Question 1

For the production function Q = aL + bK,where a and b are constants,the 
A) declines as the firm substitutes labor for capital.
B) remains constant as the firm substitutes labor for capital.
C) implies upward-sloping, straight-line isoquants.
D) is undefined.

Accepted Answer

The marginal product of labor (MPL) is a, which is a constant, and the marginal product of capital (MPK) is b, which is also a constant. Therefore, the marginal product of labor does not change as the firm substitutes labor for capital, and the marginal product of capital does not change as the firm substitutes capital for labor. Thus, the total output (Q) increases linearly with the increase in the total input of either labor or capital, and the slope of the isoquants is constant. Therefore, the marginal rate of technical substitution (MRTS) between labor and capital remains constant, which implies that the total output does not change as the firm substitutes labor for capital.

Question 2

Which of the following is true? A) The Cobb-Douglas production function is given by the general formula Q = AL^αK^β and the constant elasticity of substitution is equal to 0. B) The Cobb-Douglas production function is given by the general formula Q = AL^αK^β and the constant elasticity of substitution is equal to 1. C) The Cobb-Douglas production function does not exhibit a constant elasticity of substitution. D) The Cobb-Douglas production function always takes the form Q = K²L².

Accepted Answer

The Cobb-Douglas production function is given by the general formula Q = AL^αK^β and the constant elasticity of substitution is equal to 1.

Question 3

A fixed proportions production function
A) is not observed in practice.
B) has straight line isoquants.
C) has L-shaped isoquants.
D) has a constant marginal rate of technical substitution as the firm substitutes labor for capital.

Accepted Answer

A fixed proportions production function has L-shaped isoquants, indicating that inputs must be used in fixed proportions to produce any given level of output. This means that there is no substitution between inputs, and only one combination of inputs can produce a given output level.

Question 4

Suppose every molecule of salt requires exactly one sodium atom,NA,and one chlorine atom,CL.The production function that describes this is
A) Q = NA + CL
B) Q = NA x CL
C) Q = min(NA, CL)
D) Q = max(NA, CL)

Accepted Answer

The production function that describes the requirement of one sodium atom and one chlorine atom for every molecule of salt is Q = min(NA, CL). This is because the limiting factor in the production of salt is whichever of the two atoms is in lesser quantity. Thus, the function takes the minimum of the two inputs.

Question 5

The production function  exhibits
A) increasing returns to scale.
B) constant returns to scale.
C) decreasing returns to scale.
D) undefined returns to scale.

Accepted Answer

The answer of The production function  exhibits
A) increasing returns...

Question 6

If capital cannot easily be substituted for labor,then the elasticity of substitution is
A) negative.
B) close to zero.
C) close to one.
D) approaching infinity.

Accepted Answer

When capital cannot easily be substituted for labor, the elasticity of substitution is close to zero, indicating that substituting one for the other in production is difficult or nearly impossible.

Question 7

Consider the production function  .The  is
A) 2.00
B) 1.50
C) 1.00
D) 0.50

Accepted Answer

According to the production function, doubling the amount of labor (and holding capital constant) results in a doubling of output. This indicates constant returns to scale, meaning that doubling the inputs (labor and capital) will result in a doubling of output. Therefore, the best choice is to increase both labor and capital by the same proportion, so the answer is A) 2.00.

Question 8

Consider a production function Q = 3K + 4L,when L is graphed on the x-axis and K is graphed on the y-axis,the marginal rate of technical substitution is equal to
A) 4/3 and the isoquant is convex to the origin.
B) 4/3 and the isoquant is a straight line.
C) ¾ and the isoquant is a straight line.
D) 12 and the isoquant is convex to the origin.

Accepted Answer

The formula for the marginal rate of technical substitution (MRTS) is MRTS = MPL/MPK. In this case, MPL = 4 and MPK = 3, so MRTS = 4/3. Since the production function is linear, the isoquant will also be a straight line.

Question 9

For the production function  ,the equation for a typical isoquant is
A) 
B) 
C) 
D)

Accepted Answer

The answer of For the production function  ,the equation...

Question 10

When a production function can be expressed as  ,the relationship between capital and labor in the production function is that
A) capital and labor are perfect substitutes, and the isoquants are linear.
B) capital and labor must be combined in fixed proportions, and the isoquants are L-shaped.
C) capital and labor are easily substituted, and the isoquants are convex to the origin.
D) capital and labor are perfect substitutes, and the isoquants are L-shaped.

Accepted Answer

The answer of When a production function can be expressed...

Question 11

The region of upward sloping backward bending isoquants is
A) Economic region of production
B) Uneconomic region of production
C) Marginal rate of production
D) Marginal rate of technical substitution

Accepted Answer

The upward sloping backward bending isoquants indicate that the marginal product of the input initially increases and then decreases as more of it is used. This means that beyond a certain point, the cost of using an additional unit of input exceeds the benefit, making it an uneconomic region of production.

Question 12

The marginal rate of technical substitution in production is analogous to the marginal rate of substitution for the consumer's optimization problem in that
A) the slope of the consumer's indifference curve is the opposite of the ratios of the marginal utilities of the two goods, whereas the slope of the production isoquant is the opposite of the ratio of the marginal product of labor relative to the marginal product of capital.
B) the slope of the consumer's indifference curve is equal to the ratio of the marginal utilities of the two goods, whereas the slope of the production isoquant is the opposite of the ratio of the marginal product of labor relative to the marginal product of capital.
C) the slope is equal in both instances.
D) they are calculated by subtracting the price ratio from the output level.

Accepted Answer

The marginal rate of technical substitution (MRTS) in production measures the rate at which one input (e.g., labor) can be substituted for another (e.g., capital) while keeping output constant, analogous to the marginal rate of substitution (MRS) in consumption, which measures the rate at which a consumer can substitute one good for another while maintaining the same level of utility. The slope of the consumer's indifference curve represents the MRS and is the ratio of the marginal utilities of two goods, while the slope of the production isoquant represents the MRTS and is the ratio of the marginal products of two inputs, typically labor and capital.

Question 13

Consider the CES production function  .The elasticity of substitution is
A) 0.3
B) 1.5
C) 0.67
D) 3.00

Accepted Answer

The answer of Consider the CES production function  .The...

Question 14

A measure of how quickly the marginal rate of technical substitution of labor for capital changes as we move along an isoquant is the
A) capital-labor ratio
B) elasticity of substitution
C) input substitution possibility frontier
D) rate of technological progress

Accepted Answer

The elasticity of substitution measures the percentage change in the capital-labor ratio in response to a one percent change in the marginal rate of technical substitution. Therefore, it measures how quickly the marginal rate of technical substitution changes as we move along an isoquant.

Question 15

For the production function  ,the equation for a typical isoquant is
A) 
B) 
C) 
D)

Accepted Answer

The equation for a typical isoquant for this production function is Q = K^(0.5) * L^(0.5)/2. Taking natural log on both sides, we get ln(Q) = 0.5ln(K) + 0.5ln(L) - ln(2). This is the equation of a straight line with slope 0.5 for a given level of output Q. Therefore, the best choice is option B which represents a straight line equation.

Question 16

A production function of the form  is a(n)
A) isoquant function
B) Cobb-Douglas production function
C) fixed-proportions function
D) perfect compliments function

Accepted Answer

The Cobb-Douglas production function has the form Y = A*K^alpha * L^beta, where Y is output, A is total factor productivity, K is capital input, L is labor input, and alpha and beta are the output elasticities of capital and labor, respectively. The production function given in the question has a similar form, which suggests that it is a Cobb-Douglas production function.

Question 17

Compare and match the following

Accepted Answer

The answer of Compare and match the following ...

Question 18

Returns to scale refers to
A) the increase in output that accompanies an increase in one input, all other inputs held constant.
B) a change in a production process that enables a firm to achieve more output from a given combination of inputs.
C) the number of units of increase in output that can be obtained from an increase in one unit of input.
D) the percentage by which output will increase when all inputs are increased by a given percentage.

Accepted Answer

Returns to scale refers to how output changes when all inputs are scaled up or down by the same proportion, which is accurately described by option D.

Question 19

When a production function has the form Q = aL + bK,we can say that
A) the production function is linear and the inputs are perfect substitutes.
B) the production function is linear and the inputs are perfect complements.
C) the production function is linear and the inputs are used in fixed factor proportions only.
D) the production function is non-linear and the inputs are perfect substitutes.

Accepted Answer

A production function with the form Q = aL + bK is linear because it has a constant rate of increase. Furthermore, the inputs are perfect substitutes because the production function indicates that an increase in one input can fully offset a decrease in the other input.

Question 20

A type of production function that includes linear production functions,fixed-proportions production functions,and Cobb-Douglas production functions as special cases is
A) Cobb-Douglas production function
B) Constant elasticity of substitution (CES) production function
C) Fixed proportions production functions
D) Linear production functions

Accepted Answer

The Constant Elasticity of Substitution (CES) production function is a general type of production function that includes linear, fixed-proportions, and Cobb-Douglas production functions as special cases. It allows for varying degrees of substitutability between inputs and can represent a wide range of production technologies.

Quiz 6: Inputs and Production Functions

For the production function Q = aL + bK,where a and b are constants,the

Which of the following is true?

A fixed proportions production function

Suppose every molecule of salt requires exactly one sodium atom,NA,and one chlorine atom,CL.The production function that describes this is

The production function exhibits

If capital cannot easily be substituted for labor,then the elasticity of substitution is

Consider the production function .The is

Consider a production function Q = 3K + 4L,when L is graphed on the x-axis and K is graphed on the y-axis,the marginal rate of technical substitution is equal to

For the production function ,the equation for a typical isoquant is

When a production function can be expressed as ,the relationship between capital and labor in the production function is that

The region of upward sloping backward bending isoquants is

The marginal rate of technical substitution in production is analogous to the marginal rate of substitution for the consumer's optimization problem in that

Consider the CES production function .The elasticity of substitution is

A measure of how quickly the marginal rate of technical substitution of labor for capital changes as we move along an isoquant is the

For the production function ,the equation for a typical isoquant is

A production function of the form is a(n)

Compare and match the following

Returns to scale refers to

When a production function has the form Q = aL + bK,we can say that

A type of production function that includes linear production functions,fixed-proportions production functions,and Cobb-Douglas production functions as special cases is