Deck 17: A: Technology

Question 1

A firm uses 3 factors of production. Its production function is f(x, y, z) = min{ }. If the amount of each input is multiplied by 2, its output will be multiplied by a. 8.
B) 4.
C) 16.
D) 0.22.
E) The answer depends on the original choice of x, y, and z.

Answer 1

A

Question 2

This problem will be easier if you have done Problem 1. A firm has the production function $f(x₁, x₂) = x¹₁x^0.50₂. The isoquant on which output is has the equation

A) = 2.
B) x₂ = 80x^-0.50₁.
C) x₂ = 80x^-2₁.
D) x₂ = 80x²_1.
E) x₁ = 0.50x^-0.50₂

Answer 2

C

Question 3

A firm has the production function f(x, y) = x^1.10y^1.30. This firm has

A) decreasing returns to scale and diminishing marginal product for factor x.
B) increasing returns to scale and decreasing marginal product for factor x.
C) constant returns to scale.
D) decreasing returns to scale and increasing marginal product for factor x.
E) None of the above.

Answer 3

E

Question 4

A firm uses 3 factors of production. Its production function is f(x, y, z) = min{ }. If the amount of each input is multiplied by 5, its output will be multiplied by a. 0.04.
B) 125.
C) 625.
D) 25.
E) The answer depends on the original choice of x, y, and z.

Question 5

A firm has the production function f(x, y) = x^1.10y¹. This firm has

A) constant returns to scale.
B) decreasing returns to scale and diminishing marginal product for factor x.
C) increasing returns to scale and decreasing marginal product for factor x.
D) decreasing returns to scale and increasing marginal product for factor x.
E) None of the above.

Question 6

A firm has a production function f(x, y) = 0.70(x^0.20 + y^0.20)⁴ whenever x > 0 and y > 0. When the amounts of both inputs are positive, this firm has

A) increasing returns to scale.
B) decreasing returns to scale.
C) constant returns to scale.
D) increasing returns to scale if x + y > 1 and decreasing returns to scale otherwise.
E) increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

Question 7

A firm has a production function f(x, y) = 0.70(x^0.80 + y^0.80)² whenever x > 0 and y > 0. When the amounts of both inputs are positive, this firm has

A) increasing returns to scale if x + y > 1 and decreasing returns to scale otherwise.
B) increasing returns to scale.
C) decreasing returns to scale.
D) constant returns to scale.
E) increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

Question 8

A firm uses 3 factors of production. Its production function is f(x, y, z) = min{ }. If the amount of each input is multiplied by 3, its output will be multiplied by a. 81.
B) 27.
C) 243.
D) 0.04.
E) The answer depends on the original choice of x, y, and z.

Question 9

This problem will be easier if you have done Problem 1. A firm has the production function $f(x₁, x₂) = x^2.50₁x^0.50₂. The isoquant on which output is has the equation

A) x₂ = 50x^-5₁.
B) x₂ = 50x²₁.
C) = 5.
D) x₂ = 50x^-0.50_1.
E) x₁ = 0.50x^-0.50₂.

Question 10

A firm has a production function f(x, y) = 1.80(x^0.80 + y^0.80)¹ whenever x > 0 and y > 0. When the amounts of both inputs are positive, this firm has

A) increasing returns to scale.
B) constant returns to scale.
C) decreasing returns to scale.
D) increasing returns to scale if x + y > 1 and decreasing returns to scale otherwise.
E) increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

Question 11

A firm has the production function f(x, y) = x^1.20y². This firm has

A) constant returns to scale.
B) decreasing returns to scale and increasing marginal product for factor x.
C) increasing returns to scale and decreasing marginal product for factor x.
D) decreasing returns to scale and diminishing marginal product for factor x.
E) None of the above.

Question 12

This problem will be easier if you have done Problem 1. A firm has the production function $f(x₁, x₂) = x^0.90₁x^0.30₂. The isoquant on which output is has the equation

A) x₂ = 80x^3.33₁.
B) x₂ = 80x²³₁.
C) = 3.
D) x₂ = 80x^-0.30_1.
E) x₁ = 0.30x^-0.70₂.

Question 13

A firm has a production function f(x, y) = 1.80(x^0.10 + y^0.10)² whenever x > 0 and y > 0. When the amounts of both inputs are positive, this firm has

A) increasing returns to scale.
B) decreasing returns to scale.
C) constant returns to scale.
D) increasing returns to scale if x + y > 1 and decreasing returns to scale otherwise.
E) increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

Question 14

This problem will be easier if you have done Problem 1. A firm has the production function $f(x₁, x₂) = x^0.50₁x^0.10₂. The isoquant on which output is has the equation

A) = 5.
B) x₂ = 40x¹⁰₁.
C) x₂ = 40x^-5₁.
D) x₂ = 40x^-0.10_1.
E) x₁ = 0.10x^-0.90₂.

Question 15

A firm has a production function f(x, y) = 2(x^0.90 + y^0.90)⁵ whenever x > 0 and y > 0. When the amounts of both inputs are positive, this firm has

A) increasing returns to scale if x + y > 1 and decreasing returns to scale otherwise.
B) increasing returns to scale.
C) decreasing returns to scale.
D) constant returns to scale.
E) increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

Question 16

A firm has the production function f(x, y) = x^1.40y^1.40. This firm has

A) constant returns to scale.
B) decreasing returns to scale and increasing marginal product for factor x.
C) decreasing returns to scale and diminishing marginal product for factor x.
D) increasing returns to scale and decreasing marginal product for factor x.
E) None of the above.

Question 17

A firm uses 3 factors of production. Its production function is f(x, y, z) = min{ }. If the amount of each input is multiplied by 6, its output will be multiplied by

A) 6.
B) 36.
C) 0.16.
D) 216.
E) The answer depends on the original choice of x, y, and z.

Question 18

A firm has the production function f(x, y) = x^1.40y^1.90. This firm has

A) decreasing returns to scale and diminishing marginal product for factor x.
B) increasing returns to scale and decreasing marginal product for factor x.
C) decreasing returns to scale and increasing marginal product for factor x.
D) constant returns to scale.
E) None of the above.

Question 19

This problem will be easier if you have done Problem 1. A firm has the production function $f(x₁, x₂) = x^0.40₁x^0.20₂. The isoquant on which output is has the equation

A) x₂ = 50x⁵₁.
B) x₂ = 50x^-0.20₁.
C) = 2.
D) x₂ = 50x^-2_1.
E) x₁ = 0.20x^-0.80₂.

Question 20

A firm uses 3 factors of production. Its production function is f(x, y, z) = min{ }. If the amount of each input is multiplied by 6, its output will be multiplied by

A) 216.
B) 36.
C) 6.
D) 0.16.
E) The answer depends on the original choice of x, y, and z.

Question 21

In Problem 8, if a = 2.10, b = 1.10, and c = 1.20, the marginal products of x₁, x₂, and x₃ (in this order) are

A) all increasing.
B) decreasing, increasing, and decreasing.
C) all decreasing.
D) increasing, decreasing, and constant.
E) all increasing if A > 1.

Question 22

In Problem 8, if a = 2.10, b = 0.90, and c = 1, the marginal products of x₁, x₂, and x₃ (in this order) are

A) decreasing, increasing, and decreasing.
B) all increasing.
C) increasing, decreasing, and constant.
D) all decreasing.
E) all increasing if A > 1.

Question 23

In Problem 3, if the exponents in the production function were 0.80 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) constant, would
B) decreasing, would not
C) increasing, would
D) constant, would not
E) decreasing, would

Question 24

In Problem 3, if the exponents in the production function were 0.60 for x₁ and 0.40 for x₂, this production function would exhibit (constant, increasing, decreasing) returns to scale and (would, would not) have diminishing technical rate of substitution.

A) constant, would not
B) increasing, would
C) decreasing, would not
D) constant, would
E) decreasing, would

Question 25

In Problem 3, if the exponents in the production function were 0.40 for x₁ and 0.40 for x₂, this production function would exhibit (constant, increasing, decreasing) returns to scale and (would, would not) have diminishing technical rate of substitution.

A) increasing, would
B) decreasing, would not
C) constant, would
D) constant, would not
E) decreasing, would

Question 26

In Problem 8, if a = 2.50, b = 0.60, and c = 1, the marginal products of x₁, x₂, and x₃ (in this order) are

A) increasing, decreasing, and constant.
B) decreasing, increasing, and decreasing.
C) all increasing.
D) all decreasing.
E) all increasing if A > 1.

Question 27

In Problem 3, 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

Question 28

In Problem 8, if a = 2.10, b = 0.40, and c = 1, the marginal products of x₁, x₂, and x₃ (in this order) are

A) all decreasing.
B) increasing, decreasing, and constant.
C) decreasing, increasing, and decreasing.
D) all increasing.
E) all increasing if A > 1.

Question 29

In Problem 8, if a = 2.40, b = 0.50, and c = 1, the marginal products of x₁, x₂, and x₃ (in this order) are

A) increasing, decreasing, and constant.
B) all increasing.
C) all decreasing.
D) decreasing, increasing, and decreasing.
E) all increasing if A > 1.

Question 30

In Problem 3, if the exponents in the production function were 0.30 for x₁ and 0.30 for x₂, this production function would exhibit (constant, increasing, decreasing) returns to scale and (would, would not) have diminishing technical rate of substitution.

A) constant, would
B) constant, would not
C) decreasing, would not
D) increasing, would
E) decreasing, would