Question 1

To calculate the firm's expansion path using calculus, we need to solve its:

Accepted Answer

A)  quantity maximization problem. 
B)  cost minimization problem, with rental cost of capital R and wage W treated as variables. 
C)  cost minimization problem with quantity Q fixed. 
D)  cost minimization problem with quantity Q treated as variable. 
A)  quantity maximization problem. 
B)  cost minimization problem, with rental cost of capital R and wage W treated as variables. 
C)  cost minimization problem with quantity Q fixed. 
D)  cost minimization problem with quantity Q treated as variable.

Question 2

Using a Lagrangian equation for a firm's cost minimization problem, you can solve for all of the following EXCEPT:

Accepted Answer

A)  the optimal level of labor input. 
B)  the average cost of production. 
C)  the demand function for capital. 
D)  the equation for the expansion path. 
A)  the optimal level of labor input. 
B)  the average cost of production. 
C)  the demand function for capital. 
D)  the equation for the expansion path.

Question 3

Suppose a firm with a production function given by Q = 4K0.25L0.75 produces 100 units of output. The firm pays a wage of $30 per units and pays a rental rate of capital of $10 per unit.
(Note:  
)
The minimum cost of producing 100 units of output is:

Accepted Answer

A)  $3,000. 
B)  $2,250. 
C)  $800. 
D)  $1,000. 
A)  $3,000. 
B)  $2,250. 
C)  $800. 
D)  $1,000.

Question 4

In the long run, because firms can adjust both capital and labor:

Accepted Answer

A)  firms will grow. 
B)  production is more expensive because firms must invest in both labor and capital. 
C)  the impact of diminishing marginal returns is lessened. 
D)  firms fire workers, replacing the labor productivity with capital. 
A)  firms will grow. 
B)  production is more expensive because firms must invest in both labor and capital. 
C)  the impact of diminishing marginal returns is lessened. 
D)  firms fire workers, replacing the labor productivity with capital.

Question 5

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table.   The marginal product of labor of the second unit of labor is ____.

Accepted Answer

A)  50 
B)  40 
C)  30 
D)  20 
A)  50 
B)  40 
C)  30 
D)  20

Question 6

(Figure: Capital and Labor V) Put these four panels in order from the easiest case of input substitutability to the hardest case of input substitutability.

Accepted Answer

A)  b, a, c, d 
B)  a, c, d, b 
C)  d, c, a, b 
D)  a, d, c, b 
A)  b, a, c, d 
B)  a, c, d, b 
C)  d, c, a, b 
D)  a, d, c, b

Question 7

Define a production function and give an example of a Cobb-Douglas production function with constant returns to scale.

Accepted Answer

A production function is a mathematical

Question 8

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L0.5.   The marginal product of labor for L = 16, assuming that labor is infinitely divisible, is ____.

Accepted Answer

A)  1 
B)  0.75 
C)  0.5 
D)  0.25 
A)  1 
B)  0.75 
C)  0.5 
D)  0.25

Question 9

The production function for laser eye surgery is given by Q = 20K0.5L0.5, where Q is the number of laser eye surgeries performed per day, K is the number of eye surgery machines (which is fixed at 2 in the short run), and L is the number of employees. The marginal product of labor for L = 2 is ____.

Accepted Answer

A)  28.28 
B)  11.71 
C)  9.43 
D)  8.99 
A)  28.28 
B)  11.71 
C)  9.43 
D)  8.99

Question 10

A firm has the production function Q = K0.1L0.9, where Q measures output, K represents machine hours, and L measures labor hours. Suppose that the wage rate is $45, and the firm wants to produce 100,000 units of output. Use calculus to:
a. derive the demand for capital.
b. confirm that the demand for capital satisfies the law of demand.
c. determine the optimal level of capital if the rental rate on capital is $25.

Accepted Answer

a. We could solve this problem using a L

Question 11

Suppose a firm with a production function given by Q = K0.25L0.75 produces 1,500 units of output. The firm pays a wage of $50 per unit and pays a rental rate of capital of $50 per unit.
(Note:  
)
To minimize the cost of producing 1,500 units of output, the firm should use:

Accepted Answer

A)  3 times as many units of labor as units of capital. 
B)  equal amounts of labor and capital. 
C)  1.25 times as many units of capital as units of labor. 
D)  16 units of capital and 6,814 units of labor. 
A)  3 times as many units of labor as units of capital. 
B)  equal amounts of labor and capital. 
C)  1.25 times as many units of capital as units of labor. 
D)  16 units of capital and 6,814 units of labor.

Question 12

(Figure: Capital and Labor VII) Based on the isocost line, the ratio of the wage rate (W) to rental rate of capital (R) is:

Accepted Answer

A)  1.5. 
B)  4.0. 
C)  0.67. 
D)  0.50. 
A)  1.5. 
B)  4.0. 
C)  0.67. 
D)  0.50.

Question 13

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table.   The average product of labor when there are three units of labor is ____.

Accepted Answer

A)  50 
B)  40 
C)  33.33 
D)  30 
A)  50 
B)  40 
C)  33.33 
D)  30

Question 14

(Table: Capital and Labor XIV) Consider the production function that this table shows.   Suppose the firm is using 1 unit of capital and 1 unit of labor. The marginal product of capital for K = 2 is ____.

Accepted Answer

A)  41.42 
B)  40.24 
C)  31.78 
D)  26.79 
A)  41.42 
B)  40.24 
C)  31.78 
D)  26.79

Question 15

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table.   The marginal product of labor with one unit of labor is ____.

Accepted Answer

A)  50 
B)  40 
C)  30 
D)  20 
A)  50 
B)  40 
C)  30 
D)  20

Question 16

The short-run production function for a firm is given by Q = 40L2/3. What is the average product?

Accepted Answer

A)  APL = 16.67L 
B)  APL = 40/L 
C)  APL = 40/L1/3 
D)  APL = 1/40L 
A)  APL = 16.67L 
B)  APL = 40/L 
C)  APL = 40/L1/3 
D)  APL = 1/40L

Question 17

You've been asked by your manager to choose between the following three production functions based on returns to scale:
Q = 10K2L1
Q = 10K0.5L0.5
Q = 10K0.25L0.5
She would like you to choose the one that exhibits increasing returns to scale and to provide evidence to support your decision.

Accepted Answer

a. With this production function, a doub

Question 18

(Figure: Production Function I) Which of the following statements is (are) TRUE?   I. At L = 5, MPTL > APL.
II) At L = 2, MPL = APL.
III) For this production function, MPL is greater at L = 2 than at L = 8.
IV) For this production function, MPL is always greater than APL.

Accepted Answer

A)  I and II 
B)  III 
C)  I and IV 
D)  II 
A)  I and II 
B)  III 
C)  I and IV 
D)  II

Question 19

Suppose that a firm's production function is   . The marginal rate of technical substitution is ____.

Accepted Answer

A)  0.5KL 
B)  KL 
C)  2KL-1 
D)  0.5KL-1 
A)  0.5KL 
B)  KL 
C)  2KL-1 
D)  0.5KL-1

Question 20

Suppose the production function for a bakery is:
Q = 4K0.4L0.6
Where Q is the number of loaves of bread produced per day, K is the number of ovens, and L is the number of workers employed. Suppose that the wage rate is $5 per hour and the rental rate of capital is $10 per hour. The firm's expansion path is ____.

Accepted Answer

A)  K = 0.5L 
B)  K = L 
C)  K = 2L 
D)  K = L2 
A)  K = 0.5L 
B)  K = L 
C)  K = 2L 
D)  K = L2

To calculate the firm's expansion path using calculus, we need to solve its:

Using a Lagrangian equation for a firm's cost minimization problem, you can solve for all of the following EXCEPT:

Suppose a firm with a production function given by Q = 4K^0.25L^0.75 produces 100 units of output. The firm pays a wage of $30 per units and pays a rental rate of capital of $10 per unit. (Note: ) The minimum cost of producing 100 units of output is:

In the long run, because firms can adjust both capital and labor:

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The marginal product of labor of the second unit of labor is ____.

(Figure: Capital and Labor V) Put these four panels in order from the easiest case of input substitutability to the hardest case of input substitutability.

Define a production function and give an example of a Cobb-Douglas production function with constant returns to scale.

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L^0.5. The marginal product of labor for L = 16, assuming that labor is infinitely divisible, is ____.

Suppose a firm with a production function given by Q = K^0.25L^0.75 produces 1,500 units of output. The firm pays a wage of $50 per unit and pays a rental rate of capital of $50 per unit. (Note: ) To minimize the cost of producing 1,500 units of output, the firm should use:

(Figure: Capital and Labor VII) Based on the isocost line, the ratio of the wage rate (W) to rental rate of capital (R) is:

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The average product of labor when there are three units of labor is ____.

(Table: Capital and Labor XIV) Consider the production function that this table shows. Suppose the firm is using 1 unit of capital and 1 unit of labor. The marginal product of capital for K = 2 is ____.

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The marginal product of labor with one unit of labor is ____.

The short-run production function for a firm is given by Q = 40L^2/3. What is the average product?

You've been asked by your manager to choose between the following three production functions based on returns to scale: Q = 10K²L¹ Q = 10K^0.5L^0.5 Q = 10K^0.25L^0.5 She would like you to choose the one that exhibits increasing returns to scale and to provide evidence to support your decision.

(Figure: Production Function I) Which of the following statements is (are) TRUE? I. At L = 5, MPT_L > AP_L. II) At L = 2, MP_L = AP_L. III) For this production function, MP_L is greater at L = 2 than at L = 8. IV) For this production function, MP_L is always greater than AP_L.

Suppose that a firm's production function is . The marginal rate of technical substitution is ____.

Adventures in Microeconomics

Supply and Demand

Using Supply and Demand to Analyze Markets

Consumer Behavior

Individual and Market Demand

Costs

Supply in a Competitive Market

Market Power and Monopoly

Market Power and Pricing Strategies

Imperfect Competition

Game Theory

Factor Markets

Investment, Time, and Insurance

General Equilibrium

Asymmetric Information

Externalities and Public Goods

Behavioral and Experimental Economics

Filters

Exam 6: Producer Behavior

To calculate the firm's expansion path using calculus, we need to solve its:

Using a Lagrangian equation for a firm's cost minimization problem, you can solve for all of the following EXCEPT:

Suppose a firm with a production function given by Q = 4K0.25L0.75 produces 100 units of output. The firm pays a wage of $30 per units and pays a rental rate of capital of $10 per unit. (Note: ) The minimum cost of producing 100 units of output is:

In the long run, because firms can adjust both capital and labor:

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The marginal product of labor of the second unit of labor is ____.

(Figure: Capital and Labor V) Put these four panels in order from the easiest case of input substitutability to the hardest case of input substitutability.

Define a production function and give an example of a Cobb-Douglas production function with constant returns to scale.

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L0.5. The marginal product of labor for L = 16, assuming that labor is infinitely divisible, is ____.

Suppose a firm with a production function given by Q = K0.25L0.75 produces 1,500 units of output. The firm pays a wage of $50 per unit and pays a rental rate of capital of $50 per unit. (Note: ) To minimize the cost of producing 1,500 units of output, the firm should use:

(Figure: Capital and Labor VII) Based on the isocost line, the ratio of the wage rate (W) to rental rate of capital (R) is:

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The average product of labor when there are three units of labor is ____.

(Table: Capital and Labor XIV) Consider the production function that this table shows. Suppose the firm is using 1 unit of capital and 1 unit of labor. The marginal product of capital for K = 2 is ____.

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The marginal product of labor with one unit of labor is ____.

The short-run production function for a firm is given by Q = 40L2/3. What is the average product?

You've been asked by your manager to choose between the following three production functions based on returns to scale: Q = 10K2L1 Q = 10K0.5L0.5 Q = 10K0.25L0.5 She would like you to choose the one that exhibits increasing returns to scale and to provide evidence to support your decision.

(Figure: Production Function I) Which of the following statements is (are) TRUE? I. At L = 5, MPTL > APL. II) At L = 2, MPL = APL. III) For this production function, MPL is greater at L = 2 than at L = 8. IV) For this production function, MPL is always greater than APL.

Suppose that a firm's production function is . The marginal rate of technical substitution is ____.

Adventures in Microeconomics

Supply and Demand

Using Supply and Demand to Analyze Markets

Consumer Behavior

Individual and Market Demand

Costs

Supply in a Competitive Market

Market Power and Monopoly

Market Power and Pricing Strategies

Imperfect Competition

Game Theory

Factor Markets

Investment, Time, and Insurance

General Equilibrium

Asymmetric Information

Externalities and Public Goods

Behavioral and Experimental Economics

Filters

Suppose a firm with a production function given by Q = 4K^0.25L^0.75 produces 100 units of output. The firm pays a wage of $30 per units and pays a rental rate of capital of $10 per unit. (Note: ) The minimum cost of producing 100 units of output is:

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L^0.5. The marginal product of labor for L = 16, assuming that labor is infinitely divisible, is ____.

Suppose a firm with a production function given by Q = K^0.25L^0.75 produces 1,500 units of output. The firm pays a wage of $50 per unit and pays a rental rate of capital of $50 per unit. (Note: ) To minimize the cost of producing 1,500 units of output, the firm should use:

The short-run production function for a firm is given by Q = 40L^2/3. What is the average product?

You've been asked by your manager to choose between the following three production functions based on returns to scale: Q = 10K²L¹ Q = 10K^0.5L^0.5 Q = 10K^0.25L^0.5 She would like you to choose the one that exhibits increasing returns to scale and to provide evidence to support your decision.

(Figure: Production Function I) Which of the following statements is (are) TRUE? I. At L = 5, MPT_L > AP_L. II) At L = 2, MP_L = AP_L. III) For this production function, MP_L is greater at L = 2 than at L = 8. IV) For this production function, MP_L is always greater than AP_L.