Which of the following is a Cobb–Douglas production function?

I. Q = f(K, L)

II. Q = 5K + 2.5L

III. Q=min{K, 2L}

IV. Q= K50L0.75

Question

Which of the following is a Cobb–Douglas production function?

I. Q = f(K, L)

II. Q = 5K + 2.5L

III. Q=min{K, 2L}

IV. Q= K50L0.75

BlackTom AI · Accepted Answer

The question asks which of the given functional forms is a Cobb–Douglas production function. I will evaluate each option in turn.
Option I: Q = f(K, L). This is a generic statement indicating a production function with capital K and labor L, but it provides no specific functional form. A Cobb–Douglas production function is a precise functional form with multiplicative powers of inputs, typically Q = A K^α L^β. Simply writing f(K, L) does not identify a Cobb–Douglas form, so this option is not necessarily a Cobb–Douglas function.
Option II: Q = 5K + 2.5L. This is a linear additive (sum) form in K and L, i.e., a linear production function. Cobb–Douglas functions are multiplicative in inputs and exhibit constant elasticity of substitution of unity only in log-linear form, not additive in inputs. Therefore, this option does not represent a Cobb–Douglas function.
Option III: Q = min{K, 2L}. This is a Leontief (perfect complements) production function, where output is constrained by the bottleneck input. Cobb–Douglas functions do not take a min form; they are smooth and differentiable with diminishing marginal products. Hence, this is not Cobb–Douglas.
Option IV: Q = K^{0.5} L^{0.75} (written as Q = K50L0.75 with the implied exponents). This is a multiplicative function of K and L with exponents that sum to 1.25, which indicates constant returns to scale only if the sum equals 1; in this case the sum is 0.5 + 0.75 = 1.25, which would imply increasing returns to scale. Nevertheless, the functional form—Q = A K^α L^β with α, β > 0—is the defining characteristic of a Cobb–Douglas production function. The specific powers show the Cobb–Douglas structure, even if the returns to scale are not unit. Therefore, this option matches the Cobb–Douglas form.
In summary, each option was evaluated against the defining characteristics of a Cobb–Douglas production function: a smooth, multiplicative form with inputs raised to constant exponents. Only the fourth option exhibits this multiplicative power structure with K and L raised to positive exponents, characterizing a Cobb–Douglas specification.

ECON3200001.1251 Pre-class Quiz 4

Which of the following is a Cobb–Douglas production function? I. Q = f(K, L) II. Q = 5K + 2.5L III. Q=min{K, 2L} IV. Q= K50L0.75

View Explanation

Log in for full answers

Similar Questions

Consider the “Cobb-Douglas” production function given by where A is a positive constant. Suppose that the capital stock grows at 2% per year and the labour force grows at 1% per year. According to the production function, what will output growth be approximately?

Suppose that a firm had a production function given by: q=2L0.5K0.5. The rental rate for the firm is $10 and the wage is $5. Solve the optimization condition for K and then fill in the value that appears in front of L.K = Answer Question 2[input]L(Round to the nearest 2 decimal places if necessary.)

One of the key characteristics of the Cobb-Douglas production function with exponents (for capital) and (for labor) and a common productivity across countries (where the markets for labor and capital are competitive) is that:

In a consumer society, many adults channel creativity into buying things

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