Asked by Chloe Guida on May 23, 2024
Verified
if the exponents in the production function were 0.30 for x1 and 0.20 for x2, this production function would exhibit (constant, increasing, decreasing) returns to scale and (would, would not) have diminishing technical rate of substitution.
A) decreasing, would not
B) constant, would not
C) increasing, would
D) constant, would
E) decreasing, would
Production Function
A mathematical representation that describes the relationship between inputs used in production and the output achieved.
Returns To Scale
A term in economics that describes how the change in the amount of input affects the change in output of a production process.
- Discern the different categories of returns to scale (augmenting, lessening, invariant) by scrutinizing the coefficients in production functions.
- Investigate production functions to detect the presence or lack of a decreasing technical rate of substitution.
Verified Answer
NS
Naresh SharmaMay 29, 2024
Final Answer :
E
Explanation :
The sum of the exponents in each term of the production function is 0.30+1+1+0.11+0.20+1+1+0.12=4.84 for x1 and 0.20+1+1+1+1+1+0.12=5.32 for x2. Since both are less than 6, which is the minimum value for increasing returns to scale, the production function exhibits decreasing returns to scale. Also, both terms have exponents less than 1, which means the technical rate of substitution between inputs is diminishing, hence the answer is "would".
Learning Objectives
- Discern the different categories of returns to scale (augmenting, lessening, invariant) by scrutinizing the coefficients in production functions.
- Investigate production functions to detect the presence or lack of a decreasing technical rate of substitution.