Question 1

For the production function Q(K,L) = 3K + 2L, the marginal rate of technical substitution MRTSLK is:

Accepted Answer

A)  2/3. 
B)  3/2. 
C)  2L/3K. 
D)  3K/2L. 
A)  2/3. 
B)  3/2. 
C)  2L/3K. 
D)  3K/2L.

Question 2

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table.   The total output with two units of labor is ____.

Accepted Answer

A)  80 
B)  40 
C)  30 
D)  20 
A)  80 
B)  40 
C)  30 
D)  20

Question 3

Suppose the production function for a coffee shop is:
Q = 2K + 5L
Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal rate of technical substitution is ____.

Accepted Answer

A)  5 
B)  2.5 
C)  2 
D)  0.4 
A)  5 
B)  2.5 
C)  2 
D)  0.4

Question 4

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 average product of labor for L = 9 is ____.

Accepted Answer

A)  28.28 
B)  11.71 
C)  9.43 
D)  7.07 
A)  28.28 
B)  11.71 
C)  9.43 
D)  7.07

Question 5

(Figure: Capital and Labor XVI) Consider the production function Q = L0.5K0.5, with MPK = L0.5/K0.5 and MPL = K0.5/L0.5.   The slope of the isoquant at Point A is ____.

Accepted Answer

A)  -81 
B)  81 
C)  -9 
D)  9 
A)  -81 
B)  81 
C)  -9 
D)  9

Question 6

(Figure: Capital and Labor XVI) Consider the production function Q = L0.5K0.5, with MPK = L0.5/K0.5 and MPL = K0.5/L0.5.   
a. Define the marginal rate of technical substitution.
b. Calculate the marginal rate of technical substitution for K = 5 and L = 10.
c. Figure 6.16 shows an isoquant based on the production function referred to in the question. Calculate the slope of the isoquant at point A and point B.

Accepted Answer

a. The marginal rate of technical substi

Question 7

Suppose the production function for a small plumbing company is:
Q = 6KL
where Q is the number of water heaters installed, K is the number of machine hours from plumbing supplies, and L is the number of plumbers.
a. Suppose that the wage rate is $20 per hour and the rental rate of capital is $30 per hour. If the construction company has a contract to install 100 new water heaters, what is the cost-minimizing bundle of capital and labor?
b. Derive the company's expansion path.

Accepted Answer

"a. First, set up the company's cost min

Question 8

A firm spends $12,000 per day producing a good. The wage rate per worker is $200 per day and rental per unit of capital is $600 per day. The equation for the firm's isocost line would be _____.

Accepted Answer

The generic form of the isocos

Question 9

(Table: Capital and Labor II) This table illustrates a _____ production function because capital and labor _____.

Accepted Answer

A)  short-run; are used in equal increments 
B)  long-run; can both be varied 
C)  long-run; are used in equal increments 
D)  short-run; can both be varied 
A)  short-run; are used in equal increments 
B)  long-run; can both be varied 
C)  long-run; are used in equal increments 
D)  short-run; can both be varied

Question 10

Between 1994 and 2008, the share of the workforce employed in manufacturing _____ and manufacturing output _____.

Accepted Answer

A)  decreased; decreased 
B)  increased; increased 
C)  decreased; increased 
D)  increased; decreased 
A)  decreased; decreased 
B)  increased; increased 
C)  decreased; increased 
D)  increased; decreased

Question 11

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L0.5.   The average product of labor for L = 2 is ____.

Accepted Answer

A)  1 
B)  0.705 
C)  0.577 
D)  0.5 
A)  1 
B)  0.705 
C)  0.577 
D)  0.5

Question 12

For the following questions, assume that the marginal product of capital =   
and the marginal product of labor =   
. 
a. If the firm is hiring 10 workers at $100 per worker and 5 units of capital at $50 per unit, is the firm minimizing its cost of production? If not, what should the firm do?
b. If the firm is hiring 10 workers at $100 per worker and 5 units of capital at $200 per unit, is the firm minimizing its cost of production? If not, what should the firm do?
c. If the firm is minimizing its costs of production by hiring an equal number of workers and units of capital, what is the slope of the isocost line?

Accepted Answer

a. Cost minimization requires that MRTS

Question 13

Suppose that a community health center finds that, regardless of the number of physicians or nurse practitioners employed, it can always replace one family practice physician by using two additional nurse practitioners without affecting the quantity or quality of patient office visits. This finding implies that:

Accepted Answer

A)  physicians and nurse practitioners are perfect substitutes in production. 
B)  physicians and nurse practitioners are perfect complements in production. 
C)  diminishing returns will occur as the health center hires more nurse practitioners. 
D)  the marginal product of physicians will increase by two with every nurse practitioner hired. 
A)  physicians and nurse practitioners are perfect substitutes in production. 
B)  physicians and nurse practitioners are perfect complements in production. 
C)  diminishing returns will occur as the health center hires more nurse practitioners. 
D)  the marginal product of physicians will increase by two with every nurse practitioner hired.

Question 14

Suppose the firm's production function is Q = K1/3L2/3, where the MPK =   
and MPL =   
. 
a. If the rental rate of capital R = $30 and the wage rate W = $40, what is the cost-minimizing capital-to-labor ratio?
b. If the rental rate of capital R is $35 and the wage rate W is $70, how many units of labor and capital should the firm use to produce 12 units of output?

Accepted Answer

a. Set MRTS = W/R: MP_L/MP_K = W/R @#IMG-DLM& 2K/L = 4

Question 15

Suppose that a firm's production function is given by Q = KL (MPK = L and MPL = K), where Q is quantity of output, K is units of capital, and L is units of labor. The price per unit of labor and capital are $30 and $20, respectively. How many units of labor and capital should the firm use if it wants to minimize the cost of producing 600 units of output?

Accepted Answer

A)  L = 20; K = 30 
B)  L = 30; K = 20 
C)  L = 40; K = 60 
D)  L = 25; K = 25 
A)  L = 20; K = 30 
B)  L = 30; K = 20 
C)  L = 40; K = 60 
D)  L = 25; K = 25

Question 16

(Figure: Capital and Labor XV) Answer the following questions.   
a. Define isoquant.
b. In this figure, what things are wrong with the isoquants?

Accepted Answer

a. An isoquant is a curve showing all co

Question 17

Suppose the production function for a coffee shop is:
Q = 2K + 5L
Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal product of capital is ____.

Accepted Answer

A)  5 
B)  2.5 
C)  2 
D)  0.4 
A)  5 
B)  2.5 
C)  2 
D)  0.4

Question 18

Suppose the firm's production function is Q = K1/3L2/3, where the MPK =   and MPL =  
)
If the rental rate of capital R is $35 and the wage rate W is $70, how many units of labor and capital should the firm use to produce 12 units of output?

Accepted Answer

A)  L = 18; K = 9 
B)  L = 9; K = 18 
C)  L = 12; K = 12 
D)  L = 24; K = 24 
A)  L = 18; K = 9 
B)  L = 9; K = 18 
C)  L = 12; K = 12 
D)  L = 24; K = 24

Question 19

Suppose the wage rate is $25 per hour and the rent on capital is $50 per hour. The equation for the isocost line is given by:

Accepted Answer

A)  C = 75LK. 
B)  C = 25L + 50K. 
C)  C = 75(L + K). 
D)  C = 2K/L. 
A)  C = 75LK. 
B)  C = 25L + 50K. 
C)  C = 75(L + K). 
D)  C = 2K/L.

Question 20

Suppose the production function for a coffee shop is:
Q = 2K + 5L
where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. Use calculus to:
a. determine a function for the marginal product of labor.
b. determine a function for the marginal product of capital.
c. find the marginal rate of technical substitution.
d. discuss how MRTSLK changes as the firm uses more labor, holding output constant.

Accepted Answer

"a. Marginal product of labor is the par

For the production function Q(K,L) = 3K + 2L, the marginal rate of technical substitution MRTS_LK is:

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The total output with two units of labor is ____.

Suppose the production function for a coffee shop is: Q = 2K + 5L Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal rate of technical substitution is ____.

(Figure: Capital and Labor XVI) Consider the production function Q = L^0.5K^0.5, with MP_K = L^0.5/K^0.5 and MP_L = K^0.5/L^0.5. The slope of the isoquant at Point A is ____.

A firm spends $12,000 per day producing a good. The wage rate per worker is $200 per day and rental per unit of capital is $600 per day. The equation for the firm's isocost line would be _____.

(Table: Capital and Labor II) This table illustrates a _ production function because capital and labor _.

Between 1994 and 2008, the share of the workforce employed in manufacturing _ and manufacturing output _.

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L^0.5. The average product of labor for L = 2 is ____.

(Figure: Capital and Labor XV) Answer the following questions. a. Define isoquant. b. In this figure, what things are wrong with the isoquants?

Suppose the production function for a coffee shop is: Q = 2K + 5L Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal product of capital is ____.

Suppose the firm's production function is Q = K^1/3L^2/3, where the MPK = and MP_L = ) If the rental rate of capital R is $35 and the wage rate W is $70, how many units of labor and capital should the firm use to produce 12 units of output?

Suppose the wage rate is $25 per hour and the rent on capital is $50 per hour. The equation for the isocost line is given by:

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

For the production function Q(K,L) = 3K + 2L, the marginal rate of technical substitution MRTSLK is:

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The total output with two units of labor is ____.

Suppose the production function for a coffee shop is: Q = 2K + 5L Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal rate of technical substitution is ____.

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 average product of labor for L = 9 is ____.

(Figure: Capital and Labor XVI) Consider the production function Q = L0.5K0.5, with MPK = L0.5/K0.5 and MPL = K0.5/L0.5. The slope of the isoquant at Point A is ____.

A firm spends $12,000 per day producing a good. The wage rate per worker is $200 per day and rental per unit of capital is $600 per day. The equation for the firm's isocost line would be _____.

(Table: Capital and Labor II) This table illustrates a _____ production function because capital and labor _____.

Between 1994 and 2008, the share of the workforce employed in manufacturing _____ and manufacturing output _____.

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L0.5. The average product of labor for L = 2 is ____.

(Figure: Capital and Labor XV) Answer the following questions. a. Define isoquant. b. In this figure, what things are wrong with the isoquants?

Suppose the production function for a coffee shop is: Q = 2K + 5L Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal product of capital is ____.

Suppose the firm's production function is Q = K1/3L2/3, where the MPK = and MPL = ) If the rental rate of capital R is $35 and the wage rate W is $70, how many units of labor and capital should the firm use to produce 12 units of output?

Suppose the wage rate is $25 per hour and the rent on capital is $50 per hour. The equation for the isocost line is given by:

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

For the production function Q(K,L) = 3K + 2L, the marginal rate of technical substitution MRTS_LK is:

(Figure: Capital and Labor XVI) Consider the production function Q = L^0.5K^0.5, with MP_K = L^0.5/K^0.5 and MP_L = K^0.5/L^0.5. The slope of the isoquant at Point A is ____.

(Table: Capital and Labor II) This table illustrates a _ production function because capital and labor _.

Between 1994 and 2008, the share of the workforce employed in manufacturing _ and manufacturing output _.

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L^0.5. The average product of labor for L = 2 is ____.

Suppose the firm's production function is Q = K^1/3L^2/3, where the MPK = and MP_L = ) If the rental rate of capital R is $35 and the wage rate W is $70, how many units of labor and capital should the firm use to produce 12 units of output?