Question 1

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

Accepted Answer

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

Question 2

A firm has the production function f(X, Y) =  , where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of 23. The straight line we drew

Accepted Answer

If the isoquants have a slope of 23 wherever they intersect the line, then the line must also have a slope of 23 at those points. The only option that fits this requirement is a ray through the origin with a slope of 3 (since slope = dy/dx = Y/X = 3/1). Therefore, the answer is (C) a ray through the origin with slope 3.

Question 3

A firm has the production function f(x, y) = x^1.40y¹. This firm has

Accepted Answer

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

Question 4

A firm has the production function f(x, y) = x^1.40y^0.90. This firm has

Accepted Answer

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

Question 5

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 3, its output will be multiplied by

Accepted Answer

The answer of A firm uses 3 factors to produce...

Question 6

A firm has the production function f(x, y) = x + min{x, y}. The isoquants for the firm

Accepted Answer

The production function f(x,y) = x + min{x,y} implies that the firm uses both inputs x and y in production and the amount of output produced depends on the minimum value of x and y. 
To derive the isoquants, we set f(x,y) equal to a constant level of output (e.g. Q=1) and solve for y in terms of x:
y = Q - x + min{x,y}
y = 1 - x + min{x,y}
If x is less than y, the minimum value is x so we have y = 1. If x is greater than or equal to y, the minimum value is y so we have y = 1 - x + y, which simplifies to y = 1/2. 
Therefore, the isoquant for Q=1 consists of two line segments, one vertical at x=1/2 and the other with a slope of -1 passing through the point (1,0). The isoquants for higher levels of output will have the same two line segments but with different vertical positions. Thus, the answer is C.

Question 7

A firm uses only two inputs to produce its output. These inputs are perfect substitutes. This firm

Accepted Answer

Since the inputs are perfect substitutes, the firm could increase the output by simply increasing the quantity of either input. This suggests that there are economies of scale, or increasing returns to scale. However, it is also possible that the marginal productivity of the inputs decreases at a certain point, leading to decreasing returns to scale. Thus, the firm could have any type of returns to scale (increasing, constant, or decreasing) depending on the specifics of the production function.

Question 8

A firm has the production function f(x, y) =  . The slope of the firm's isoquant at the point (x, y) = (20, 40) is (pick the closest one)

Accepted Answer

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

Question 9

A firm has the production function f(x₁, x₂) = (x^b₁ + x_b²)c, where b > 0 and c > 0. This firm will have

Accepted Answer

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

Question 10

Suppose that the production function is f(x₁, x₂) = (x^a₁ + x^a₂)b, where a and b are positive constants. For what values of a and b is there a diminishing technical rate of substitution?

Accepted Answer

The answer of Suppose that the production function is f(x₁,...

Question 11

A firm has the production function f(X, Y) =  , where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -9. The straight line we drew

Accepted Answer

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

Question 12

A firm has the production function f(x₁, x₂) = x^0.60₁x^0.30₂. The isoquant on which output is has the equation

Accepted Answer

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

Question 13

A firm has the production function f(x, y) =  . The slope of the firm's isoquant at the point (x, y) = (50, 70) is (pick the closest one)

Accepted Answer

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

Question 14

A firm has the production function f(X, Y) =  , where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -9. The straight line we drew

Accepted Answer

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

Question 15

A firm has the production function f(x, y) = x^0.90y^0.80. This firm has

Accepted Answer

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

Question 16

A firm has the production function f(x, y) =  . The slope of the firm's isoquant at the point (x, y) = (40, 80) is (pick the closest one)

Accepted Answer

The slope of isoquant at point (x,y) is given by -∂f(x,y)/∂x / ∂f(x,y)/∂y. 
Substituting the production function, we get
-6x/y = -6(40)/80 = -3/4 = -0.75
Rounding off to nearest integer, we get the answer as -1. Hence, the closest option is answer choice D (-8).

Question 17

If output is produced with two factors of production and with increasing returns to scale,

Accepted Answer

With increasing returns to scale, doubling all inputs leads to more than double the output. This can be seen as moving along a ray from the origin on a graph of production isoquants. Therefore, option C is correct. Choices A, B, D, and E are not necessarily true with increasing returns to scale and two factors of production.

Question 18

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 3, its output will be multiplied by

Accepted Answer

Given the production function, f(x, y, z) = min{ 11e6, y, 11e6 }

If we increase the amount of each input by 3, the new production function becomes,
f(3x, 3y, 3z) = min{ 11e6*3, y*3, 11e6*3 }
f(3x, 3y, 3z) = min{ 33e6, 3y, 33e6 }

As we can see, the minimum of the three values is now much higher than before. This means that the output has increased by a factor of 9 when the inputs are multiplied by 3.

Hence, the answer is C) 9.

Question 19

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 2, its output will be multiplied by

Accepted Answer

The answer of A firm uses 3 factors to produce...

Question 20

A firm has the production function f(x₁, x₂) = x^0.80₁x^0.20₂. The isoquant on which output is has the equation

Accepted Answer

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

Quiz 17: Technology

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

A firm has the production function f(x, y) = x^1.40y¹. This firm has

A firm has the production function f(x, y) = x^1.40y^0.90. This firm has

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 3, its output will be multiplied by

A firm has the production function f(x, y) = x + min{x, y}. The isoquants for the firm

A firm uses only two inputs to produce its output. These inputs are perfect substitutes. This firm

A firm has the production function f(x, y) = . The slope of the firm's isoquant at the point (x, y) = (20, 40) is (pick the closest one)

A firm has the production function f(x₁, x₂) = (x^b₁ + x_b²) c, where b > 0 and c > 0. This firm will have

Suppose that the production function is f(x₁, x₂) = (x^a₁ + x^a₂) b, where a and b are positive constants. For what values of a and b is there a diminishing technical rate of substitution?

A firm has the production function f(x₁, x₂) = x^0.60₁x^0.30₂. The isoquant on which output is has the equation

A firm has the production function f(x, y) = . The slope of the firm's isoquant at the point (x, y) = (50, 70) is (pick the closest one)

A firm has the production function f(x, y) = x^0.90y^0.80. This firm has

A firm has the production function f(x, y) = . The slope of the firm's isoquant at the point (x, y) = (40, 80) is (pick the closest one)

If output is produced with two factors of production and with increasing returns to scale,

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 3, its output will be multiplied by

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 2, its output will be multiplied by

A firm has the production function f(x₁, x₂) = x^0.80₁x^0.20₂. The isoquant on which output is has the equation

Quiz 17: Technology

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

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

A firm has the production function f(x, y) = x1.40y0.90. This firm has

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y2, }. If the amount of each input is multiplied by 3, its output will be multiplied by

A firm has the production function f(x, y) = x + min{x, y}. The isoquants for the firm

A firm uses only two inputs to produce its output. These inputs are perfect substitutes. This firm

A firm has the production function f(x, y) = . The slope of the firm's isoquant at the point (x, y) = (20, 40) is (pick the closest one)

A firm has the production function f(x1, x2) = (xb1 + xb2) c, where b > 0 and c > 0. This firm will have

Suppose that the production function is f(x1, x2) = (xa1 + xa2) b, where a and b are positive constants. For what values of a and b is there a diminishing technical rate of substitution?

A firm has the production function f(x1, x2) = x0.601x0.302. The isoquant on which output is has the equation

A firm has the production function f(x, y) = . The slope of the firm's isoquant at the point (x, y) = (50, 70) is (pick the closest one)

A firm has the production function f(x, y) = x0.90y0.80. This firm has

A firm has the production function f(x, y) = . The slope of the firm's isoquant at the point (x, y) = (40, 80) is (pick the closest one)

If output is produced with two factors of production and with increasing returns to scale,

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y2, }. If the amount of each input is multiplied by 3, its output will be multiplied by

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y2, }. If the amount of each input is multiplied by 2, its output will be multiplied by

A firm has the production function f(x1, x2) = x0.801x0.202. The isoquant on which output is has the equation

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

A firm has the production function f(x, y) = x^1.40y¹. This firm has

A firm has the production function f(x, y) = x^1.40y^0.90. This firm has

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 3, its output will be multiplied by

A firm has the production function f(x₁, x₂) = (x^b₁ + x_b²) c, where b > 0 and c > 0. This firm will have

Suppose that the production function is f(x₁, x₂) = (x^a₁ + x^a₂) b, where a and b are positive constants. For what values of a and b is there a diminishing technical rate of substitution?

A firm has the production function f(x₁, x₂) = x^0.60₁x^0.30₂. The isoquant on which output is has the equation

A firm has the production function f(x, y) = x^0.90y^0.80. This firm has

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 3, its output will be multiplied by

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 2, its output will be multiplied by

A firm has the production function f(x₁, x₂) = x^0.80₁x^0.20₂. The isoquant on which output is has the equation