Deck 19: B: Technology

Question 1

A firm has a production function f(x,y)=1.80(x^0.10 + y^0.10)² whenever x $\gt$ 0 and y $\gt$ 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 $\gt$ 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.

Answer 1

decreasing returns to scale.

Question 2

A firm has a production function f(x,y)=0.70(x^0.20 +y^0.20)⁴ whenever x $\gt$ 0 and y $\gt$ 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 $\gt$ 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.

Answer 2

decreasing returns to scale.

Question 3

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

Answer 3

decreasing,would

Question 4

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.

Question 5

This problem will be easier if you have done Problem 1.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 ^{- 5}₁.
D) x₂ =40x ^{- 0.10}₁.
E) x₁=0.10x ^{- 0.90}₂.

Question 6

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

A) increasing returns to scale if x + y $\gt$ 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 7

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

A) increasing returns to scale if x+ y $\gt$ 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

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 9

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 10

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 11

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 80^3/10 has the equation

A) x₂ =80x^3.33₁.
B) x₂ =80x²³₁.
C) x₁/x₂ =3.
D) x₂ =80x ^{- 0.30}₁.
E) x₁ =0.30x ^{- 0.70}₂.

Question 12

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 13

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 14

This problem will be easier if you have done Problem 1.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 ^{- 0.20}₁.
C) x₁/x₂=2.
D) x₂=50x ^{- 2}₁.
E) x₁ =0.20x ^{- 0.80}₂.

Question 15

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 16

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 17

A firm has a production function f(x,y)=1.80(x^0.80 + y^0.80)¹ whenever x $\gt$ 0 and y $\gt$ 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 $\gt$ 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 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)=x¹₁x^0.50₂.The isoquant on which output is 80^5/10 has the equation

A) x₁/x₂ = 2.
B) x₂ =80x ^{- 0.50}₁.
C) x₂= 80x ^{- 2}₁.
D) x₂ =80x²₁.
E) x₁ = 0.50x ^{- 0.50}₂

Question 20

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 50^5/10 has the equation

A) x₂ =50x ^{- 5}₁.
B) x₂ =50x²₁.
C) x₁/x₂=5.
D) x₂ =50x ^{- 0.50}₁.
E) x₁ = 0.50x ^{- 0.50}₂.

Question 21

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 $\gt$ 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 $\gt$ 1.

Question 23

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 $\gt$ 1.

Question 24

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 $\gt$ 1.

Question 25

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 $\gt$ 1.