The production function Y=K1/3L2/3−G exhibits________ returns to scale in K and L. (Assume G is a positive real number.)

Question

The production function  Y=K1/3L2/3−G  exhibits________ returns to scale in K and L. (Assume G is a positive real number.)

BlackTom AI · Accepted Answer

The production function is Y = K^{1/3} L^{2/3} − G, where G > 0.

First, consider homogeneous components: K^{1/3} L^{2/3} is a Cobb-Douglas function with exponents summing to 1, which by itself would exhibit constant returns to scale if it were the entire production function.

However, the −G term is a fixed amount that does not depend on K or L. This fixed cost term changes how output scales when we scale inputs.

Let us scale inputs by a factor t > 1: f(tK, tL) = (tK)^{1/3} (tL)^{2/3} − G = t^{1/3} t^{2/3} K^{1/3} L^{2/3} − G = t (K^{1/3} L^{2/3}) − G.

Now compare f(tK, tL) to t f(K, L): t f(K, L) = t [K^{1/3} L^{2/3} − G] = t K^{1/3} L^{2/3} − t G.

Subtracting, we get f(tK, tL) − t f(K, L) = [t (K^{1/3} L^{2/3}) − G] − [t K^{1/3} L^{2/3} − t G] = (t − 1) G.

Since G > 0 and t > 1, (t − 1) G > 0, so f(tK, tL) > t f(K, L) for all t > 1. This is the hallmark of increasing returns to scale in K and L.

Therefore, the function exhibits increasing returns to scale in K and L because the fixed cost term G causes the total output to scale more than proportionally when inputs are scaled up. The key takeaway is that the −G term breaks the pure constant-returns-to-scale property of the K^{1/3} L^{2/3} part, leading to increasing returns due to the fixed deduction becoming relatively less significant at larger scales.

FA25 ECON 302 002 Homework #2 (Model of Production)

The production function Y=K1/3L2/3−G exhibits________ returns to scale in K and L. (Assume G is a positive real number.)

View Explanation

Log in for full answers

Similar Questions

Gale Furniture uses labor, capital, and wood as inputs in its production of office desks. When Gale Furniture doubles the quantity of labor, capital, and wood, the quantity of office desks doubles. Gale Furniture’s production process is characterized by

Question5 According to Andreoni and Levinson (2001), the sweeper analogy is an example of: None of the other options are correct Decreasing returns to scale No returns to scale Increasing returns to scale ResetMaximum marks: 1 Flag question undefined

Indivisibility of capital causes _ returns to scale due to in the __ production model.

Question at position 12 Which of the following is NOT a reason for decreasing returns to scale?technology changegrowth of bureaucracyworker disaffectionmanagement command and control problems

Suppose General Motors could triple its production of Cavaliers by tripling its production facility for those cars. This is an example of

If bread is produced by using a constant returns to scale production function, then if the:

A firm's production function is Y=F(K,L). If the firm doubles both K and L, output less than doubles. This implies

10. When a firm doubles its inputs and finds that its output has more than doubled, this is known as: A. Economies of scale B. Constant returns to scale C. Diseconomies of scale D. A violation of the law of diminishing returns

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler

FA25 ECON 302 002 Homework #2 (Model of Production)

The production function Y=K1/3L2/3−G exhibits________ returns to scale in K and L. (Assume G is a positive real number.)

View Explanation

Log in for full answers

Similar Questions

Gale Furniture uses labor, capital, and wood as inputs in its production of office desks. When Gale Furniture doubles the quantity of labor, capital, and wood, the quantity of office desks doubles. Gale Furniture’s production process is characterized by

Question5 According to Andreoni and Levinson (2001), the sweeper analogy is an example of: None of the other options are correct Decreasing returns to scale No returns to scale Increasing returns to scale ResetMaximum marks: 1 Flag question undefined

Indivisibility of capital causes _________ returns to scale due to ________ in the __________ production model.

Question at position 12 Which of the following is NOT a reason for decreasing returns to scale?technology changegrowth of bureaucracyworker disaffectionmanagement command and control problems

Suppose General Motors could triple its production of Cavaliers by tripling its production facility for those cars. This is an example of

If bread is produced by using a constant returns to scale production function, then if the:

A firm's production function is Y=F(K,L). If the firm doubles both K and L, output less than doubles. This implies

10. When a firm doubles its inputs and finds that its output has more than doubled, this is known as: A. Economies of scale B. Constant returns to scale C. Diseconomies of scale D. A violation of the law of diminishing returns

More Practical Tools for Students Powered by AI Study Helper

Making Your Study Simpler

Indivisibility of capital causes _ returns to scale due to in the __ production model.