The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12. Table 5-1 $\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\ \text { workers } \end{array} & \text { Total output } \\ \hline 1 & 8 \\ \hline 2 & 18 \\ \hline 3 & 30 \\ \hline 4 & 41 \\ \hline 5 & 50 \\ \hline 6 & 55 \\ \hline 7 & 59 \\ \hline 8 & 61 \\ \hline 9 & 62 \\ \hline \end{array}$ -Refer to Table 5-1. Diminishing returns occurs beyond:

A) 2 workers. B) 3 workers. C) 4 workers. D) 5 workers. E) 6 workers. A) 2 workers. B) 3 workers. C) 4 workers. D) 5 workers. E) 6 workers.

The following table shows the total output produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $32. Table 5-1 $\begin{array} { | c | c | } \hline \begin{array} { c } \text { Number of } \\ \text { workers } \end{array} & \text { Total output } \\ \hline 1 & 8 \\ \hline 2 & 18 \\ \hline 3 & 30 \\ \hline 4 & 41 \\ \hline 5 & 50 \\ \hline 6 & 56 \\ \hline 7 & 60 \\ \hline 8 & 61 \\ \hline 9 & 62 \\ \hline \end{array}$ -Refer to Table 5-1. What is the marginal product of the 5th worker?

A) 9 units B) 2 units C) 8 units D) 6 units E) 11 units A) 9 units B) 2 units C) 8 units D) 6 units E) 11 units

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12. Table 5-1 $\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\ \text { workers } \end{array} & \text { Total output } \\ \hline 1 & 8 \\ \hline 2 & 18 \\ \hline 3 & 30 \\ \hline 4 & 41 \\ \hline 5 & 50 \\ \hline 6 & 55 \\ \hline 7 & 59 \\ \hline 8 & 61 \\ \hline 9 & 62 \\ \hline \end{array}$ -Refer to Table 5-1. What is the total revenue that accrues to the firm when it employs 4 workers?

A) $36 B) $112 C) $100 D) $60 E) $82 A) $36 B) $112 C) $100 D) $60 E) $82

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12. Table 5-1 $\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\ \text { workers } \end{array} & \text { Total output } \\ \hline 1 & 8 \\ \hline 2 & 18 \\ \hline 3 & 30 \\ \hline 4 & 41 \\ \hline 5 & 50 \\ \hline 6 & 55 \\ \hline 7 & 59 \\ \hline 8 & 61 \\ \hline 9 & 62 \\ \hline \end{array}$ -Refer to Table 5-1. What is the marginal profit of the 2nd worker?

A) $24 B) $20 C) $12 D) $8 E) $0 A) $24 B) $20 C) $12 D) $8 E) $0

The following table shows the total output produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $32. Table 5-1 $\begin{array} { | c | c | } \hline \begin{array} { c } \text { Number of } \\ \text { workers } \end{array} & \text { Total output } \\ \hline 1 & 8 \\ \hline 2 & 18 \\ \hline 3 & 30 \\ \hline 4 & 41 \\ \hline 5 & 50 \\ \hline 6 & 56 \\ \hline 7 & 60 \\ \hline 8 & 61 \\ \hline 9 & 62 \\ \hline \end{array}$ -Refer to Table 5-1. Diminishing returns to labor occurs beyond:

A) 4 workers. B) 3 workers. C) 5 workers. D) 9 workers. E) 8 workers. A) 4 workers. B) 3 workers. C) 5 workers. D) 9 workers. E) 8 workers.

Exam 5: Production

A firm produces according to the following production function: Q = K^.25L^.75. The price of K is $4 per unit, and the price of L is $6 per unit. What is the optimal capital/labor ratio?

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Question 1

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The firm employs inputs in an optimal ratio when MP_K/P_K = MP_L/P_L
MP_K = .25K^-^.⁷⁵L^.⁷⁵ and MP_L = .75K^.²⁵L^-^.²⁵. By substitution, (.25K^-.75L^.⁷⁵)/4 = (.75K^.²⁵L^-.25)/6
Cross multiplying leads to: 6(.25K^-.75L^.⁷⁵) = 4(.75K^.²⁵L^-.25) or 1.5K^-.75L^.⁷⁵ = 3K^.²⁵L^-.25
This simplifies to 1.5L = 3K, or L = 2K. The firm should use twice as many units of labor as units of capital or the optimal capital/labor ratio is 1:2.

Carefully define marginal rate of technical substitution. What are the assumptions on the basis of which it is calculated?

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The marginal rate of technical substitution, MRTS, denotes the rate at which one input substitutes for another in production. When using isoquants, it can be measured as:
(-MP_L/MP_K), where MP_L and MP_K refer to the marginal products of labor and capital respectively. While calculating MRTS, it is assumed that Q or output is constant; that is, inputs are substituted along the same isoquant.

Standale Plastics produces plastic dustpans, using a semi-automated system of five machines to produce pans. The amount of labor to tend the machines, repair, adjust input flows, and remove completed pans, is variable, and output tends to follow the formula: Q = 300L.6, where Q = units of output produced per day and L = number of daily workers. (a) Compute the total product per day and the marginal product of labor for the first five workers. (b) Standale sells the dustpans to retailers at a rice of $1 each, and can hire labor at a wage of $125 per day. What is the optimal amount of abor to hire? What is the optimal output of dustpans? (c) Suppose that the price of the dustpans increases to $1.25. What is the new optimal amount of labor?

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Question 3

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a.The last row of the accompanying table lists the total product Q produced perday and marginal product of labor, MP_L, for 5 workers, according to the equations: Q =300L^.6and MP_L = ∂Q/∂L = (0.6)(300)(L)^-.4. $\begin{array} { | c | c | c | } \hline \mathrm { L } & \mathrm { Q } & \mathrm { MP } _ { \mathrm { L } } \\\hline 1 & 300 & 180 \\\hline 2 & 455 & 136.4 \\\hline 3 & 580 & 116 \\\hline 4 & 689 & 103.4 \\\hline 5 & 788 & 94.7 \\\hline\end{array}$
b.Optimal use of an input requires that the marginal revenue product of labor equals the marginal cost of labor: MRP_L = (MR)(MP_L) = MC_L. Given that MRP_L = $1 and MC_L = $125, it follows that MP_L = $125. The firm should use two workers because the marginal product of a third worker falls short of the threshold value of $125. Total output is 455 units.
c.The new threshold value for MP_L becomes: ($1.25) × (MP_L) = $125 or MP_L = 100 units. The increase in price prompts the firm to increase its labor to four workers.

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12. Table 5-1 Nurnber of workers Total output 1 8 2 18 3 30 4 41 5 50 6 55 7 59 8 61 9 62 -Refer to Table 5-1. Diminishing returns occurs beyond:

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Question 4

What does the law of diminishing marginal returns state?

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Question 5

The marginal revenue product of labor is equal to the product of:

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Question 6

When a profit-maximizing firm undertakes production in more than one plant, it will allocate a fixed level of inputs such that _____ is equal across plants.

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Question 7

Dirt Diggers (DD) is a firm that excavates roadside ditches to lay drainpipe. Its output follows the production function: Q = 10L - .1L², where Q denotes the length of the ditch in meters. The firm hires labor at a wage of $12 per hour. DD has received an offer to excavate 250 meters for a price of $500. Should it accept the offer? Suppose DD is offered as much or as little excavation work as it desires at a price of $2.00 per meter, what is the optimal quantity that it should choose to excavate?

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Question 8

Will a profit-maximizing firm seek to maximize output from a variable input? Explain.

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Question 9

The following table shows the total output produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $32. Table 5-1 Number of workers Total output 1 8 2 18 3 30 4 41 5 50 6 56 7 60 8 61 9 62 -Refer to Table 5-1. What is the marginal product of the 5th worker?

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Question 10

If there is a change in input prices, what is the most likely impact on production isoquants?

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Question 11

A firm has carefully estimated its production function to be: Q = K.55L.45. What is output elasticity in this case? What sort of returns to scale does the firm face? Explain.

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Question 12

The slope of an isocost line shows:

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Question 13

Output elasticity is the percentage change in output that results from a 1 percent increase _____.

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Question 14

A firm produces a good in two factories: one in Tucson and one in Phoenix. Historically, the plants' long-run average costs have been comparable. Engineers have found that output elasticity at the Tucson plant is 1.1, while at Phoenix it is .93. A senior production manager has recommended expanding the scale of production in Tucson over the next few years and cutting production in Phoenix. Examine the validity of this proposal.

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Question 15

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12. Table 5-1 Nurnber of workers Total output 1 8 2 18 3 30 4 41 5 50 6 55 7 59 8 61 9 62 -Refer to Table 5-1. What is the total revenue that accrues to the firm when it employs 4 workers?

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Question 16

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12. Table 5-1 Nurnber of workers Total output 1 8 2 18 3 30 4 41 5 50 6 55 7 59 8 61 9 62 -Refer to Table 5-1. What is the marginal profit of the 2nd worker?

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Question 17

The following table shows the total output produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $32. Table 5-1 Number of workers Total output 1 8 2 18 3 30 4 41 5 50 6 56 7 60 8 61 9 62 -Refer to Table 5-1. Diminishing returns to labor occurs beyond:

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Question 18

Carefully explain why the marginal product of labor first rises and then falls as the use of labor increases. In which portion of the marginal product of labor curve will the firm typically produce?

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Question 19

A factory produces product A according to the production function Q_A = 100X_A, where X_A denotes the amount of input and Q_A is the quantity produced. It also produces product B according to the production function Q_B = 200X_B - X_B², where X_B denotes the amount of input and Q_B is the quantity produced. The total available amount of input X is 100 units. The firm's profit-maximizing allocation of input X is:

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Question 20

Showing 1 - 20 of 51

A firm produces according to the following production function: Q = K^.25L^.75. The price of K is $4 per unit, and the price of L is $6 per unit. What is the optimal capital/labor ratio?

Carefully define marginal rate of technical substitution. What are the assumptions on the basis of which it is calculated?

What does the law of diminishing marginal returns state?

The marginal revenue product of labor is equal to the product of:

When a profit-maximizing firm undertakes production in more than one plant, it will allocate a fixed level of inputs such that _____ is equal across plants.

Will a profit-maximizing firm seek to maximize output from a variable input? Explain.

If there is a change in input prices, what is the most likely impact on production isoquants?

A firm has carefully estimated its production function to be: Q = K.55L.45. What is output elasticity in this case? What sort of returns to scale does the firm face? Explain.

The slope of an isocost line shows:

Output elasticity is the percentage change in output that results from a 1 percent increase _____.

Carefully explain why the marginal product of labor first rises and then falls as the use of labor increases. In which portion of the marginal product of labor curve will the firm typically produce?

Introduction to Economic Decision Making

Optimal Decisions Using Marginal Analysis

Demand Analysis and Optimal Pricing

Estimating and Forecasting Demand

Cost Analysis

Perfect Competition

Monopoly

Oligopoly

Game Theory and Competitive Strategy

Regulation, Public Goods, and Benefit-Cost Analysis

Decision Making Under Uncertainty

The Value of Information

Asymmetric Information and Organizational Design

Bargaining and Negotiation

Linear Programming

Auctions and Competitive Bidding Available Online

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Exam 5: Production

A firm produces according to the following production function: Q = K.25L.75. The price of K is $4 per unit, and the price of L is $6 per unit. What is the optimal capital/labor ratio?

Carefully define marginal rate of technical substitution. What are the assumptions on the basis of which it is calculated?

What does the law of diminishing marginal returns state?

The marginal revenue product of labor is equal to the product of:

When a profit-maximizing firm undertakes production in more than one plant, it will allocate a fixed level of inputs such that _____ is equal across plants.

Will a profit-maximizing firm seek to maximize output from a variable input? Explain.

If there is a change in input prices, what is the most likely impact on production isoquants?

A firm has carefully estimated its production function to be: Q = K.55L.45. What is output elasticity in this case? What sort of returns to scale does the firm face? Explain.

The slope of an isocost line shows:

Output elasticity is the percentage change in output that results from a 1 percent increase _____.

Carefully explain why the marginal product of labor first rises and then falls as the use of labor increases. In which portion of the marginal product of labor curve will the firm typically produce?

Introduction to Economic Decision Making

Optimal Decisions Using Marginal Analysis

Demand Analysis and Optimal Pricing

Estimating and Forecasting Demand

Cost Analysis

Perfect Competition

Monopoly

Oligopoly

Game Theory and Competitive Strategy

Regulation, Public Goods, and Benefit-Cost Analysis

Decision Making Under Uncertainty

The Value of Information

Asymmetric Information and Organizational Design

Bargaining and Negotiation

Linear Programming

Auctions and Competitive Bidding Available Online

Filters

A firm produces according to the following production function: Q = K^.25L^.75. The price of K is $4 per unit, and the price of L is $6 per unit. What is the optimal capital/labor ratio?