Deck 14: Advanced Techniques for Profit Maximization

Question 1

refer to the following:
A firm sells two goods (X and Y) that are related in consumption. The estimated inverse demand and cost functions are:


-What are the profit-maximizing levels of output for the two goods?

A) = 6, = 3
B) = 40, = 40
C) = 58, = 30
D) = 240, = 270
E) none of the above

Answer 1

= 58, = 30

Question 2

refer to the following:
A firm sells two goods (X and Y) that are related in consumption. The estimated inverse demand and cost functions are:


-What are the profit-maximizing prices for the two goods?

A) = $40, = $32.50
B) = $53.50, = $61
C) = $80, = $55
D) = $112.50, = $87.75
E) none of the above

Answer 2

= $53.50, = $61

Question 3

refer to the following:
A firm produces two products (X and Y) that are substitutes in production; both products are produced on an assembly line that operates only 18 hours per day. The firm faces the following demand and "production" functions:


-In order to maximize profit, how should the firm allocate the 18 hours of assembly line time between the two products?

A) use 10 hours to produce X, 8 hours to produce Y
B) use 11.4 hours to produce X, 6.6 hours to produce Y
C) use 12 hours to produce X, 6 hours to produce Y
D) use 15 hours to produce X, 3 hours to produce Y
None of the above.

Answer 3

use 15 hours to produce X, 3 hours to produce Y
None of the above.

Question 4

refer to the following:
A firm produces two products (X and Y) that are substitutes in production; both products are produced on an assembly line that operates only 18 hours per day. The firm faces the following demand and "production" functions:


-What are the profit-maximizing levels of output for X and Y?

A) 100 units of X and 320 units of Y
B) 114 units of X and 264 units of Y
C) 120 units of X and 240 units of Y
D) 150 units of X and 120 units of Y
E) none of the above.

Question 5

refer to the following:
A firm produces two products (X and Y) that are substitutes in production; both products are produced on an assembly line that operates only 18 hours per day. The firm faces the following demand and "production" functions:


-What are the profit-maximizing prices for the two products?

A) $100 for X, $25 for Y
B) $160 for X, $50 for Y
C) $172 for X, $65 for Y
D) $200 for X, $500 for Y
E) none of the above.

Question 6

refer to the following:
A publishing company has a production line that can print two types of magazines, MachoMan and RealLove. The production line runs 24 hours a day and the firm is currently allocating 10 hours a day to publishing MachoMan and 14 hours a day to RealLove. Marginal product is 20 for both magazines, the last issue to MachoMan added $2 to total revenue, and the last issue to RealLove added $3 to total revenue.

-The firm

A) is maximizing profit.
B) should allocate more hours to MachoMan and fewer to RealLove.
C) should allocate more hours to RealLove and fewer to MachoMan.
D) should allocate 12 hours to each magazine.

Question 7

refer to the following:
A publishing company has a production line that can print two types of magazines, MachoMan and RealLove. The production line runs 24 hours a day and the firm is currently allocating 10 hours a day to publishing MachoMan and 14 hours a day to RealLove. Marginal product is 20 for both magazines, the last issue to MachoMan added $2 to total revenue, and the last issue to RealLove added $3 to total revenue.

-If the firm allocates 15 hours a day to RealLove and 9 hours to MachoMan instead;

A) total revenue will decrease $1
B) total revenue will decrease $40
C) total revenue will increase $1
D) total revenue will increase $20
E) total revenue will increase $60

Question 8

Use the figure below

The figure shows the MRP curves for a firm producing two products, X and Y, which are substitutes in production. The MC curve measures the additional cost of another unit of the production facility.

-What is the profit-maximizing total level of use of the production facility?

A) F1
B) F2
C) F3
D) F4
E) F5

Question 9

Use the figure below

The figure shows the MRP curves for a firm producing two products, X and Y, which are substitutes in production. The MC curve measures the additional cost of another unit of the production facility.

-What level of use of the production facility should be devoted to producing X?

A) F1
B) F2
C) F3
D) F4
E) F5

Question 10

Use the figure below

The figure shows the MRP curves for a firm producing two products, X and Y, which are substitutes in production. The MC curve measures the additional cost of another unit of the production facility.

-What level of use of the production facility should be devoted to producing Y?

A) F1
B) F2
C) F3
D) F4
E) F5

Question 11

refer to the following:
A firm sells two goods (X and Y) that are related in consumption. The estimated demand and cost conditions are:


-What are the profit-maximizing levels of output for the two goods?

A)
B)
C)
D)
E) none of the above

Question 12

refer to the following:
A firm sells two goods (X and Y) that are related in consumption. The estimated demand and cost conditions are:


-What are the profit-maximizing prices for the two goods?

A)
B)

C)

D)

Question 13

refer to the following:


-What are the profit-maximizing levels of output for the two goods?

A)= 30,= 34

B)= 63,= 66
C)=142,63,11eebf61_e1d7_4b23_8659_271747c2aff4_TB10434_11= 110

D) = 191,= 163

Question 14

refer to the following:


-What are the profit-maximizing prices for the two goods?

A) = $375, = $284
B) = $423, = $712
C) = $166, = $324
D) = $481, = $588

Question 15

refer to the following figure:
?
The Hilton Hotel chain serves both business and vacation travelers. ? represent the demand and marginal revenue for business travelers, while ? are the demand and marginal revenue for vacation travelers.

-If marginal cost decreases to the point that total marginal revenue (MR_T is not shown in the figure) for Hilton at the profit-maximizing level of total output is $40, what price should the Hilton charge BUSINESS travelers?

A) $60
B) $80
C) $100
D) $120
E) $140

Question 16

using the following information:
Drill Quest, Inc. manufactures drill bits for the oil industry. Drill Quest uses cost-plus pricing to set the price of its bits. Currently Drill Quest applies a 50 percent markup on average total cost. Average variable cost of producing bits is constant and equal to $6,000 per bit. Total fixed cost at Drill Quest is $550,000. DrillQuest currently produces 690 bits. Statistical estimation of demand for Drill Quest brand bits produces the following linear demand equation (where Q is the number of bits demanded and P is the price of bits):
?

-Use the MR = SMC approach to finding the profit-maximizing point on the demand for Drill Quest's bits. The maximum possible profit is $___________.

A) $2,895,000
B) $2,345,000
C) $3,500,000
D) $3,895,000
E) $4,895,000

Question 17

Marvel Cleaning Service, Inc. is a firm that specializes in cleaning business offices, and Marvel enjoys a monopoly position because it is the only firm allowed to provide cleaning service at the TechCenter industrial office park - the monopoly is believed to enhance security. There are 25 equal-sized offices in TechCenter, each one leased to a different company. TechCenter is closed 45 days a year (Sundays plus official federal holidays), which limits the demand for Marvel's cleaning services to a maximum of 320 cleanings per year for each one of the 25 companies leasing offices.
Marvel believes it faces an identical demand by each one of the 25 businesses in TechCenter. This demand curve is shown below. Marvel's costs are constant and equal to $30 per office cleaning.
The owner of Marvel Cleaning Service is considering three types of pricing: (1) uniform pricing, (2) first-degree price discrimination, and (3) block pricing with three pricing blocks.
-If Marvel practices uniform pricing, it will charge $________ for an office cleaning and will face a quantity demanded from each of the 25 identical firms of __________ cleanings per year. At TechCenter, Marvel's total profit per year is $__________(i.e., the sum of the profits from the 25 businesses in TechCenter). Each one of the businesses enjoys $____________ of consumer surplus under uniform pricing.

Question 18

Marvel Cleaning Service, Inc. is a firm that specializes in cleaning business offices, and Marvel enjoys a monopoly position because it is the only firm allowed to provide cleaning service at the TechCenter industrial office park - the monopoly is believed to enhance security. There are 25 equal-sized offices in TechCenter, each one leased to a different company. TechCenter is closed 45 days a year (Sundays plus official federal holidays), which limits the demand for Marvel's cleaning services to a maximum of 320 cleanings per year for each one of the 25 companies leasing offices.
Marvel believes it faces an identical demand by each one of the 25 businesses in TechCenter. This demand curve is shown below. Marvel's costs are constant and equal to $30 per office cleaning.
The owner of Marvel Cleaning Service is considering three types of pricing: (1) uniform pricing, (2) first-degree price discrimination, and (3) block pricing with three pricing blocks.
-If Marvel can practice first-degree price discrimination, it will collect total revenue from each firm in at TechCenter of $_________. Under perfect price discrimination, Marvel will be hired to clean each office _________ times per year, and Marvel will earn total annual profit of $_____________ (i.e., the sum of the profits from the 25 businesses in TechCenter). Each one of the businesses enjoys $____________ of consumer surplus under perfect price discrimination.

Question 19

Marvel Cleaning Service, Inc. is a firm that specializes in cleaning business offices, and Marvel enjoys a monopoly position because it is the only firm allowed to provide cleaning service at the TechCenter industrial office park - the monopoly is believed to enhance security. There are 25 equal-sized offices in TechCenter, each one leased to a different company. TechCenter is closed 45 days a year (Sundays plus official federal holidays), which limits the demand for Marvel's cleaning services to a maximum of 320 cleanings per year for each one of the 25 companies leasing offices.
Marvel believes it faces an identical demand by each one of the 25 businesses in TechCenter. This demand curve is shown below. Marvel's costs are constant and equal to $30 per office cleaning.
The owner of Marvel Cleaning Service is considering three types of pricing: (1) uniform pricing, (2) first-degree price discrimination, and (3) block pricing with three pricing blocks.
-If Marvel employs block pricing by choosing three pricing blocks -$60, $40, and $20- the total expenditure by each business can be expressed as follows:
‪
Under this three block pricing plan, each of the businesses in TechCenter will buy ______ cleanings per year. The total expenditure by each business is $__________, and Marvel will earn total annual profit of $_____________ (i.e., the sum of the profits from the 25 businesses in TechCenter). Each one of the businesses enjoys $____________ of consumer surplus under this block-pricing plan.

Question 20

Shell Designs, Inc. faces the following monthly demand for its designer coffee mugs, which are hand-made using a special clay from imported from Costa Rica:
The average cost of producing each hand-made coffee mug is $8, and costs are constant.
-If Shell Designs decides to sell its coffee mugs over the Internet, it will have to charge a uniform price. The profit-maximizing uniform price is $________ per mug, and it will sell __________ hand-made mugs per month on the Internet. Shell's monthly profit will be $______________ per month.

Question 21

Shell Designs, Inc. faces the following monthly demand for its designer coffee mugs, which are hand-made using a special clay from imported from Costa Rica:
The average cost of producing each hand-made coffee mug is $8, and costs are constant.
-The trouble with selling coffee mugs on the Internet at uniform prices is that consumers enjoy $______________ of consumer surplus, which could be captured if Shell Designs sold its mugs at art and craft shows where it could practice first-degree price discrimination (at least in theory).

Question 22

Shell Designs, Inc. faces the following monthly demand for its designer coffee mugs, which are hand-made using a special clay from imported from Costa Rica:
The average cost of producing each hand-made coffee mug is $8, and costs are constant.
-Not only does Shell Designs lose profit in the amount of the consumer surplus computed in part b, but it also could make $____________ of additional profit on the extra coffee mugs it could sell if each buyer could be forced to pay their individual maximum price (i.e., "mugged" into paying their demand price) instead of the uniform price under perfect price discrimination.

Question 23

Shell Designs, Inc. faces the following monthly demand for its designer coffee mugs, which are hand-made using a special clay from imported from Costa Rica:
The average cost of producing each hand-made coffee mug is $8, and costs are constant.
-If Shell Designs decides to sell its mugs only at art and craft shows and employs a sales person with the uncanny-perhaps even supernatural-ability to look at buyers' eyes and know precisely the maximum price they will pay for a hand-made coffee mug, the company can sell _________ mugs per month under perfect (i.e., first-degree) price discrimination.

Question 24

Shell Designs, Inc. faces the following monthly demand for its designer coffee mugs, which are hand-made using a special clay from imported from Costa Rica:
The average cost of producing each hand-made coffee mug is $8, and costs are constant.
-Under first-degree price discrimination, the sales person will have to negotiate or haggle with every customer, in effect, charging _______ different prices.

Question 25

Shell Designs, Inc. faces the following monthly demand for its designer coffee mugs, which are hand-made using a special clay from imported from Costa Rica:
The average cost of producing each hand-made coffee mug is $8, and costs are constant.
-Under perfect price discrimination, Shell Designs earns $_________ total revenue each month and incurs $_________ total costs. Profit under first-degree price discrimination is $__________ per month, which exceeds the uniform profit by $________ per month.

Question 26

A firm is selling its product in two markets, A and B, the demand and marginal revenue functions in which are shown as D_A, D_B, MR_A, and MR_B in the following figure along with the marginal cost function.

-To maximize profit the firm will sell a total output of ______ units of which ______ units will be sold in market A and ______ units in market B.

Question 27

A firm is selling its product in two markets, A and B, the demand and marginal revenue functions in which are shown as D_A, D_B, MR_A, and MR_B in the following figure along with the marginal cost function.

-The firm will charge a price of $______ in market A and $______ in B.

Question 28

A firm is selling its product in two markets, A and B, the demand and marginal revenue functions in which are shown as D_A, D_B, MR_A, and MR_B in the following figure along with the marginal cost function.

-In equilibrium the demand elasticity is ______ in market A and ______ in B. Does the relation between elasticities conform to the theoretical relation between prices? Why or why not?

Question 29

A firm is selling in two separate markets, A and B.
-The firm should produce the total output at which ______ equals ______.

Question 30

A firm is selling in two separate markets, A and B.
-It should allocate this total output between the two markets in a way such that ______.

Question 31

A firm is selling in two separate markets, A and B.
-If the price charged in A is $12 and the price charged in B is $10, compare the elasticities in the two markets.

Question 32

F A firm is selling in two markets. Its marginal revenue in market A is $18; its marginal revenue in market B is $13. The firm should raise price in ______ and lower price in ______. It should continue until ______.

Question 33

SEQ CHAPTER \h \r 1The Financial Herald, a weekly newspaper specializing in corporate financial news, is purchased by both business people and students. A marketing research firm has estimated the two linear marginal revenue functions to be:
where MR_B is the estimated marginal revenue for the business readers, and MR_S is the estimated marginal revenue for the student readers. The production department at The Herald estimates a linear marginal cost function for newspaper production, which is

-The Herald should print a total of ___________copies each week.

Question 34

SEQ CHAPTER \h \r 1The Financial Herald, a weekly newspaper specializing in corporate financial news, is purchased by both business people and students. A marketing research firm has estimated the two linear marginal revenue functions to be:
where MR_B is the estimated marginal revenue for the business readers, and MR_S is the estimated marginal revenue for the student readers. The production department at The Herald estimates a linear marginal cost function for newspaper production, which is

-The Herald should sell ___________ copies to business readers and sell ___________ copies to students.

Question 35

SEQ CHAPTER \h \r 1The Financial Herald, a weekly newspaper specializing in corporate financial news, is purchased by both business people and students. A marketing research firm has estimated the two linear marginal revenue functions to be:
where MR_B is the estimated marginal revenue for the business readers, and MR_S is the estimated marginal revenue for the student readers. The production department at The Herald estimates a linear marginal cost function for newspaper production, which is

-The Herald should charge business readers a price of $_______ and charge students a price of $________.

Question 36

A firm is producing two goods, X and Y, that are related in consumption. The demands are

-The two goods are ______.

Question 37

A firm is producing two goods, X and Y, that are related in consumption. The demands are

-To maximize profit the firm should set ______ equal to ______ for each good, and determine the levels of X and Y by ______.

Question 38

A firm is allocating 16 hours a day on its assembly line to producing goods A and B, 12 hours to A and 8 to B. The marginal product of the facility for A is 50 and for B is 40. The marginal revenue of A is $20 and the marginal revenue of B is $30.
-The firm should allocate more time to ______ and less to ______.

Question 39

A firm is allocating 16 hours a day on its assembly line to producing goods A and B, 12 hours to A and 8 to B. The marginal product of the facility for A is 50 and for B is 40. The marginal revenue of A is $20 and the marginal revenue of B is $30.
-If the firm allocates 13 hours to A and 7 to B, revenue will ______ by $______.

Question 40

A firm is allocating 16 hours a day on its assembly line to producing goods A and B, 12 hours to A and 8 to B. The marginal product of the facility for A is 50 and for B is 40. The marginal revenue of A is $20 and the marginal revenue of B is $30.
-If the firm allocates 11 hours to A and 9 to B, revenue will ______ by $______.

Question 41

A firm sells in two separate markets, A and B. The demand functions in the two markets are
Q_A = 4,000 - 50P_A and Q_B = 3,200 - 160P_B.
-The inverse demands in the two markets are:
P_A = ____________________________
P_B = ____________________________

Question 42

A firm sells in two separate markets, A and B. The demand functions in the two markets are
Q_A = 4,000 - 50P_A and Q_B = 3,200 - 160P_B.
-The marginal revenue functions in the two markets are:
MR_A = ____________________________
MR_B = ____________________________

Question 43

A firm sells in two separate markets, A and B. The demand functions in the two markets are
Q_A = 4,000 - 50P_A and Q_B = 3,200 - 160P_B.
-The total marginal revenue function is
MR_T = ____________________________

Question 44

A firm sells in two separate markets, A and B. The demand functions in the two markets are
Q_A = 4,000 - 50P_A and Q_B = 3,200 - 160P_B.
-If the firm wants to produce 3,200 units of output, in order to maximize revenue from this output it should produce ______ units in plant A and ______ units in B.

Question 45

The firm in the previous question wishes to practice price discrimination. The firm's marginal cost function is

-To maximize profit the firm would produce a total of ______ units of output. ______ units would be sold in market A and ______ units in B.

Question 46

The firm in the previous question wishes to practice price discrimination. The firm's marginal cost function is


-The firm would charge a price of $______ in market A and a price of $______ in B.

Question 47

The firm in the previous question wishes to practice price discrimination. The firm's marginal cost function is


-In equilibrium the demand elasticity is ______ in A and ______ in B. (Hint: use the E = P/(P-a) formula) This relation would be expected because ______ is greater than ______.

Question 48

A firm produces two goods that are substitutes in consumption, X and Y. The demands for the two goods are
Q_X = 100,000 - 4,000P_X + 2,000P_Y
Q_Y = 120,000 -2,000P_Y + 1,000P_X
The two marginal cost functions are
MC_X = 7.667 + 0.0005Q_X
MC_Y = 15 + 0.0005Q_Y

-The inverse demand for good X is ______ and is ______ for good Y. (Solve simultaneously for P_X and P_Y as functions of Q_X and Q_Y.)

Question 49

A firm produces two goods that are substitutes in consumption, X and Y. The demands for the two goods are
Q_X = 100,000 - 4,000P_X + 2,000P_Y
Q_Y = 120,000 -2,000P_Y + 1,000P_X
The two marginal cost functions are
MC_X = 7.667 + 0.0005Q_X
MC_Y = 15 + 0.0005Q_Y

-The marginal revenue functions for X and Y are respectively ______ and ______.

Question 50

A firm produces two goods that are substitutes in consumption, X and Y. The demands for the two goods are
Q_X = 100,000 - 4,000P_X + 2,000P_Y
Q_Y = 120,000 -2,000P_Y + 1,000P_X
The two marginal cost functions are
MC_X = 7.667 + 0.0005Q_X
MC_Y = 15 + 0.0005Q_Y

-The profit-maximizing quantity of X is ______ and is ______ for Y.

Question 51

A firm produces two goods that are substitutes in consumption, X and Y. The demands for the two goods are
Q_X = 100,000 - 4,000P_X + 2,000P_Y
Q_Y = 120,000 -2,000P_Y + 1,000P_X
The two marginal cost functions are
MC_X = 7.667 + 0.0005Q_X
MC_Y = 15 + 0.0005Q_Y

-The profit-maximizing prices are P_X = $______ and P_Y = $______.

Question 52

A firm produces two goods, X and Y, that are complements in production. One unit of the joint product, Q_j, produces one unit of Q_X and one unit of Q_Y (similar to the Chem Tech problem in the text). The demands for X and Y are Q_X = 150,000 -500P_X and Q_Y = 160,000 - 400P_Y. The joint marginal cost function is MC_j = 40 + 0.002Q_j.

-The inverse demands for X and Y are, respectively, ______ and ______.

Question 53

A firm produces two goods, X and Y, that are complements in production. One unit of the joint product, Q_j, produces one unit of Q_X and one unit of Q_Y (similar to the Chem Tech problem in the text). The demands for X and Y are Q_X = 150,000 -500P_X and Q_Y = 160,000 - 400P_Y. The joint marginal cost function is MC_j = 40 + 0.002Q_j.

-The marginal revenue functions for X and Y are, respectively, ______ and ______.

Question 54

A firm produces two goods, X and Y, that are complements in production. One unit of the joint product, Q_j, produces one unit of Q_X and one unit of Q_Y (similar to the Chem Tech problem in the text). The demands for X and Y are Q_X = 150,000 -500P_X and Q_Y = 160,000 - 400P_Y. The joint marginal cost function is MC_j = 40 + 0.002Q_j.

-What is the joint marginal revenue function?

Question 55

A firm produces two goods, X and Y, that are complements in production. One unit of the joint product, Q_j, produces one unit of Q_X and one unit of Q_Y (similar to the Chem Tech problem in the text). The demands for X and Y are Q_X = 150,000 -500P_X and Q_Y = 160,000 - 400P_Y. The joint marginal cost function is MC_j = 40 + 0.002Q_j.

-The profit-maximizing level of the joint product is ______. The profit maximizing prices are P_X = $______ and P_Y = $______.

Question 56

A firm produces two goods, X and Y, that are complements in production. One unit of the joint product, Q_j, produces one unit of Q_X and one unit of Q_Y (similar to the Chem Tech problem in the text). The demands for X and Y are Q_X = 150,000 -500P_X and Q_Y = 160,000 - 400P_Y. The joint marginal cost function is MC_j = 40 + 0.002Q_j.

-The quantities of X and Y at which their marginal revenue becomes negative are Q_X = ______ and Q_Y = ______.
Now suppose the joint marginal cost becomes

Question 57

A firm produces two goods, X and Y, that are complements in production. One unit of the joint product, Q_j, produces one unit of Q_X and one unit of Q_Y (similar to the Chem Tech problem in the text). The demands for X and Y are Q_X = 150,000 -500P_X and Q_Y = 160,000 - 400P_Y. The joint marginal cost function is MC_j = 40 + 0.002Q_j.

-Now the firm will produce a total output of ______. It will sell ______ units of X at a price of ______. It will sell ______ units of Y at a price of ______.

Question 58

In the analysis in the text of products that are substitutes in production we used the example of Surefire Products, a firm that produced two goods, X and Y, with the same production facility. The inverse demand and marginal revenue for X were
P_X = 120 - 2Q_X and MR_X = 120 - 4Q_X
and for Y were
P_Y = 60 - 1.5Q_Y and MR_Y = 60 -3Q_Y
One hour on the production facility could produce 2 units of X or 4 units of Y
Q_X = 2H_X and Q_Y = 4H_Y
Thus the marginal revenue product functions were
MRP_X = 240 - 16H_X and MRP_Y = 240 - 48H_X
so the horizontal summation yielded the total marginal revenue product function
MRP_T = 240 -12H_T
Now let the new marginal cost function be
MC = 58 + 2H_T

-What is the profit-maximizing number of hours to use the production facility? The firm should use ______ hours to produce X and ______ hours to produce Y.

Question 59

In the analysis in the text of products that are substitutes in production we used the example of Surefire Products, a firm that produced two goods, X and Y, with the same production facility. The inverse demand and marginal revenue for X were
P_X = 120 - 2Q_X and MR_X = 120 - 4Q_X
and for Y were
P_Y = 60 - 1.5Q_Y and MR_Y = 60 -3Q_Y
One hour on the production facility could produce 2 units of X or 4 units of Y
Q_X = 2H_X and Q_Y = 4H_Y
Thus the marginal revenue product functions were
MRP_X = 240 - 16H_X and MRP_Y = 240 - 48H_X
so the horizontal summation yielded the total marginal revenue product function
MRP_T = 240 -12H_T
Now let the new marginal cost function be
MC = 58 + 2H_T

-The firms should sell ______units of X at a price of $______ and ______ units of Y at a price of $______.

Question 60

Dr. Jones, a respected chiropractic physician, believes his skills at aligning spines should earn 50 percent as much as the costs of providing alignment services, so he chooses a markup of 50 percent on his average total costs. A marketing research firm has estimated the demand for his work as a linear function of the price he charges:
Q = 300 - 1/3 P
where Q is the number of back alignments performed each month, and P is the average price of a back alignment. His accountant tells him that his average variable costs are constant and equal to $204 per alignment. Total fixed cost is $9,900 per month.
-Derive the inverse demand for Dr. Jones's spine alignments.
P = ____________________________

Question 61

Dr. Jones, a respected chiropractic physician, believes his skills at aligning spines should earn 50 percent as much as the costs of providing alignment services, so he chooses a markup of 50 percent on his average total costs. A marketing research firm has estimated the demand for his work as a linear function of the price he charges:
Q = 300 - 1/3 P
where Q is the number of back alignments performed each month, and P is the average price of a back alignment. His accountant tells him that his average variable costs are constant and equal to $204 per alignment. Total fixed cost is $9,900 per month.
-Derive the marginal revenue for Dr. Jones's spine alignments.
MR = ____________________________
Currently Dr. Jones has a full schedule of patients and enjoys a waiting list each month of 50 patients who cannot get in to see him. He plans his work schedule to see 150 patients per month. Currently, he charges a price of $300 per patient.

Question 62

Dr. Jones, a respected chiropractic physician, believes his skills at aligning spines should earn 50 percent as much as the costs of providing alignment services, so he chooses a markup of 50 percent on his average total costs. A marketing research firm has estimated the demand for his work as a linear function of the price he charges:
Q = 300 - 1/3 P
where Q is the number of back alignments performed each month, and P is the average price of a back alignment. His accountant tells him that his average variable costs are constant and equal to $204 per alignment. Total fixed cost is $9,900 per month.

-Explain why Dr. Jones currently experiences a waiting list of 50 patients each month.

Question 63

Dr. Jones, a respected chiropractic physician, believes his skills at aligning spines should earn 50 percent as much as the costs of providing alignment services, so he chooses a markup of 50 percent on his average total costs. A marketing research firm has estimated the demand for his work as a linear function of the price he charges:
Q = 300 - 1/3 P
where Q is the number of back alignments performed each month, and P is the average price of a back alignment. His accountant tells him that his average variable costs are constant and equal to $204 per alignment. Total fixed cost is $9,900 per month.
-Currently, Dr. Jones's costs to service 150 patients per month are:
AVC = $________, AFC = $________, and ATC = $________
The doctor's monthly profit is $______________.

Question 64

Dr. Jones, a respected chiropractic physician, believes his skills at aligning spines should earn 50 percent as much as the costs of providing alignment services, so he chooses a markup of 50 percent on his average total costs. A marketing research firm has estimated the demand for his work as a linear function of the price he charges:
Q = 300 - 1/3 P
where Q is the number of back alignments performed each month, and P is the average price of a back alignment. His accountant tells him that his average variable costs are constant and equal to $204 per alignment. Total fixed cost is $9,900 per month.
-As mentioned above, Dr. Jones decides to begin setting his price using a 50 percent markup on his current average total costs (use ATC from part d):
m = ________ and P = $________

Question 65

Dr. Jones, a respected chiropractic physician, believes his skills at aligning spines should earn 50 percent as much as the costs of providing alignment services, so he chooses a markup of 50 percent on his average total costs. A marketing research firm has estimated the demand for his work as a linear function of the price he charges:
Q = 300 - 1/3 P
where Q is the number of back alignments performed each month, and P is the average price of a back alignment. His accountant tells him that his average variable costs are constant and equal to $204 per alignment. Total fixed cost is $9,900 per month.
-After implementing the cost-plus price computed in part e above, the doctor plans to treat all patients who come for treatment (i.e., he no longer limits his patient load to just 150 patients per month). His profit when he implements the cost-plus price in part e will be $_____________.

Question 66

Dr. Jones, a respected chiropractic physician, believes his skills at aligning spines should earn 50 percent as much as the costs of providing alignment services, so he chooses a markup of 50 percent on his average total costs. A marketing research firm has estimated the demand for his work as a linear function of the price he charges:
Q = 300 - 1/3 P
where Q is the number of back alignments performed each month, and P is the average price of a back alignment. His accountant tells him that his average variable costs are constant and equal to $204 per alignment. Total fixed cost is $9,900 per month.
-Dr. Jones, while happy that cost-plus pricing has improved his profits, wonders if he actually maximizing his profit. To find out, he hires a consultant who applies the MR = MC rule to find the profit-maximizing price, number of patients, and profit. The consultant reports the following values:
P* = $________, Q* = ________, and maximum profit = $____________

Question 67

Dr. Jones, a respected chiropractic physician, believes his skills at aligning spines should earn 50 percent as much as the costs of providing alignment services, so he chooses a markup of 50 percent on his average total costs. A marketing research firm has estimated the demand for his work as a linear function of the price he charges:
Q = 300 - 1/3 P
where Q is the number of back alignments performed each month, and P is the average price of a back alignment. His accountant tells him that his average variable costs are constant and equal to $204 per alignment. Total fixed cost is $9,900 per month.
-Explain why cost-plus pricing in part e failed to maximize Dr. Jones's profit.