Deck 19: A: Technology

Question 1

It is possible to have decreasing marginal products for all inputs,and yet have increasing returns to scale.

Answer 1

True

Question 2

The production function f(x,y)=x^2/3+ y^2/3 has increasing returns to scale.

Answer 2

False

Question 3

The production function f(x,y)=x + y has constant returns to scale.

Answer 3

True

Question 4

Which of the following production functions exhibit constant returns to scale? In each case y is output and K and L are inputs.(1)y = K^1/2 L^1/3.(2)y = 3K^1/2 L^1/2.(3)y =K^1/2 = L^1/2.(4)y + 2K = 3L.

A) 1,2,and 4
B) 2,3,and 4
C) 1,3,and 4
D) 2 and 3
E) 2 and 4

Question 5

If the production function is f(x,y)=min{12x,3y},then there is convexity in production.

Question 6

A production isoquant is a locus of combinations of inputs that are equally profitable.

Question 7

A firm has the production function f(x,y)=x.₅ + y,where x is the amount of factor x it uses and y is the amount of factor y.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 the slopes of all the isoquants that it meets have the same slope at the point where they meet this line.The straight line we drew was

A) vertical.
B) horizontal.
C) diagonal through the origin with slope 0.5.
D) diagonal with slope 2.
E) diagonal with slope greater than 2.

Question 8

If the production function is f(x,y)=min{2x+y,x +2y},then there are constant returns to scale.

Question 9

If there is one input used in production and if there are decreasing returns to scale,then the marginal product for the input will be diminishing.

Question 10

In any production process,the marginal product of labor equals

A) the value of total output minus the cost of the fixed capital stock.
B) the change in output per unit change in labor input for "small" changes in the amount of input.
C) total output divided by total labor inputs.
D) total output produced with the given labor inputs.
E) the average output of the least-skilled workers employed by the firm.

Question 11

If there are constant returns to scale,then doubling the amount of any input will exactly double the amount of output.

Question 12

A production function has well-defined marginal products at every input combination.If factor x is shown on the horizontal axis and factor y is shown on the vertical axis,the slope of the isoquant through a point (x*,y*)is the negative of the ratio of the marginal product of x to the marginal product of y.

Question 13

The economist's distinction between the long run and the short run captures the idea that quantities of some factor inputs can be varied in the short run but not in the long run.

Question 14

If the marginal product of each factor decreases as the amount of that factor used increases,then there must be decreasing returns to scale.

Question 15

If the production function is f(x₁,x₂)=x₁x₂,then there are constant returns to scale.

Question 16

A firm has two variable factors and a production function f(x₁,x₂)=(2x₁ + 4x₂)^1/2.The technical rate of substitution between x₁ and x₂ is constant.

Question 17

If the production function is f(x,y)= x+min{x,y},then there are constant returns to scale.

Question 18

A firm's production function is f(x₁,x₂)=x₁ + 2x₂.This means that x₂ is twice as expensive as x₁.

Question 19

If a firm moves from one point on a production isoquant to another point on the same isoquant,which of the following will certainly not happen?

A) A change in the level of output
B) A change in the ratio in which the inputs are combined
C) A change in the marginal products of the inputs
D) A change in the rate of technical substitution
E) A change in profitability

Question 20

The production set of a firm is the set of all products the firm can produce.

Question 21

A firm has the production function f(X,Y)=X^3/4 Y^1/4,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 -.The straight line we drew

A) is a ray through the origin with slope 3.
B) is a ray through the origin with slope 4.
C) is vertical.
D) is horizontal.
E) has a negative slope.

Question 22

A firm has a production function f(x,y)=1.80(x^0.80 +y^0.80)³ 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) decreasing returns to scale.
C) constant returns to scale.
D) increasing 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 23

The production function Q=50K^0.25L^0.25 exhibits

A) increasing returns to scale.
B) constant returns to scale.
C) decreasing returns to scale.
D) increasing,then diminishing returns to scale.
E) negative returns to scale.

Question 24

A firm has a production function f(x,y)=1.80(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) decreasing returns to scale.
B) constant returns to scale.
C) increasing returns to scale if x +y $\gt$ 1 and decreasing returns to scale otherwise.
D) increasing 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 25

A firm has the production function f(X,Y)= X ^1/2 Y ^1/2,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

A) is vertical.
B) is horizontal.
C) is a ray through the origin with slope 3.
D) is a ray through the origin with slope 4.
E) has a negative slope.

Question 26

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) For any value of a if b $\lt$ 1
B) For any values of a and b if ab $\lt$ 1
C) For any values of a and b if a $\gt$ b
D) For any value of b if a $\lt$ 1
E) None of the above.

Question 27

A firm has the production function f(x,y)= 60x ^4/5 y^1/5.The slope of the firm's isoquant at the point (x,y)=(40,80)is (pick the closest one)

A) -0.50.
B) -4.
C) -0.25.
D)-8.

Question 28

A firm has the production function f(X,Y)=X^3/4 Y^1/4,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

A) is horizontal.
B) is a ray through the origin with slope 3.
C) is vertical.
D) is a ray through the origin with slope 4.
E) has a negative slope.

Question 29

A firm has a production function f(x,y)=1.40(x^0.60 + y^0.60)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.

Question 30

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

A) decreasing returns to scale and diminishing marginal products for factor x.
B) increasing returns to scale and decreasing marginal product of 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 31

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

A) there cannot be diminishing marginal rate of substitution.
B) all inputs must have increasing marginal products.
C) on a graph of production isoquants,moving along a ray from the origin,output more than doubles as the distance from the origin doubles.
D) the marginal product of at least one input must be increasing.
E) all inputs must have decreasing marginal products.

Question 32

A firm has the production function f(x,y)=20x^3/5 y^2/5.The slope of the firm's isoquant at the point (x,y)= (20,40)is (pick the closest one)

A) -3.
B) -0.67.
C) -1.50.
D)-0.50.
E) -0.25.

Question 33

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

A) must have increasing returns to scale.
B) must have constant returns to scale.
C) could have increasing returns to scale,constant returns to scale,or decreasing returns to scale.
D) must have decreasing returns to scale.
E) must have decreasing returns to scale in the short run and constant returns to scale in the long run.

Question 34

A firm has the production function f(x,y)=20x^3/5 y^2/5.The slope of the firm's isoquant at the point (x,y)=(50,70)is (pick the closest one)

A) -1.50.
B) -0.67.
C) -0.71.
D) -2.10.
E) -0.36.

Question 35

A firm has the production function f(x₁,x₂)=x^0.60₁x^0.30₂.The isoquant on which output is 80^3/10 has the equation

A) x₂ =80x^-2₁.
B) x₂ =80x^3.33₁.
C) x₁/x₂ =2.
D) x₂ =80x^-0.30₁.
E) x₁ =0.30x^-0.70₂.

Question 36

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

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

Question 37

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

A) are L-shaped with the corners of the L's on the line y = x.
B) are L-shaped with the corners of the L's on the line y = x + 1.
C) consist of two line segments,one vertical and the other with a slope of -1.
D) consist of two line segments,one horizontal and the other with a slope of -1.
E) are upside down L-shaped.

Question 38

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

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

Question 39

A firm has the production function f(x₁,x₂)=x¹¹x^0.50₂.The isoquant on which output is 30^5/10 has the equation

A) x₂ =30x^-21.
B) x₂ = 30x²¹.
C) x₂ =30x^-0.50₁.
D) x₁/x₂ = 2.
E) x₁ =0.50x^-0.50₂.

Question 40

A firm has the production function f(x₁,x₂)=x^0.80₁x^0.20₂.The isoquant on which output is 70^2/10 has the equation

A) x₂=70x⁵₁.
B) x₁/x₂ =4.
C) x₂=70x^-4₁.
D) x₂ =70x^-0.20₁.
E) x₁ =0.20x^-0.80₂.

Question 41

On separate axes,draw typical production isoquants for each of the following production functions.
a.f(x,y)= min{2x,x + y}.
b.f(x,y)= xy.
c.f(x,y)= x +min{x,y}.
d.(x,y)= x + y^1/2.

Question 42

The UJava espresso stand needs two inputs,labor and coffee beans,to produce its only output,espresso.Producing an espresso always requires the same amount of coffee beans and the same amount of time.Which of the following production functions would appropriately describe the production process at UJava,where B represents ounces of coffee beans,and L represents hours of labor?

A) Q = min(2B,60L).
B) Q = B^0.40L^0.60.
C) Q = B/2 + L/30.
D) Q= 0.5B + 0.5L^0.5.
E) None of the above.

Question 43

For each of the following production functions,draw a diagram showing the general shape of its corresponding isoquant.Comment on the ease at which labor and capital can be substituted for one another relative to the other two production functions.
a.Q = K + L.
b.Q = K^0.5L^0.5.
c.Q = min(K,L).

Question 44

The production function Q=50K^0.25L^0.75 exhibits

A) increasing returns to scale.
B) decreasing returns to scale.
C) constant returns to scale.
D) increasing,then diminishing returns to scale.
E) negative returns to scale.

Question 45

The UJava espresso stand needs two inputs,labor and coffee beans,to produce its only output,espresso.Producing an espresso always requires the same amount of coffee beans and the same amount of time.Which of the following production functions would appropriately describe the production process at UJava,where B represents ounces of coffee beans,and L represents hours of labor?

A) Q = 0.5B + 0.5L^0.5.
B) Q =B^0.80L^0.20.
C) Q = min(2B,60L).
D) Q =B/2+ L/30.
E) None of the above.

Question 46

The UJava espresso stand needs two inputs,labor and coffee beans,to produce its only output,espresso.Producing an espresso always requires the same amount of coffee beans and the same amount of time.Which of the following production functions would appropriately describe the production process at UJava,where B represents ounces of coffee beans,and L represents hours of labor?

A) Q = B^0.60L^0.40.
B) Q =B/2 +L/2.
C) Q = min(2B,60L).
D) Q = 0.5B +0.5L^0.5.
E) None of the above.

Question 47

The production function Q =50K^0.25L^0.75 exhibits

A) increasing,then diminishing returns to scale.
B) increasing returns to scale.
C) decreasing returns to scale.
D) constant returns to scale.
E) negative returns to scale.

Question 48

For each of the following production functions,comment on the ability to substitute capital for labor.
a.Q = K + L.
b.Q = K^0.5L^0.5.
c.Q = min(K,L).