Deck 19: Extension: A: Technology

Question 1

A firm uses 3 factors of production.Its production function is f(x, y, z)=min{x³/y, y², (z⁴ - x⁴)/y²}.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.

Answer 1

36.

Question 2

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 2

None of the above.

Question 3

A firm has the production function $f(x₁, x₂)=^0.50₁x^0.10₂.The isoquant on which output is 40^1/10 has the equation

A)x₁/x₂ = 5.
B)x₂ = 40x¹⁰₁.
C)x₂ =40x^-5₁.
D)x₂ = 40x^-0.10₁.
E)x₁ =0.10x^-0.90₂.

Answer 3

x₂ =40x^-5₁.

Question 4

A firm has the production function $f(x₁, x₂)= x¹₁x^0.50₂.The isoquant on which output is 80^5/10 has the equation

A)x₁/x₂ = 2.
B)x₂ = 80x^-0.50₁.
C)x₂ =80x^-2₁.
D)x₂ =80x²₁.
E)x₁=0.50x^-0.50₂

Question 5

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 6

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 7

A firm uses 3 factors of production.Its production function is f(x, y, z)=min{x³/y, y², (z⁴ -x⁴)/y²}.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 8

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 9

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 10

A firm uses 3 factors of production.Its production function is f(x, y, z)= min{x⁵/y, y⁴,(z⁶ -x⁶)/y²}.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 11

A firm uses 3 factors of production.Its production function is f(x, y, z)=min{x⁴/y, y³,(z⁵ -x⁵)/y²}.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 12

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 13

A firm has the production function $f(x₁, x₂)=x^2.50₁x^0.50₂.The isoquant on which output is 50^5/10 has the equation

A)x₂ =50x^-5₁.
B)x₂ =50x²₁.
C)x₁/x₂ = 5.
D)x₂ = 50x^-0.50₁.
E)x₁ =0.50x^-0.50₂.

Question 14

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 15

A firm uses 3 factors of production.Its production function is f(x, y, z)=min{x⁴/y, y³,(z⁵ -x⁵)/y²}.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.

Question 16

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 17

A firm has the production function $f(x₁, x₂)=x^0.90₁x^0.30₂.The isoquant on which output is 80^3/10 has the equation

A)x₂ = 80x^3.33₁.
B)x₂ =80x²³₁.
C)x₁/x₂ = 3.
D)x₂ = 80x^-0.30₁.
E)x₁ = 0.30^-0.70₂.

Question 18

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 19

A firm has the production function $f(x₁, x₂)=^0.40₁x^0.20₂.The isoquant on which output is 50^2/10 has the equation

A)x₂ =50x⁵₁.
B)x₂ =50x^-0.20₁.
C)x₁/x₂ = 2.
D)x₂ =50x^-2₁.
E)x₁ = 0.20x^-0.80₂.

Question 20

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 21

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 22

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 23

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 24

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 25

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 26

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 27

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 28

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

Question 29

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

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