Question 1

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

Accepted Answer

A) True 
 B)False  False

Question 2

A firm has the production function f(x1, x2)= x11x0.502.The isoquant on which output is 305/10 has the equation

Accepted Answer

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

Question 3

A firm has a production function f(x, y)= 1.40(x0.60 +y0.60)2 whenever x > 0 and y > 0.When the amounts of both inputs are positive, this firm has

Accepted Answer

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. 
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. A

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

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 = K1/2 L1/3.(2)y = 3K1/2 L1/2.(3)y = K1/2 + L1/2.(4)y = 2K + 3L.

Accepted Answer

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

Question 7

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?

Accepted Answer

A) Q = 0.5B + 0.5L0.5. 
B) Q =B0.80L0.20. 
C) Q = min(2B, 60L). 
D) Q = B/2 + L/30. 
E) None of the above. 
A) Q = 0.5B + 0.5L0.5. 
B) Q =B0.80L0.20. 
C) Q = min(2B, 60L). 
D) Q = B/2 + L/30. 
E) None of the above.

Question 8

A firm uses 3 factors to produce its output.Its production function is f(x, y, z)= min{x3/y, y2, (z4 - x4)/y2}.If the amount of each input is multiplied by 3, its output will be multiplied by

Accepted Answer

A) 27. 
B) 9. 
C) 3. 
D) 0.30. 
E) The answer depends on the original choice of x, y, and z. 
A) 27. 
B) 9. 
C) 3. 
D) 0.30. 
E) The answer depends on the original choice of x, y, and z.

Question 9

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.

Accepted Answer

A) True 
 B)False

Question 10

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.

Accepted Answer

A) True 
 B)False

Question 11

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

Accepted Answer

A) increasing returns to scale if and only if 2b + c > 1. 
B) increasing returns to scale if and only if bc > 1. 
C) increasing returns to scale if and only if b + c > 1. 
D) constant returns to scale if and only if c = 1. 
E) constant returns to scale if and only if b = c. 
A) increasing returns to scale if and only if 2b + c > 1. 
B) increasing returns to scale if and only if bc > 1. 
C) increasing returns to scale if and only if b + c > 1. 
D) constant returns to scale if and only if c = 1. 
E) constant returns to scale if and only if b = c.

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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

Accepted Answer

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 F-1. 
E) are upside down L-shaped. 
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 F-1. 
E) are upside down L-shaped.

Question 14

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?

Accepted Answer

A) For any value of a if b  b 
D) For any value of b if a < 1 
E) None of the above. 
A) For any value of a if b  b 
D) For any value of b if a < 1 
E) None of the above.

Question 15

A firm uses 3 factors to produce its output.Its production function is f(x, y, z)= min{x3/y, y2, (z4 - x4)/y2}.If the amount of each input is multiplied by 2, its output will be multiplied by

Accepted Answer

A) 2. 
B) 4. 
C) 8. 
D) 0.40. 
E) The answer depends on the original choice of x, y, and z. 
A) 2. 
B) 4. 
C) 8. 
D) 0.40. 
E) The answer depends on the original choice of x, y, and z.

Question 16

A firm has the production function f(x1, x2)= x0.601x0.302.The isoquant on which output is 803/10 has the equation

Accepted Answer

A) x2 = 80x-21. 
B) x2 = 80x3.331. 
C) x1/x2 = 2. 
D) x2 = 80x-0.301. 
E) x1 = 0.30x-0.702. 
A) x2 = 80x-21. 
B) x2 = 80x3.331. 
C) x1/x2 = 2. 
D) x2 = 80x-0.301. 
E) x1 = 0.30x-0.702.

Question 17

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

Accepted Answer

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. 
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 18

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 + y1/2.

Accepted Answer

a.The isoquants have a kink at the line

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

A) True 
 B)False

Exam 17: Technology-Part A

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

A firm has the production function f(x1, x2)= x11x0.502.The isoquant on which output is 305/10 has the equation

A firm has a production function f(x, y)= 1.40(x0.60 +y0.60)2 whenever x > 0 and y > 0.When the amounts of both inputs are positive, this firm has

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

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

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 = K1/2 L1/3.(2)y = 3K1/2 L1/2.(3)y = K1/2 + L1/2.(4)y = 2K + 3L.

A firm uses 3 factors to produce its output.Its production function is f(x, y, z)= min{x3/y, y2, (z4 - x4)/y2}.If the amount of each input is multiplied by 3, its output will be multiplied by

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.

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.

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

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

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

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 uses 3 factors to produce its output.Its production function is f(x, y, z)= min{x3/y, y2, (z4 - x4)/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)= x0.601x0.302.The isoquant on which output is 803/10 has the equation

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

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 + y1/2.

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

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

Budget Constraint-Part A

Budget Constraint-Part B

Preferences-Part A

Preferences-Part B

Utility-Part A

Utility-Part B

Choice-Part A

Choice-Part B

Demand-Part A

Demand-Part B

Revealed Preference-Part A

Revealed Preference-Part B

Slutsky Equation-Part A

Slutsky Equation-Part B

Buying and Selling-Part A

Buying and Selling-Part B

Intertemporal Choice-Part A

Intertemporal Choice-Part B

Asset Markets-Part A

Asset Markets-Part B

Uncertainty-Part A

Uncertainty-Part B

Risky Assets-Part A

Risky Assets-Part B

Consumers Surplus-Part A

Consumers Surplus-Part B

Market Demand-Part A

Market Demand-Part B

Equilibrium-Part A

Equilibrium-Part B

Auctions-Part A

Auctions-Part B

Technology-Part B

Profit Maximization-Part A

Profit Maximization-Part B

Cost Minimization-Part A

Cost Minimization-Part B

Cost Curves-Part A

Cost Curves-Part B

Firm Supply-Part A

Firm Supply-Part B

Industry Supply-Part A

Industry Supply-Part B

Monopoly-Part A

Monopoly-Part B

Monopoly Behavior-Part A

Monopoly Behavior-Part B

Factor Markets-Part A

Factor Markets-Part B

Oligopoly-Part A

Oligopoly-Part B

Game Theory-Part A

Game Theory-Part B

Game Applications-Part A

Game Applications-Part B

Behavioral Economics

Exchange-Part A

Exchange-Part B

Production-Part A

Production-Part B

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

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 firm has a production function f(x, y)= 1.40(x^0.60 +y^0.60)² whenever x > 0 and y > 0.When the amounts of both inputs are positive, this firm has

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 firm uses 3 factors to produce its output.Its production function is f(x, y, z)= min{x³/y, y², (z⁴ - x⁴)/y²}.If the amount of each input is multiplied by 3, its output will be multiplied by

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.

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 uses 3 factors to produce its output.Its production function is f(x, y, z)= min{x³/y, y², (z⁴ - x⁴)/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^0.60₁x^0.30₂.The isoquant on which output is 80^3/10 has the equation

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.

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