# Demand Curve and Total Cost Curve

Please study these, you will see them again.

1. Question 1 - 4 using the information presented in question 1.

A monopoly faces the following demand curve and total cost curve:

Q = 2400 -100P

TC = 150,000 + 6Q.

Find the profit maximizing level of price

a. P = $15

b. P = $16

c. P = $17

d. P = 19

2. Find the profit maximizing output:

a. Q = 100 units

b. Q = 900 units

c. Q = 1000 units

d. Q = 90 units

e. cannot be derived

3. The total cost (TC) of the monopolist corresponding to the profit maximizing level of output is:

a. $150,000

b. $206,000

c. $155,400

d. impossible to determine with the given information

e. $200,000

4. The average total cost (ATC)of the firm corresponding to the profit maximizing level of output is:

a. $166.66

b. $132.32

c. $160

d. $172.66

5 . In the long run, new firms will keep entering a monopolistically competitive industry:

a. provided economies of scale are being realized.

b. even though losses are incurred in the short run.

c. until minimum average total cost is achieved.

d. until economic profits are zero.

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#### Solution Preview

1. Questtion 1 - 4 using the information presented in question 1.

A monopoly faces the following demand curve and total cost curve:

Q = 2400 -100P

TC = 150,000 + 6Q. Find the profit maximizing level of price

a. P = $15

b. P = $16

c. P = $17

d. P = 19

The demand curve can be written into

P=24 - 0.01 Q

Then total revenue is

TR = P*Q = (24 - 0.01 Q)*Q = 24Q - 0.01 Q^2

So marginal revenue is

MR = dTR / dQ = 24 - 0.02Q

From TC = 150,000 + 6Q we calculate ...

#### Solution Summary

In the long run, new firms will keep entering a monopolistically competitive industry:

a. provided economies of scale are being realized.

b. even though losses are incurred in the short run.

c. until minimum average total cost is achieved.

d. until economic profits are zero.

Economic Optimization

CHAPTER 3-DEMAND AND SUPPLY

Note: You must show all your calculations

MULTIPLE CHOICE

1. Surplus is a condition of:

a. excess supply.

b. a deficiency in supply.

c. market equilibrium.

d. excess demand.

2. A demand curve expresses the relation between the quantity demanded and:

a. income.

b. advertising.

c. price.

d. all of these.

3. Demand is the total quantity of goods or services that customers:

a. are willing to purchase.

b. are able to purchase.

c. are willing and able to purchase.

d. need.

4. Demand for consumption goods and services is:

a. derived demand.

b. direct demand.

c. product demand.

d. utility.

5. The demand function for a product states the relation between the aggregate quantity demanded and:

a. all factors that influence demand.

b. the aggregate quantity supplied.

c. consumer utility.

d. the market price, holding all the other factors that influence demand constant.

6. The supply curve expresses the relation between the aggregate quantity supplied and:

a. price, holding constant the effects of all other variables.

b. aggregate quantity demanded, holding constant the effects of all other variables.

c. profit, holding constant the effects of all other variables.

d. each factor that affects supply.

7. The equilibrium market price of a service is the:

a. price that buyers are willing and able to pay.

b. price where shortages exceed surpluses.

c. price that maximizes profit for sellers.

d. price where the quantity demanded equals the quantity supplied.

8. The equilibrium market price and quantity of beef would increase if:

a. consumers increasingly view beef as unhealthy.

b. the price of cattle feed decreased.

c. consumer income increased.

d. herd sizes fell following a severe drought.

PROBLEM

1. Demand and Supply Curves. The following relations describe demand and supply conditions in the milk industry:

QD = 315,000  250,000P (Demand)

QS = 165,000 + 550,000P (Supply)

where Q is quantity measured in millions of gallons and P is price in dollars.

A. Complete the following table:

Price (1) Quantity Supplied (2) Quantity Demanded (3) Surplus (+) or Shortage ()

(4) = (2)  (3)

$0.90

0.80

0.70

0.60

0.50

2. Demand and Supply Curves. The following relations describe demand and supply conditions in the oil industry:

QD = 525,000  7,500P (Demand)

QS = 150,000 + 15,000P (Supply)

where Q is quantity measured in millions of barrels and P is price in dollars.

A. Complete the following table:

Price (1) Quantity Supplied (2) Quantity Demanded (3) Surplus (+) or Shortage ()

(4) = (2)  (3)

$35

30

25

20

15

3. Comparative Statics. Coupon Promotions, Inc., is a coupon book publisher with markets in several southwestern states. CPI coupon books are sold directly to the public, sold through religious and other charitable organizations, or given away as promotional items. Operating experience during the past year suggests the following demand function for its coupon books:

Q = 10,000  5,000P + 0.02Pop + 0.4I + 0.6A

where Q is quantity, P is price ($), Pop is population, I is disposable income per capita ($), and A is advertising expenditures ($).

A. Determine the demand curve faced by CPI in a typical market where P = $5, Pop = 1,000,000 persons, I = $35,000 and A = $10,000. Show the demand curve with quantity expressed as a function of price, and price expressed as a function of quantity.

B. Calculate the quantity demanded at prices of $5, $2.50, and $0.

C. Calculate the prices necessary to sell 10,000, 25,000, and 50,000 units.

4. . Quantity Demanded. The Sharper Edge, Inc. is a leading retailer of Yingsu Knives, a set of kitchen cutlery, which it markets on a nationwide basis. SEI knife sets are either sold directly to the public through national television marketing programs, or given away as promotional items. Operating experience during the past year suggests the following demand function for its knife sets:

Q = 4,000  4,000P + 10,000N + 0.25I + 0.4A

Where Q is quantity, P is the price ($), N is the average Nielson rating of television programs during which SEI advertises Yingsu Knives, I is average disposable income per household ($), and A is advertising expenditures ($).

A. Determine the demand curve faced by SEI in a typical market where P = $35, N = 18.5, I = $44,000, and A = $500,000. Show the demand curve with quantity expressed as a function of price, and price expressed as a function of quantity.

B. Calculate the quantity demanded at prices of $40, $35, and $30.

C. Calculate the prices necessary to sell 264,000, 292,000, and 320,000 sets of knives.

5 . Demand Curve Analysis. The Badger Bus Company is a regional bus line providing service between Milwaukee, Wisconsin and Chicago, Illinois. An analysis of the monthly demand for service has revealed the following demand relation:

Q = 1,750  40P  15PC + 30BAI  1,700S

Where Q is quantity measured by the number of passengers per month, P is the price ($), PC is a price index for connecting bus routes (1992 = 100.), BAI is a business activity index (1992 = 100) and S, a binary or dummy variable, equals 1 in summer months, zero otherwise.

A. Determine the demand curve facing the bus service during the winter month of February if P = $40, PC = 120, BAI = 175, and S = 0.

B. Calculate the quantity demanded and total revenues during the summer month of August if all price-related variables are as specified above.

6. Demand Curve Analysis. Papa's Pizza, Ltd., provides delivery and carryout service to the city of South Bend, Indiana. An analysis of the daily demand for pizzas has revealed the following demand relation:

Q = 1,400  100P  2PS + 0.01CSP + 750S

where Q is the quantity measured by the number of pizzas per day, P is the price ($), PS is a price index for soda pop (1992 = 100), CSP is the college student population and S, a binary or dummy variable, equals 1 on Friday, Saturday and Sunday, zero otherwise.

A. Determine the demand curve facing Papa's Pizza on Tuesdays if P = $10, PS = 125, and CSP = 35,000, and S = 0.

B. Calculate the quantity demanded and total revenues on Fridays if all price-related variables are as specified above.

7. Supply Curve Analysis. A review of industry-wide data for the domestic wine manufacturing industry suggests the following industry supply function:

Q = 7,000,000 + 400,000P  2,000,000PL  1,500,000P K + 1,000,000W

where Q is cases supplied per year, P is the wholesale price per case ($), PL is the average price paid for unskilled labor ($), PK is the average price of capital (in percent), and W is weather measured by the average seasonal rainfall in growing areas (in inches).

A. Determine the industry supply curve for a recent year when P = $80, PL = $10, PK = 12%, and W = 25 inches of rainfall. Show the industry supply curve with quantity expressed as a function of price and price expressed as a function of quantity.

B. Calculate the quantity supplied by the industry at prices of $50, $75 and $100 per case.

C. Calculate the prices necessary to generate a supply of 10 million, 25 million, and 50 million cases.

8. Supply Curve Analysis. Computers.com is a leading Internet retailer of high-performance desktop computers. Based on an analysis of monthly cost and output data, the company has estimated the following relation between its marginal cost of production and monthly output:

MC =  TC/  Q = $100 + $0.005Q

A. Calculate the marginal cost of production at 100,000, 200,000, and 300,000 units of output.

B. Express output as a function of marginal cost. Calculate the level of output at which MC = $1,000, $1,500 and $2,000.

C. Calculate the profit-maximizing level of output if prices are stable in the industry at $1,500 per unit and, therefore, P = MR = $1,500.

D. Again assuming prices are stable in the industry, derive the firm's supply curve. Express price as a function of quantity and quantity as a function of price.

9. Industry Supply. Columbia Pharmaceuticals, Inc., and Princeton Medical, Ltd., supply a generic drug equivalent of an antibiotic used to treat postoperative infections. Proprietary cost and output information for each company reveal the following relations between marginal cost and output:

MCC = TCC/ Q = $5 + $0.001QC (Columbia)

MCP = TCP/ Q = $6 + $0.00025QP (Princeton)

The wholesale market for generic drugs is vigorously price-competitive, and neither firm is able to charge a premium for its products. Thus, P = MR in this market.

A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm's supply curve.)

B. Calculate the quantity supplied by each firm at prices of $5, $7.50, and $10. What is the minimum price necessary for each individual firm to supply output?

C. Determine the industry supply curve when P < $6.

D. Determine the industry supply curve when P > $6. To check your answer, calculate quantity at an industry price of $10 and compare your answer with part B.

10. Market Equilibrium. Florida Orange Juice is a product of Florida's Orange Growers' Association. Demand and supply of the product are both highly sensitive to changes in the weather. During hot summer months, demand for orange juice and other beverages grows rapidly. On the other hand, hot dry weather has an adverse effect on supply by reducing the size of the orange crop.

Demand and supply functions for Florida orange juice are as follows:

QD = 4,500,000  1,200,000P + 2,000,000PS

+ 1,500Y + 100,000T (Demand)

QS = 8,000,000 + 2,400,000P  500,000PL

 80,000PK  120,000T (Supply)

where P is the average price of Florida ($ per case), PS is the average retail price of canned soda ($ per case), Y is income (GNP in $billions), T is the average daily high temperature (degrees), PL is the average price of unskilled labor ($ per hour), and PK is the average cost of capital (in percent).

A. When quantity is expressed as a function of price, what are the Florida demand and supply curves if P = $11, PS = $5, Y = $12,000 billion, T = 75 degrees, PL = $6, and PK = 12.5%.

B. Calculate the surplus or shortage of Florida orange juice when P = $5, $10, and $15.

C. Calculate the market equilibrium price-output combination.

MULTIPLE CHOICE

1. An equation is:

a. an analytical expression of functional relationships.

b. a visual representation of data.

c. a table of electronically stored data.

d. a list of economic data.

e. Demand and Supply

2. The breakeven level of output occurs where:

a. marginal cost equals average cost.

b. marginal profit equals zero.

c. total profit equals zero.

d. marginal cost equals marginal revenue.

3. Incremental profit is:

a. the change in profit that results from a unitary change in output.

b. total revenue minus total cost.

c. the change in profit caused by a given managerial decision.

d. the change in profits earned by the firm over a brief period of time.

4. Which of the following short run strategies should a manager select to obtain the highest degree of sales penetration?

a. maximize revenues.

b. minimize average costs.

c. minimize total costs.

d. maximize profits.

5. Total revenue is maximized at the point where marginal:

a. revenue equals zero.

b. cost equals zero.

c. revenue equals marginal cost.

d. profit equals zero.

6. Marginal profit equals:

a. the change in total profit following a one-unit change in output.

b. the change in total profit following a managerial decision.

c. average revenue minus average cost.

d. total revenue minus total cost.

7. Profit per unit is rising when marginal profit is:

a. greater than average profit per unit.

b. less than average profit per unit.

c. equal to average profit per unit.

d. positive.

8. If average profit increases with output marginal profit must be:

a. decreasing.

b. greater than average profit.

c. less than average profit.

d. increasing.

9. At the profit-maximizing level of output:

a. marginal profit equals zero.

b. marginal profit is less than average profit.

c. marginal profit exceeds average profit.

d. marginal cost equals average cost

N

10. If profit is to rise as output expands, then marginal profit must be:

a. falling.

b. constant.

c. positive.

d. rising.

PROBLEM

1. Marginal Analysis. Consider the price (P) and output (Q) data in the following table.

Q P TR MR AR

0 $35

1 30

2 25

3 20

4 15

5 10

6 5

7 0

A. Calculate the related total revenue (TR), marginal revenue (MR), and average revenue (AR) figures.

B. At what output level is revenue maximized?

2. Marginal Analysis. Evaluate the price (P) and the output (Q) data in the following table.

Q P TR MR AR

0 $80

1 70

2 60

3 50

4 40

5 30

6 20

7 10

8 0

A. Compute the related total revenue (TR), marginal revenue (MR), and average revenue (AR) figures:

B. At what output level is revenue maximized?

3. Profit Maximization. Fill in the missing data for price (P), total revenue (TR), marginal revenue (MR), total cost (TC), marginal cost (MC), profit (), and marginal profit (M) in the following table.

Q P TR = PQ MR = TR/ Q TC MC = TC/ Q  =

TR  TC M = / Q

0 $200 $ 0 -- $ 0 -- $ 0 --

1 180 180 $180 100 $100 80 $ 80

2 320 175 65

3 420 100 240 65 180

4 120 60 55 185 5

5 100 500 350 55 150 35

6 80 480 20 400 70

7 60 60 450 50 30 110

8 320 100 55 185 155

9 20 180 570 65 205

10 10 80 750 180 650 260

A. At what output (Q) level is profit maximized?

B. At what output (Q) level is revenue maximized?

4. Profit Maximization. Fill in the missing data for price (P), total revenue (TR), marginal revenue (MR), total cost (TC), marginal cost (MC), profit (), and marginal profit (M) in the following table.

Q P TR MR TC MC  M

0 $230 $ 0 $ -- $ 0 $ -- $ 0 $ --

1 210 10 200

2 380 20 150

3 170 130 30 450

4 600 100 40 50

5 130 60 490 10

6 660 160 430

7 630 30 310 110

8 70 70 400 90 160 160

A. At what output (Q) level is profit maximized?

B. At what output (Q) level is revenue maximized?

5. Marginal Analysis: Tables. Bree Van De Camp is a regional sales representative for Snappy Tools, Inc., and sells hand tools to auto mechanics in New England states. Van De Camp's goal is to maximize total monthly commission income, which is figured at 6.25% of gross sales. In reviewing experience over the past year, Van De Camp found the following relations between days spent in each state and weekly sales generated.

Days Maine Sales New Hampshire Sales Vermont Sales

0 $ 4,000 $ 3,000 $ 1,900

1 10,000 7,000 5,200

2 15,000 10,600 7,400

3 19,000 13,800 8,600

4 22,000 16,600 9,200

5 24,000 19,000 9,600

6 25,000 21,000 9,800

A. Construct a table showing Van De Camp's marginal sales per day in each state.

B. If Van De Camp is limited to 6 selling days per week, how should they be spent?

C. Calculate Van De Camp's maximum weekly commission income.

6. Profit Maximization: Equations. Woodland Instruments, Inc. operates in the highly competitive electronics industry. Prices for its R2-D2 control switches are stable at $100 each. This means that P = MR = $100 in this market. Engineering estimates indicate that relevant total and marginal cost relations for the R2-D2 model are:

TC = $500,000 + $25Q + $0.0025Q2

MC = TC/ Q = $25 + $0.005Q

A. Calculate the output level that will maximize R2-D2 profit.

B. Calculate this maximum profit.

7. Profit Maximization: Equations. Austin Heating & Air Conditioning, Inc., offers heating and air conditioning system inspections in the Austin, Texas, market. Prices are stable at $50 per unit. This means that P = MR = $50 in this market. Total cost (TC) and marginal cost (MC) relations are:

TC = $1,000,000 + $10Q + $0.00025Q2

MC = TC/ Q = $10 + $0.0005Q

A. Calculate the output level that will maximize profit.

B. Calculate this maximum profit.

8 Optimal Profit. Hardwood Cutters offers seasoned, split fireplace logs to consumers in Toledo, Ohio. The company is the low-cost provider of firewood in this market with fixed costs of $10,000 per year, plus variable costs of $25 for each cord of firewood. Annual demand and marginal revenue relations for the company are:

P = $225  $0.125Q

MR = TR/ Q = $225  $0.25Q

A. Calculate the profit-maximizing activity level.

B. Calculate the company's optimal profit and return-on-sales levels.

9. Average Cost Minimization. Commercial Recording, Inc., is a manufacturer and distributor of reel-to-reel recording decks for commercial recording studios. Revenue and cost relations are:

TR = $3,000Q  $0.5Q2

MR = TR/ Q = $3,000  $1Q

TC = $100,000 + $1,500Q + $0.1Q2

MC = TC/ Q = $1,500 + $0.2Q

A. Calculate output, marginal cost, average cost, price, and profit at the average cost-minimizing activity level.

B. Calculate these values at the profit-maximizing activity level.

C. Compare and discuss your answers to parts A and B.

10. Revenue Maximization. Restaurant Marketing Services, Inc., offers affinity card marketing and monitoring systems to fine dining establishments nationwide. Fixed costs are $600,000 per year. Sponsoring restaurants are paid $60 for each card sold, and card printing and distribution costs are $3 per card. This means that RMS's marginal costs are $63 per card. Based on recent sales experience, the estimated demand curve and marginal revenue relations for are:

P = $130  $0.000125Q

MR = TR/ Q = $130  $0.00025Q

A. Calculate output, price, total revenue, and total profit at the revenue-maximizing activity level.

B. Calculate output, price, total revenue, and total profit at the profit-maximizing activity level.

C. Compare and discuss your answers to parts A and B.