Deck 2: Optimal Decisions Using Marginal Analysis

Question 1

Which of the following is true of a firm facing a downward sloping demand curve?

A) In order to sell more units, the firm needs to lower its price.
B) A price cut will reduce total revenue.
C) The firm's total revenue and price are directly correlated.
D) The marginal revenue from each unit sold is constant.
E) The firm faces a constant marginal cost curve.

Answer 1

A

Question 2

If a firm's profit is given by  = -150 + 360Q - 36Q2, then its optimal output is:

A) 12 units.
B) 5 units.
C) 2 units.
D) 20 units.
E) 36 units.

Answer 2

B

Question 3

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product.
Table 2-1
$\begin{array} { | c | c | c | c | } \hline \text { Price } & \text { Quantity } & \text { Total Revenue } & \text { Total Cost } \\\hline 15 & 1 & 15 & 3 \\\hline 14 & 2 & 28 & 7 \\\hline 13 & 3 & 39 & 12 \\\hline 12 & 4 & 48 & 18 \\\hline 11 & 5 & 55 & 25 \\\hline 10 & 6 & 60 & 33 \\\hline\end{array}$

-Refer to Table 2-1. What is the marginal revenue associated with the sale of the 5th unit of the good?

A) $55
B) $8
C) $7
D) $48
E) $4

Answer 3

$7

Question 4

The following table shows the total revenue and total cost (in dollars) from different sales volumes of the good.
Table 2-1
$\begin{array} { | c | c | c | c | } \hline \text { Price } & \text { Quantity } & \text { Total Revenue } & \text { Total Cost } \\\hline 15 & 1 & 15 & 3 \\\hline 14 & 2 & 28 & 7 \\\hline 13 & 3 & 39 & 12 \\\hline 12 & 4 & 48 & 18 \\\hline 11 & 5 & 55 & 25 \\\hline 10 & 6 & 60 & 33 \\\hline\end{array}$


-Refer to Table 2-1. What is the firm's profit from selling 3 units of the good?

A) $13
B) $11
C) $12
D) $39
E) $27

Question 5

If a firm's demand function is of the form P = a - bQ, what is its marginal revenue equation?

A) MR = a - Q
B) MR = a - 2bQ
C) MR = a - 2Q
D) MR = a - 2b
E) MR = a + 2bQ

Question 6

Suppose a firm's inverse demand function is P = 40 - 8Q. What is the firm's revenue function?

A) R = 40Q - 8Q²
B) R = 40 - 16Q
C) R = -8Q
D) R = 40/Q - 8
E) R = 40Q - 4Q²

Question 7

The demand for a product is given by P = 1,750 - 25Q. If the firm wishes to sell 50 units, each unit should be priced at:

A) $100.
B) $200,
C) $300.
D) $400.
E) $500.

Question 8

Suppose a firm's profit is given by the equation π = -200 + 80Q - .2Q². Which of the following is true?

A) The firm's marginal profit is given by the equation: M $\pi$ = 80 - .2Q.
B) The firm's profit-maximizing output is Q = 400.
C) The firm's profit-maximizing output is Q = 200.
D) The firm's marginal profit is given by the equation: M $\pi$ = 80 - 2Q.
E) The firm's profit-maximizing output is Q = 800.

Question 9

Which of the following correctly defines marginal cost?

A) Marginal cost is the addition made to fixed cost when an extra unit is produced.
B) Marginal cost is the additional cost of producing an extra unit of output.
C) Marginal cost is the additional cost of increasing the scale of production in the long run.
D) Marginal cost is the difference between price and marginal revenue for the last unit sold.
E) Marginal cost is the same as the firm's variable cost at all levels of output.

Question 10

A firm's demand curve is given by Q = 800 - 2P, where P = price and Q = quantity. Therefore, its inverse demand equation is:

A) MR = 800 - 4P
B) P = 800 - 2Q
C) P = 400 - .5Q
D) P = 800 - .5Q
E) 800 = Q + 2P

Question 11

A firm's total revenue function is given by R = 100 + 100Q - 2Q2. At Q = 10, which of the following is true?

A) The firm's marginal revenue is $80.
B) The firm's marginal revenue is constant.
C) The firm's average revenue is $50.
D) The firm's total revenue is $500.
E) The firm's marginal revenue is $60.

Question 12

Which of the following correctly defines marginal revenue?

A) Marginal revenue is the price at which the firm sells the last unit of the good.
B) Marginal revenue is the change in revenue from a unit increase in the price of the good.
C) Marginal revenue is the additional revenue from a unit increase in output and sales.
D) Marginal revenue is the additional revenue earned from an increase in demand for the good.
E) Marginal revenue is the difference between price and marginal cost for the last unit sold.

Question 13

According to the model of the firm, the management's main goal is to:

A) increase revenue from sales.
B) maximize profit.
C) maximize its market share.
D) minimize its variable cost per unit.
E) maintain a steady and predictable growth in earnings.

Question 14

The demand for a product is given by Q = 600 - 30P. At P = $15, the firm sells:

A) 100 units.
B) 150 units.
C) 300 units.
D) 450 units.
E) 600 units.

Question 15

For a downward-sloping demand curve, the associated marginal revenue curve:

A) coincides with the demand curve.
B) lies below and is parallel to the demand curve.
C) has twice the slope as the demand curve.
D) is positive for all levels of sales.
E) is parallel to the quantity axis.

Question 16

Suppose, at its current output level, a firm's marginal profit is positive. Therefore, to maximize profit, it should:

A) decrease output until marginal profit is zero.
B) increase output because MR is less than MC.
C) increase both its output and its price.
D) increase output because MR is greater than MC.
E) increase output until it is producing at full capacity.

Question 17

Given that a firm's inverse demand function is P = 100 - 5Q and total cost is given by C = 550 + 10Q, what is the firm's profit-maximizing level of output?

A) 10 units
B) 15 units
C) 9 units
D) 8 units
E) 5 units

Question 18

According to the law of demand, if a firm reduces the price of its good:

A) consumers in the market will demand more units of the good.
B) some consumers will exit the market.
C) consumers will demand fewer units than before the price cut.
D) the quantity of goods produced and sold by the firm will decline.
E) competing firms will reduce prices.

Question 19

The following table shows the total revenue and total cost (in dollars) from different sales volumes of the good.
Table 2-1
$\begin{array} { | c | c | c | c | } \hline \text { Price } & \text { Quantity } & \text { Total Revenue } & \text { Total Cost } \\\hline 15 & 1 & 15 & 3 \\\hline 14 & 2 & 28 & 7 \\\hline 13 & 3 & 39 & 12 \\\hline 12 & 4 & 48 & 18 \\\hline 11 & 5 & 55 & 25 \\\hline 10 & 6 & 60 & 33 \\\hline\end{array}$


-Refer to Table 2-1. What is the marginal profit of the firm from the sale of the 3rd unit of the good?

A) $9
B) $6
C) $2
D) $5
E) $21

Question 20

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product.
Table 2-1
$\begin{array} { | c | c | c | c | } \hline \text { Price } & \text { Quantity } & \text { Total Revenue } & \text { Total Cost } \\\hline 15 & 1 & 15 & 3 \\\hline 14 & 2 & 28 & 7 \\\hline 13 & 3 & 39 & 12 \\\hline 12 & 4 & 48 & 18 \\\hline 11 & 5 & 55 & 25 \\\hline 10 & 6 & 60 & 33 \\\hline\end{array}$

-Refer to Table 2-1. What is the profit-maximizing level of output for the firm?

A) 3 units
B) 2 units
C) 1 unit
D) 5 units
E) 6 units

Question 21

How will an increase in price affect the quantity of output sold by a firm? What are the reasons for this change?

Question 22

In each case below, find the profit-maximizing level of output. Verify that each output level is a maximum by checking the second derivative.
(a) $\pi$ = -50 + 200Q - 10Q²
(b) π = –100 + 300Q – 4Q³

Question 23

To maximize profit, the firm should set output at the level where:

A) the average cost per unit is minimized.
B) average revenue just equals average cost.
C) marginal cost equals zero.
D) marginal revenue is equal to marginal cost.
E) marginal revenue equals zero.

Question 24

War Game, Inc. produces games that simulate historical battles. The market is small but loyal, and War Game is the largest manufacturer. It is thinking about introducing a new game in honor of the sixtieth anniversary of the end of World War II. Based on historical data regarding sales, War Game management forecasts demand for this game to be P = 50 - .002Q, where Q denotes unit sales per year, and P denotes price in dollars. The cost of manufacturing (based on royalty payments to the designer of the game, and the costs of printing and distributing) is C = 140,000 + 10Q.
(a) If the goal of War Game is to maximize profit, calculate the optimal output and price.

Question 25

Due to an increase in the price of a competitor's product, the demand for a firm's product increases sharply. How is this most likely to affect the firm's marginal revenue and marginal cost?

A) Marginal revenue will increase but marginal cost will decrease.
B) Both marginal revenue and marginal cost will not be affected.
C) Both marginal revenue and marginal cost will increase.
D) Marginal revenue will not change but marginal cost will increase.
E) Marginal revenue will increase but marginal cost will not change.

Question 26

Are there any types of goods or situations where the law of demand does not hold? Explain.

Question 27

What is the law of demand? How do managers use it in decision-making?

Question 28

Assume that Turbo is a firm that produces two kinds of flash-memory drives. Its deluxe model has the inverse demand equation: P_D = 70 - .05Q_D, where QD is the number of units sold per week. For its economy model, the price equation is: P_E = 30 - .05Q_E. Turbo's marginal cost is $10 per unit for either drive, and it produces both on a single assembly line that has a maximum capacity of 875 drives per week.
(a) Determine the profit-maximizing outputs and prices of the drives.
(b) Suppose demand for the economy drive increases to: PE = 50 – .04QE. What are the profit-maximizing outputs and prices of the drives?

Question 29

Assume that a firm is producing at its profit-maximizing level of output. A decrease in fixed cost implies that:

A) marginal revenue will increase but marginal cost will decrease.
B) marginal revenue will not change but marginal cost will decrease.
C) neither average total cost nor marginal cost will change.
D) neither marginal revenue nor marginal cost will change.
E) both marginal revenue and marginal cost will decrease.

Question 30

Assume that Burger King, a fast food chain, enters into a franchise agreement. The royalty paid to Burger King by the franchisee is calculated as a percentage of the franchisee's revenue. Given that the franchisee faces a downward-sloping demand curve, which of the following is likely to be true?

A) The franchisee's revenue-maximizing output will be greater than its profit-maximizing output.
B) To maximize revenue, Burger King will want the franchisee to produce at the level where total revenue is positive but falling.
C) The franchisee will produce at the level where the slope of the total revenue curve is zero in order to maximize profits.
D) The profit-maximizing level of output for the franchisee will be at the level where marginal revenue is less than marginal cost.
E) To maximize revenue, Burger King will want the franchisee to produce at the level where marginal revenue equals marginal cost.

Question 31

Carefully explain the economic importance of the Lagrange multiplier. How might a manager use it in decision making?

Question 32

Suppose the inverse demand curve of a firm is given by the equation: P = 2,500 - 10Q. Compute the firm's total revenue and marginal revenue, and determine the quantity that maximizes total revenue.

Question 33

Given the total cost equation for a firm, the marginal cost equation can be derived by:

A) dividing total cost by total output.
B) taking the first derivative of the cost function with respect to quantity.
C) dividing total variable cost by total output.
D) subtracting variable cost from the fixed cost at all levels of output.
E) multiplying the total cost equation by price.

Question 34

A firm negotiates a new labor contract with a higher average hourly wage. What is the most likely effect of the higher wage on the firm's price and output?

A) Neither price nor output will be affected.
B) Price will increase but output will not change.
C) Both price and output will increase.
D) Price will not change but output will decrease.
E) Price will increase and output will decrease.

Question 35

Suppose that a firm sells in a competitive market at a fixed price of $12 per unit. The firm's cost function is: C = 200 + 4Q. In this case, how can the firm use marginal revenue and marginal cost to maximize its profit?

Question 36

Suppose that a firm operates in a competitive market where the commodity price is $15 per unit. The firm's cost equation is C = 25 + .25Q2, where C = total cost and Q = quantity.
(a) Find the profit-maximizing level of output for the firm. Determine its level of profit.

Question 37

A firm faces the demand curve, P = 80 - 3Q, and has the cost equation: C = 200 + 20Q, where P = price, C = total cost, and Q = quantity.
(a) Find the optimal quantity and price for the firm.

Question 38

The demand for a firm's product is given by the equation: P = 36 - .2Q. The firm's cost equation is given by C = 200 + 20Q.
(a) Determine the firm's optimal quantity and price.
(b) Suppose that the firm’s costs change to C = 100 + 24Q. Determine the new optimal quantity and price. Explain why the results differ from the previous case.

Question 39

Assume that a firm is producing at its profit-maximizing level of output. A decrease in the price of raw materials used in production is most likely to lead to:

A) an increase in quantity produced at an unchanged price.
B) a fall in the price of the good and an increase in the quantity produced.
C) a fall in both the price of the good and the quantity produced.
D) an increase in both the price of the good and the quantity produced.
E) a fall in the quantity produced of the good at an unchanged price.

Question 40

Carefully define marginal analysis, and explain how it is useful in managerial economics.

Question 41

(a) How will an increase in overhead costs affect the demand and supply curves for a firm? Will an increase in the price of a raw material used in production have the same effect?

Question 42

Max Whitley, manager of Whitley Construction, builds new homes in a booming community in the Midwest. Although sales have slowed because of a national recession, it now looks as if the recession is about to end. Max wants to be ready with material, labor, and foremen to meet the demand for housing. Last year, Max built and sold 40 starter homes which is the most popular model. Max thinks that his sales will increase to 50 units over the current year. The going market price for this model (which Max and his numerous competitors have charged) has been $275,000. In addition, Whitley Construction's marginal cost of building this model averages $245,000.
(a) Based on these facts, recommend a course of action for Max.

Question 43

KopyKat is a firm that specializes in printing business cards and résumé's, using the latest laser technology. The manager has estimated that weekly demand can be approximated by P = 25 - .001Q, where P is price and Q is output per week. The firm's cost function is C = 25,000 + 13Q + .002Q2, where C is total cost.
(a) Determine the firm's profit maximizing price and output.

Question 44

Night Timers is a small company manufacturing glow-in-the-dark products. One of the hottest items the engineering department has developed is adhesive tape that can be applied to walls and floors. Night Timers' chief engineer anticipates that the product will be sold in ten-foot rolls. At present, the company's maximum production capacity is 140,000 rolls per year. The engineer believes the cost function to be described by C = $50,000 + 0.25Q, where C is total cost and Q is number of rolls (The high fixed costs represent development cost and tooling to prepare coating equipment). Night Timers' president seeks to establish a price that maximizes profit (since she is the chief stockholder). She thinks that the firm should be able to sell at least 125,000 rolls of tape per year.
(a) If Night Timers plans to sell 125,000 rolls per year, what is the necessary price if the firm is to break even? What if it can only sell 100,000?

Question 45

A manufacturing company produces and sells small farm tractors. Its annual fixed costs are $15 million, and its marginal cost per tractor is $20,000. Demand for small tractors is given by: P = 30,000 - Q, where P denotes price in dollars and Q is annual sales.
(a) Find the firm's profit-maximizing output, price, and annual profit.

Question 46

The current manager of a small bicycle shop estimates the demand curve for a child's starter bike to be: P = 80 - 2Q. Costs are given by: C = 200 + 20Q. The former owner of the shop (now retired) urges the manager to keep prices low so as to increase sales and maximize revenue. (The shop pays the former owner 5% of each dollar of earned revenue). If current management follows the former owner's goal, what sales output and price should it set? What strategy would you recommend to maximize profits?