns to scale, (ii) decreasing returns to scale, and (iii) constant returns to scale? Notes: your answer should be in the form of inequalities involving a and/or b. For some production functions it may not be possible to exhibit each type of returns to scale. (a) ƒ (L, K) = LªK* (assume that 0 <a < 1 and 0 < b < 1) (b) ƒ (L, K) = a ( Kb + L') (assume that a > 0, b > 0) (c) f (L, K) = (aK + bL)? (assume a > 0 and b > 0) (d) ƒ (L, K) = aK Lº (assume a > 0) %3D
Transcribed Image Text:1. Under what conditions will each of the following production functions exhibit (i) increasing returns to scale, (ii) decreasing returns to scale, and (iii) constant returns to scale? Notes: your answer should be in the form of inequalities involving a and/or b. For some production functions it may not be possible to exhibit each type of returns to scale. (a) ƒ (L, K) = LªK* (assume that 0 <a < 1 and 0 < b < 1) (b) ƒ (L, K) = a ( Kb + L') (assume that a > 0, b > 0) (c) f (L, K) = (aK + bL)? (assume a > 0 and b > 0) (d) ƒ (L, K) = aK Lº (assume a > 0) %3D
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