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

Accepted Answer

According to the production function, if each input is multiplied by 6, the output will be multiplied by (6x13)/(6x12) = 1.0833. Therefore, the output will be multiplied by 6 x 1.0833 = 6.5 (rounded to the nearest tenth). This means that the best choice is to multiply each input by 6 to achieve the highest increase in output.

Question 2

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

Accepted Answer

E

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

Accepted Answer

The isoquant equation is found by setting the production function equal to the desired output level. In this case, we have:$$f(x_1, x_2) = 40^{1/10}$$$$x_1^{0.50}x_2^{0.10} = 40^{1/10}$$$$x_2 = 40x_1^{-5}$$

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

Accepted Answer

The answer of A firm has the production function $f(x₁,...

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

Accepted Answer

The production function exhibits decreasing returns to scale because the sum of the exponents on x and y (0.1 + 0.1 = 0.2) is less than 1, indicating that doubling the inputs will result in less than double the output.

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

Accepted Answer

The production function has diminishing marginal returns, which means that as more inputs are added, the increase in output becomes smaller and smaller. This leads to decreasing returns to scale, as increasing both inputs by the same factor will result in less than proportionate increase in output.

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

Accepted Answer

According to the production function, the output (S) is a function of the inputs x, y, and z. If all of the inputs are multiplied by 6, the new production function would be f(6x, 6y, 6z) = S'. 
Substituting 6x, 6y, and 6z into the original production function, we get:
S' = 10 min [ (6x / y)^(1/3) * y^(1/3) * (6z)^(1/3) * (1/3) - (6x)^(1/3) * (y / 6z)^(1/3) * (6z)^(1/3) * (1/3) ]
S' = 10 min [ (6^1/3 * x^1/3 * y^1/3 * z^1/3) - (6^1/3 * x^1/3 * y^1/3 * z^1/3) ]
S' = 0
Therefore, if all inputs are multiplied by 6, the output will be zero. This means that the production function exhibits constant returns to scale (i.e., if inputs are multiplied by a certain factor, output is multiplied by the same factor). 
To find the factor by which output is multiplied, we can set the inputs to be equal to some constant k (e.g. k=1) and determine the output, and then set the inputs to be equal to 6k and determine the new output. By dividing the new output by the original output, we can determine the factor by which output is multiplied. 
Setting x=y=z=k, we get:
S = 10 min [(k/k)^(1/3) * k^(1/3) * k^(1/3) * (1/3) - k^(1/3) * (k/k)^(1/3) * k^(1/3) * (1/3)]
S = 10 min [(1/3)k^(1/3) - (1/3)k^(1/3)]
S = 0
Setting x=y=z=6k, we get:
S' = 10 min [((6k)/(6k))^(1/3) * (6k)^(1/3) * (6k)^(1/3) * (1/3) - (6k)^(1/3) * ((k)/(6k))^(1/3) * (6k)^(1/3) * (1/3)]
S' = 10 min [(1/3)(6k)^(1/3) - (1/3)(k)^(1/3)]
S' = 10 min [(1/3)(6k)^(1/3) - (1/3)(6k)^(1/3)]
S' = 0
So output is also 0 when inputs are multiplied by 6k. Therefore, the production function exhibits constant returns to scale for any choice of x, y, and z, and the factor by which output is multiplied is equal to the factor by which inputs are multiplied, which is 6. Therefore, the answer is (B) 36.

Question 8

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

Accepted Answer

The answer of A firm has the production function f(x,...

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

Accepted Answer

The production function exhibits increasing returns to scale because the sum of the exponents on x and y (0.8 + 0.8 = 1.6) is greater than 1, indicating that a proportional increase in inputs will lead to a more than proportional increase in output.

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

Accepted Answer

The production function is homogeneous of degree 1, so if the amount of each input is multiplied by 3, the output will be multiplied by 3.

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

Accepted Answer

The production function has constant returns to scale, which means that if all inputs are multiplied by a constant factor, output will be multiplied by the same factor raised to the power of the number of inputs. In this case, there are three inputs, so if they are all multiplied by 5, output will be multiplied by 5^3 = 125. Therefore, the best choice is B.

Question 12

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

Accepted Answer

The answer of A firm has the production function f(x,...

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

Accepted Answer

The isoquant equation is found by setting the production function equal to the desired output level and solving for x₂ in terms of x₁. In this case, we have:50^5/10 = x^2.50₁x^0.50₂50 = x^2.50₁x^0.50₂x₂ = 50x^-⁵₁

Question 14

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

Accepted Answer

The answer of A firm has the production function f(x,...

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

Accepted Answer

The production function is homogeneous of degree 1, so if the amount of each input is multiplied by 2, the output will be multiplied by 2.

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

Accepted Answer

The production function exhibits decreasing returns to scale because the sum of the exponents on x and y (0.2 + 0.2 = 0.4) is less than 1, indicating that doubling the inputs will result in less than double the output.

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

Accepted Answer

The answer of A firm has the production function $f(x₁,...

Question 18

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

Accepted Answer

The answer of A firm has the production function f(x,...

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

Accepted Answer

The answer of A firm has the production function $f(x₁,...

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

Accepted Answer

The production function exhibits increasing returns to scale because the sum of the exponents (0.90 + 0.90 = 1.8) is greater than 1, indicating that scaling inputs by a factor will increase output by a greater factor.

Quiz 17: Technology-Part B

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

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

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

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

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

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

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 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

Quiz 17: Technology-Part B

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 firm has the production function f(x, y) =x1.10y1.30.This firm has

A firm has the production function $f(x1, x2) =0.501x0.102.The isoquant on which output is 401/10 has the equation

A firm has the production function $f(x1, x2) = x11x0.502.The isoquant on which output is 805/10 has the equation

A firm has a production function f(x, y) = 1.80(x0.10 + y0.10) 2 whenever x > 0 and y > 0.When the amounts of both inputs are positive, this firm has

A firm has a production function f(x, y) = 1.80(x0.80 +y0.80) 1 whenever x > 0 and y > 0.When the amounts of both inputs are positive, this firm has

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 firm has the production function f(x, y) =x1.40y1.40.This firm has

A firm has a production function f(x, y) = 0.70(x0.80 + y0.80) 2 whenever x > 0 and y > 0.When the amounts of both inputs are positive, this firm has

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 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 firm has the production function f(x, y) = x1.20y2.This firm has

A firm has the production function $f(x1, x2) =x2.501x0.502.The isoquant on which output is 505/10 has the equation

A firm has the production function f(x, y) = x1.40y1.90.This firm has

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 firm has a production function f(x, y) = 0.70(x0.20 + y0.20) 4 whenever x > 0 and y > 0.When the amounts of both inputs are positive, this firm has

A firm has the production function $f(x1, x2) =x0.901x0.302.The isoquant on which output is 803/10 has the equation

A firm has the production function f(x, y) =x1.10y1.This firm has

A firm has the production function $f(x1, x2) =0.401x0.202.The isoquant on which output is 502/10 has the equation

A firm has a production function f(x, y) = 2(x0.90 + y0.90) 5 whenever x > 0 and y > 0.When the amounts of both inputs are positive, this firm has

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

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

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

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

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

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

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 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