SOLUTIONS TO

END-OF-CHAPTER PROBLEMS

FROM

BUSINESS ECONOMICS: THEORY AND PTACTICE 5TH EDITION, 2008

PART I: MICROECONOMICS

By

Kenneth Matziorinis, Ph.D.

Canbek Publications

1.1 a) A good is a tangible product, i.e. you can touch it, lift it, store it and transport it. A service is an intangible product. You can do none of the above

A final product is a finished product that is ready to be put into

the use for which it was intended. All products purchased by consumers for personal use are final as are all the capitalized machinery and equipment and the construction of buildings, whether they are for residential, industrial, commercial or institutional use.

An intermediate product is a semi-processed or semi-finished

product that is produced by one producer and sold to another producer to be used as an input in making a third product.

b) Type of Resources and Forms of Remuneration

Labour

Wages & Salaries

Human Resources

Entrepreneurship

Profits (dividends)

Land (indestructible)

Rent

Raw Material (non-renewable)

Royalties

Natural Resources

Raw Materials (renewable)

Royalties

Financial Capital (money)

Interest

Real Capital (machinery & equipment; buildings & structures)

Royalties and Profits

Artificial or Man-made Resources

Human Capital (intellectual property: copyrights, patents & trademarks)

Royalties and Profits

c) Production is the transformation of resources into products with the help of technology. Consumption is the transformation of final products into consumer wellbeing (consumer satisfaction, or need satisfaction or utility) with the help of technology (know how or �savoir faire� or �savoir vivre� .

d) Saving is the income that we choose not to spend or consume.

Investment is the portion of our production that is not used for current consumption but to help us undertake more and better future production, therefore helps increase future consumption.

e) Physiological needs are the needs of our body, what our body

needs to survive individually or collectively, such as air, water, food, clothing, shelter and sexual reproduction. Physiological needs are part of our DNA and are transmitted genetically from one generation to the next. Psychological needs are the needs of our mind, our psyche and emotions. To live well we don�t only need to survive physically, but emotionally as well. They are the need for security, acceptance, affection, love, stimulation, joy, respect, control, achievement, justice and self-actualization. Psychological needs are learned needs, i.e. learned through exposure to our environment, or through conditioning. When we experience something good we want to experience it again, and once we begin to rely on good things we strive to maintain them.

f) Hierarchy of needs is the term that Abraham Maslow used to

describe the relationship between physiological and psychological needs as well as the inter-relationships among the psychological needs themselves. If the individual or a society are having difficulty assuring their physiological needs such as water or food, the mind is fixated on the satisfaction of the need that is most threatening to its survival and suppresses all other needs. �A hungry bear cannot dance�.

g) Productivity is economic efficiency, i.e. the efficiency of the

production process, which is the ratio of output divided by input. The more goods we produce with the same resources, the more goods are available to share among those that produced them and the community at large. Productivity is the result of working smarter, not harder. Increasing our productivity is a positive-sum-game, i.e. a win-win activity, because all stakeholders in society benefit from the rise in productivity. Workers get to be paid more, shareholders earn more, consumers pay less and/or get better products and the government gets more tax revenue to do its work.

h) Personal income is our income from all sources (earned and un-

earned such as transfer payments from government). Personal

disposable income is our personal income that is left after the payment of income (including payroll) taxes, therefore what is left and available to us to spend or to save.

1.2 a) Economic activity stems from our physiological and psychological

needs. We need to consume a range of goods and services in order to satisfy our needs, but to consumer we first need to produce the goods and services that we consume. There can be no consumption without production. Once you get started in the business of consuming and producing, then you need to carry out all other essential support activities such as exchange, trade, saving, investing, financing and government activities. If you examine all the type of industries in the economy you will realize that each of them corresponds to one or a combination of needs.

b) Economics can be defined as the study of how human societies go about producing, consuming, trading, saving and investing, among others, for the satisfaction of human needs. Economics is a behavioural social science.

1.3 a)

Road Repairs

Y0 . Y

Y1 . . X U City Xo X1 Cleanup The production possibilities boundary (PPB) shows the maximum amount of two products that can be produced by a society when making full use of all the available resources and technology. In the above example, the PPB shows the various combinations of two municipal services that can be produced by a city government based on the city�s resources. It can pave and repair roads, do city clean up or various combinations of the two while still making full use of the city�s resources.

b) The opportunity cost of moving from X to Y is: X0 � X1 ; from Y to X: Y1 � Y0; from U to Y: no opportunity cost; from X to U: X0 � X1. c) i)

ii)

iii)

iv)

v)

•

vi)

1.4 a) The opportunity cost is his hourly fee, i.e. $120.00 per hour

b) The opportunity cost is his hourly fee, i.e. $120.00 per hour c) He can save 20 hours x $10 = $200 for cleaning and 20 hours x $20

= $400 for painting, in total he can save $600 d) He benefits by not having to pay $600 but he loses by losing 40 hours

of billable time, i.e. 40 hours x $120 = $4,800 e) Hire someone else to do the painting and he stick to his work as a

lawyer. 1.5 See charts in textbook 1.6 See problem 2.7 below

2.1 a) The determinants of the demand for a product are: Qd = f ( P; T&P, I, Ps, Pc, N, E, O ) P = The market price of the product (dollars per unit);

T&P = The tastes and preferences of the individual consumers;

I = The buying power of consumers as measured by their personal disposable income Ps = The price of other products which serve as substitutes to the product in question, i.e. competing goods;

Pc = The price of other products which serve as complements to the product in question, i.e. they are consumed together;

N = The number of individual buyers in the market (individuals, families, households or the population at large);

E = The expectations of the buyers with respect to the

future price (P) of the product, their future ability to buy (I), the future prices of substitutes and complements,

and more generally, the state of consumer confidence;

O = Other factors; these can range from the weather, seasonal factors, consumption taxes such as excise and

sales taxes, advertising expenditures and others.

b) What is the law of demand?

The law of demand is the inversely proportional relationship between the price of the product (P) and the quantity demanded (Qd) of the product, all other variables remaining constant.

c) Which variables cause a �change in demand” ( a shift in the demand

curve) as opposed to a �change in the quantity demanded” ( a movement along the demand curve) ?

When any variable such as T&P, I, Ps, Pc, N, E, O change, there is a change in demand, i.e. the demand curve shifts to the right or to the left. The only time there is a change in the quantity demanded is when the price (P) changes. When the price changes there is an adjustment in the quantity demanded, i.e. a movement up or down along the same demand curve.

d) The determinants of the supply of a product are: Qs = f ( P; Tech.,Goals, Pr, Po, N, E, O)

P = The market (selling) price of the product (dollars per unit);

Tech. = Production Technology (Production Function); it refers to the

technical ability to turn inputs into outputs (output-input specificity) and the rate of utilization these inputs;

Goals = The goals of the producers as conditioned by the structure of

the industry which they occupy; these goals vary from short-term profit maximization to sales revenue maximization, market share protection, among others;

Pr = The prices paid by producers for resource inputs, e.g. wage

and salary rates; raw material and energy prices; land, building and machinery prices; interest rate and profit rates;

Po = The selling price of other products that can be produced

using the same technology and resource inputs e.g. growing corn vs wheat using the same land and farm implements;

N = The number of individual producers occupying the industry;

E = The expectations of the producers with respect to future prices of their product, resource prices or other factors

O = Other factors; these can range from the weather, seasonal

factors, taxes such as income and sales taxes, government subsidies, strikes and institutional constraints such as health and safety regulations, food and drug regulations, environmental protection laws, etc.;

e) What is the law of supply?

The law of supply is the directly proportional relationship between the price (P) of a product and the quantity supplied (Qs) of that product, all other variables remaining constant.

f) Which variables cause a �change in supply” ( a shift in the supply

curve) as opposed to a �change in the quantity supplied” ( a movement along the supply curve) ?

When any variable such as production technology, goals, Pr, Po, N, E, O change, there is a change in supply, i.e. the supply curve shifts to the right or to the left. The only time there is a change in the quantity supplied is when the price (P) changes. When the price changes there is an adjustment in the quantity supplied, i.e. a movement up or down along the same supply curve.

g) Examples of complements:

wine and cheese automobiles and gasoline computers and printers locks and keys house and mortgage loan

Examples of substitutes: wine or beer mashed potatoes or french fries buy or lease pants or skirt corn oil or olive oil

h) What is the significance of equilibrium price (Pe) and equilibrium quantity exchanged (Qe) ?

Equilibrium is the Latin word for balance, balance between two opposing forces Equilibrium price (Pe) is the price which equates the quantity demanded with the quantity supplied ( Qd = Qs ) and leaves neither a surplus nor a shortage of the product on the market. When the price is in equilibrium, there is no more pressure for the price to rise or fall, so it tends to stay at the same level

Equilibrium quantity (Qe) is the quantity which equates the demand price with the supply price ( Pd = Ps ) and leaves neither a surplus nor a shortage of the product on the market. When the quantity exchanged is in equilibrium, there is no more pressure for the quantity demanded or supplied to rise or fall, so it tends to stay at the same level.

i) What is the role of the price mechanism in a market economy?

When there is an imbalance between the demand and supply of a product it results in shortages or surpluses, which in turn place up-ward or down-ward pressure on the market price. The resulting change in the price of the product then communicates to the market participants that there is a shortage or abundance of the product on the market. Based on this information, market participants adjust their consumption and production decisions. For example, when the price is rising, the market is telling consumers that the product is scarce and that they should consume less of it while the same message tells the producers that they should supply more. The combined effect of reducing consumption and increasing production then results in the elimination of the shortage and the price stops rising. When the price is falling, the market is telling consumers that the product is plentiful and that they may consume more of it while the same message tells the producers that they should supply less. The combined effect of increasing consumption and decreasing production then results in the elimination of the surplus and the price stops falling. In other words the price mechanism, the constant upward or downward adjustment in prices through time plays the same role as traffic lights do in regulating car traffic in the city. When the light is green you go, when it is red you stop. In so doing the market helps in the allocation of resources and products in the economy. It helps determine a) which products are produced; b) in what quantity they are produced; c) how they are produced and d) for whom they are produced. Have you ever wondered how producers know what to produce and how much to produce? What is the glue that keeps markets together? What is the mechanism that coordinates the production and consumption decisions of millions of participants? The answer is the price mechanism of the market. Adam Smith, the father of Economics, in his famous book the Wealth of Nations used the phrase “the invisible hand” to describe it.

2.2

2.3

2.7 You are given the following equations for the demand and supply:

P = 10 - 0.1 Q P = 0.1 Q a) See diagram below b) The slope of the demand curve (∆P / ∆Q ) is : - 0.1

The slope of the supply curve (∆P / ∆Q ) is: + 0.1

c) The equilibrium price is P = $5 and the equilibrium quantity is Q = 50 units

d) To find the equilibrium price and quantity algebraically, solve for

Supply = Demand to find the equilibrium quantity: 0.1 Q = 10 - 0.1 Q 0.2 Q = 10 Q = 10 / 0.2 Q = 50 units Then, insert the answer to the demand equation to find the price : P = 10 - 0.1 (50) P = 10 - 5 P = $5 per unit

e) What happens if the demand changes to P = 12 - 0.1 Q?

Do the same as d) above but using the new demand equation: 0.1 Q = 12 - 0.1 Q 0.2 Q = 12 Q = 12 / 0.2 Q = 60 units Then, insert the answer to the demand equation to find the price : P = 12 - 0.1 (60) P = 12 - 6 P = $6 per unit The slope of the new demand curve remained the same at -0.1

h) Now, if the supply changes as well to P = 2 + 0.1 Q, do the same:

2 + 0.1 Q = 12 - 0.1 Q 0.2 Q = 12 - 2 0.2 Q = 10 Q = 10 / 0.2 Q = 50 units Then, insert the answer to the demand equation to find the price : P = 12 - 0.1 (50) P = 12 - 5 P = $7 per unit

P $12 D� S� $10 D S $7 $6 $5 $2 D D� 0 Q 50 60 100 120

2.8. You are presented with the following data concerning the demand

for and supply of petroleum (crude oil): Price Demand Supply ($/b) Millions of Barrels per Month

40 0 400 38 20 380 36 40 360 34 60 340 32 80 320 30 100 300

28 120 280 26 140 260 24 160 240 22 180 220 20 200 200 18 220 180 16 240 160 14 260 140 12 280 120 10 300 100 8 320 80 6 340 60 4 360 40 2 380 20 0 400 0 ____________________________________________

a) Project the values to see what will happen to the quantity demanded and supplied if the price rises. Find out at which price does the quantity demanded become zero and at which price the quantity supplied becomes zero. Since the quantity demanded falls by 20 every time the price changes, the Y-intercept occurs at P = 40. Thus this is the constant of the equation. To find the slope look for �rise over run� or ∆P/∆Q. You will see that every time the price changes by �2$ the quantity demanded rises by 20 mbp, thus the slope is �2/20 or �0.1. Thus the demand equation is: P = 40 - 0.1 Q

Similarly, the equation for supply is P = 0 + 0.1 Q b)

P S� : P = 4 + 0.1 Q 40 D: P = 40 � 0.1 Q S : P = 0.1 Q 30 22 20 10 4 D 0 180 200 400 Q/month

a) Το find the equilibrium price and quantity exchanged, solve for: supply = demand:

0.1 Q = 40 - 0.1 Q 0.2 Q = 40

Q = 40 / 0.2 Q = 200 mbpd

To find the price : P = 40 - 0.1 (200) P = 40 - 20 P = $20 per barrel

b) If the supply of petroleum is cut by 40 million barrels per month at each and every price, then the new equation becomes: P = 4 + 0.1 Q

To find the new equilibrium price and quantity exchanged solve again using the new supply equation. Thus

4 + 0.1 Q = 40 - 0.1 Q 0.2 Q = 36

Q = 36 / 0.2 Q = 180 mbpd

To find the new price : P = 40 - 0.1 (180) P = 40 - 18 P = $22 per barrel

3.1 a) Selling Price P

Quantity Sold Q

Total Sales Revenue TR

Change in Rev. ∆TR

Marginal Revenue MR

Price Elasticity Ep (arc)

10

0

0

9

20

180

+180 +9 19.00

8

40

320

+140 +7 5.67

7

60

420

+100 +5 3.00

6

80

480

+60 +3 1.86

5

100

500

+20 +1 0

1.22

4

120

480

-20 -1 0.82

3

140

420

-60 -3 0.54

2

160

320

-100 -5 0.33

1

180

180

-140 -7 0.18

0

200

0

-180 -9 0.05

3.1 b)

• Total Revenue (TR) is maximized when the Price (P) is $5 per unit

• The quantity sold (Q) is 100 units and • Total sales revenue (TR) is $500 • At that price MR = 0 and • The price elasticity of demand (Ep) = 1.00

Price (P)

D

D

0 20 40 60 80 100 120 140 160 180 200 Quantity

Sold (Q) TR ( $ ) MR TR ==MAX $ 500 $ 480

$420 TR

$320

$180

Q

Ep < 1.0

Ep > 1.0

Εp = 1.0

MR = 0

3.1 d) As the price falls from $10 per unit to $5:

• TR is rising • MR is falling, but positive and • Ep > 0, but diminishing

As the price falls from $5 per unit to $0:

• TR is falling • MR is rising but negative and • Ep < 0, and diminishing

To maximize Sales Revenue, the firm should find the price where:

• MR = 0 Or • Ep = 1.00

3.2 The price elasticity of demand for flat-screen plasma TVs is Ep = - 2.0

a) Ep = -2.00 means that the demand for the product is price elastic. That every 1% change in the price of the product results in a 2.0% change in the quantity demanded, but in the opposite direction

b) If the price increases by 10%, then the quantity demanded will fall by

20%, i.e. +10% x �2.00 = - 20%

If the price decreases by 10%, then the quantity demanded will rise by 20%, i.e. -10% x �2.00 = + 20%

c) To maximize dollar sales (TR) of the product the seller should reduce

the price 3.3 The income elasticity of demand for flat-screen plasma TVs is Ei = + 5.0

a) Ei = +5.0 means that the demand for the product is income elastic.

That every 1% change in household disposable income results in a 5.0% change in the quantity demanded of the product.

b) If the personal disposable income (PDI) increases by 5%, then the

quantity demanded will increase by 25%, i.e. +5% x +5.00 = + 25%

If the personal disposable income (PDI) decreases by 5%, then the quantity demanded will decrease by 25%, i.e. -5% x +5.00 = - 25%

c) Obviously, it is a superior good (income elastic)

3.4 The cross elasticity between the demand for flat screen plasma TVs and the

price of flat screen LCD HDTVs is Exy = + 1.2 while the cross elasticity between flat screen plasma TVs and surround sound home entertainment systems is Exy = + 1.5.

a) Since the cross elasticity between plasma TVs and LCD TVs is

positive ( Exy > 1 ) it implies that the two products are substitutes. A 10% drop in the price of LCD TVs results in a 12% drop in the demand for plasma TVs.

b) Since the cross elasticity between plasma TVs and surround sound

systems is also positive ( Exy > 1 ), it implies that the two products are substitutes. A 10% drop in the price of surround sound systems reduces the demand for plasma TVs by 15%

3.8 The market demand and supply equations for Trans-Atlantic passenger air

transportation are:

P = 1400 - 0.002 Q P = 200 + 0.001 Q

a) To find the equilibrium price (P) and quantity exchanged (Q), we have to set

the supply equation equal to the demand equation and solve:

200 + 0.0001Q = 1400 � 0.0002Q 0.0003Q = 1200 so, Q = 4,000,000 passengers P = 1400 � 0.0002 (4000000) = $600 per flight TR = $600 x 4000000 = $2,400,000,000

Diagram: P

S D [P = 1400 – 0.0002Q]

S, [P = 200 +0.0001Q]

200

400

600

800

1000

1200

1400

Q Millions 5 8

b) equat The s

1

A $40 p Adding

ion, whic

upply is

2 P = 140P = $62 TR = 62

The flig

The ne NTR: $

2

er pa

the $h be

: P =

40 +

0 � 06.67

6.67

ht fee

t reve

626.

3

3,86

sseng

40 flighcomes:

240 +

0.00010.000

.0002(

x 3899

to be

nues f

67 � 40

4

7,667

er fee is equiv

t security fee

0.0001Q, and

Q = 1400 � 03Q = 1160 Q = 3, 866,6

3,866,667)

997 = $2,423

collected by I

or the air carri

.00 = $586.67

6

alent t

to the

solve

.0002Q

67

,124,2

ATA w

ers wil

x 3,86

7

o an ex

supply

it:

09

ill be: 4

l be:

6,667

S’

Passengers

cise tax:

equation modifies the supply

0 x 3,866,667 = $154,666,680

= $2,268,457,529

3.9

a) Q = 180 - 2P Q = 180 � 2 x 30 = 120 ties per week

b) If the store wants to sell 140 ties per week,

140 = 180 � 2P P = $20 per tie

c) Q = 180 � 2 x 0 = 180 ties d) 1 = 180 � 2P

P = $89.50 per tie

f) TR = PQ = (90 � 0.5Q)Q TR = 90Q � 0.5Q MR = 90 � Q = 0 Q = 90, P = 90 � 0.5 x 90 = $45 per tie

Diagrams:

TR $

1000

2000

3000

4000TR

MR

Q

20 60 100 180

10

50

30

70

90

90Q: P=90 – 0.5Q

4.1 You are hired as an economic consultant by a company that manufactures toys. One of their plants produces the famous �Barbie Doll�. The plant manager is looking for advice as to how he can maximize the efficiency of the factory by making the best uses of the fixed and variable resources. There are two main inputs, the workers who make the dolls and the factory, which includes the space, the building and all the equipment. He supplies you with monthly production data consisting of the number of workers employed and the number of dolls produced. Attached here are the data:

a) Calculate the MPL and the APL

Marginal Product Average Product Units of Laboour (L) Total Output (Q) of Labour (MPL) of Labour (APL)

0 0 N/A N/A 10 500 50 50.0 20 1900 140 95.0 30 4100 220 136.7 40 7000 290 175.0 50 10500 350 210.0 60 14500 400 241.7 70 18900 440 270.0 80 23600 470 295.0 90 28500 490 316.7 100 33500 500 335.0 110 38400 490 349.1 120 43100 470 359.2 130 47500 440 365.4 140 51500 400 367.9 150 55000 350 366.7 160 57900 290 361.9 170 60100 220 353.5 180 61500 140 341.7 190 62000 50 326.3 200 61500 -50 307.5 210 59900 -160 285.2 220 57100 -280 259.5 ____________________________________________________________

Total Output: The Short-Run Production Function

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 2200

10

20

30

40

50

60

70Thousands

Total Output

The MPL and APL Curves

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220

Number of Workers (L)

0

200

400

600

-200

-400

Marginal & Average Product of Labour

Marginal Product of LabourAverage Product of Labour

d) How many workers should the manager employ to maximize total output (Q) in the plant?

Should employ 190 workers e) At which level of employment (L) is the MPL maximized? At which level

of employment (L) is APL maximized? Marginal productivity (MPL) is maximized at 100 workers Average productivity (APL) is maximized at 140 workers f) At which level of employment (L) is the efficiency of the labour input

maximized? At a level of employment (L) of 140 workers

At which level of employment (L) is the efficiency of the capital input maximized? At a level of employment (L) of 190 workers If the manager wants to maximize the efficiency of the labour input, how many workers should he employ then?

He should employ 140 workers g) Why does the productivity of the variable input (APL) first rise, peak

and then fall? Do you think that the change in labour productivity has an impact on the labour cost of producing each unit? Why or why not?

It takes this shape from the effects that the law of diminishing marginal

returns. Yes, as labour productivity rises, the average variable cost (AVC) falls and as the average productivity of labour falls, the average variable (AVC) cost rises. In other words, the more efficiently you produce, the less your unit production costs become.

h) State and explain the law of diminishing marginal returns.

The law of diminishing marginal returns (LDMR) states that if you are increasing the amount of one input in production (say L) while you are holding the amount of the other input you are using constant (say K), then sooner or later you are bound to experience diminishing returns in your production. The law of diminishing returns is a universal law and is also known as the law of variable proportions.

4.3 The pattern of a firm�s costs, i.e. MC and AVC or TVC and TC, in the short-

run are determined by the shape of the short-run production function. The well-behaved cubic production function has a range of increasing returns to variable input followed by a range of decreasing returns to variable input. This makes the MC and AVC curves first fall and then rise. This pattern is created by the existence of the law of diminishing marginal returns.

4.4 The four types of production systems as defined by Peter Drucker are: i) rigid mass production ii) flexible mass production iii) continuous process or flow production iv) custom order production

4.5 Technological change is the application of newer, better and more efficient technologies in the production of a product. The two types of technological change are a) product innovation and b) process innovation, the first applies to the product being produced, the second to the production process used to manufacture the product. The introduction of digital cameras is an example of the first, the introduction of robotics is an example of the second.

4.6 In the short-run the firm does not have enough time to alter its fixed inputs,

only its variable inputs. In the long-run, the firm has enough time to alter both fixed and variable inputs.

4.7 Economies of scale are cost reductions caused by producing large volumes

of production in the same plant. Mass production allows for more division of labour, greater specialization of inputs, cost savings from fixed inputs and volume price discounts. Diseconomies of scale are the result of worker alienation, of increased supervision cost and higher transport and hauling costs. The minimum efficient scale (MES) or optimal plant is the optimally-sized plant which delivers the most economies without the diseconomies of scale, therefore represents the best size of plant to build.

4.8 The three forces that drive and shape a firm�s cost functions in the long-run

are a) technology, b) economies of scale and c) competition.

5.1

Q TFC TVC TC TR (PxQ) PROFIT

0 1000 0 1000 0 -1000

10 1000 100 1100 290 -810

20 1000 150 1150 580 -570

30 1000 210 1210 870 -340

40 1000 290 1290 1160 -130

50 1000 400 1400 1450 50

60 1000 540 1540 1740 200

70 1000 720 1720 2030 310

80 1000 950 1950 2320 370

90 1000 1240 2240 2610 370

100 1000 1600 2600 2900 300

110 1000 2100 3100 3190 90

b) See below

c) The firm breaks even at Q = 46 The firm maximizes profits at Q = 80 or 90 or 85 The firm maximizes sales revenue (TR) without losing money at Q = 112

If your mandate is to maximize the firm�s profits, then you should produce at Q = 85

d) The TVC takes this shape because of the Law of diminishing marginal returns

(LDMR). No, in the short-run the firm cannot produce any amount it wants because it is constrained by the limited plant (capital stock, K) that it has. If it tries to produce more, it quickly finds out that marginal and average variable costs rise so fast that it becomes unprofitable to produce more.

0 10 20 30 40 50 60 70 80 90 100 1100

500

1000

1500

2000

2500

3000

3500Dollars

TFC TVC TC TR 5.2

a) See table below

b) See graph below

c) MC is minimized at Q = 15 AVC is minimized at Q = 30

AC is minimized at Q = 80 d) The shape of the MC and AVC is due to the law of diminishing marginal

returns. The law of diminishing marginal returns (LDMR) states that if you are

increasing the amount of one input in production (say L) while you are holding the amount of the other input you are using constant (say K), then sooner or later you are bound to experience diminishing returns in your production.

5.2

Q AFC AVC AC MC MR P - AC

0 10 29

10 100 10 110 -81 5 29

20 50 7.5 57.5 -28.5 6 29

30 33.33 7 40.33 -11.33 8 29

40 25 7.25 32.25 -3.25 11 29

50 20 8 28 1 14 29

60 16.67 9 25.67 3.33 18 29

70 14.29 10.29 24.58 4.42 23 29

80 12.5 11.88 24.38 4.62 29 29

90 11.12 13.78 24.9 4.1 36 29

100 10 16 26 3 50 29

110 9.09 19.09 28.18 0.82

0 10 20 30 40 50 60 70 80 90 100 110

10

20

30

40

50

60

70

80

90

100

110

120Dollars per Unit

0

AFC AVC AC MC MR e) The firm breaks even at Q = 47 The firm maximizes profit at Q = 85 The maximum output that can be produced without losing money is Q = 112 At the output level that profit is maximized, MR = MC

To find which quantity will maximize profit compare MR and MC and find out at which quantity the two are equated.

5.3 a)

Price (P) Quantity

(Q)

Sales Revenue

(TR) Marg. Revenue

(MR) 40 0 n/a n/a 39 10 390 39 38 20 760 37 37 30 1110 35 36 40 1440 33 35 50 1750 31 34 60 2040 29 33 70 2310 27 32 80 2560 25 31 90 2790 23 30 100 3000 21 29 110 3190 19 28 120 3360 17 27 130 3510 15 26 140 3640 13 25 150 3750 11 24 160 3840 9 23 170 3910 7 22 180 3960 5 21 190 3990 3 20 200 4000 1 19 210 3990 -1 18 220 3960 -3 17 230 3910 -5 16 240 3840 -7 15 250 3750 -9

b) Ep (80,90) = -4.0 Ep (120,130) = -2.33, Ep (160,170) = -1.5, Ep (TTL Rev @ Max) = 1.0

0 20 40 60 80 100 120 140 160 180 2000

1

2

3

4

5

6

7Thousands of Dollars

TR TFC TVC TR

0 20 40 60 80 100 120 140 160 180 2000

10

20

30

40

50

60

70

80

90

100

P MR MC AFC AVC AC

5.4 a)

Q TFC TVC TC AFC AVC AC MC 0 700 0 700 N/A N/A N/A N/A

10 700 390 1,090 70.00 39.00 109.00 39.00 20 700 700 1,400 35.00 35.00 70.00 31.00 30 700 940 1,640 23.33 31.33 54.67 24.00 40 700 1,120 1,820 17.50 28.00 45.50 18.00 50 700 1,250 1,950 14.00 25.00 39.00 13.00 60 700 1,340 2,040 11.67 22.33 34.00 9.00 70 700 1,400 2,100 10.00 20.00 30.00 6.00 80 700 1,440 2,140 8.75 18.00 26.75 4.00 90 700 1,470 2,170 7.78 16.33 24.11 3.00

100 700 1,500 2,200 7.00 15.00 22.00 3.00 110 700 1,560 2,260 6.36 14.18 20.55 6.00 120 700 1,660 2,360 5.83 13.83 19.67 10.00 130 700 1,810 2,510 5.38 13.92 19.31 15.00 140 700 2,020 2,720 5.00 14.43 19.43 21.00 150 700 2,300 3,000 4.67 15.33 20.00 28.00 160 700 2,660 3,360 4.38 16.63 21.00 36.00 170 700 3,110 3,810 4.12 18.29 22.41 45.00 180 700 3,660 4,360 3.89 20.33 24.22 55.00 190 700 4,320 5,020 3.68 22.74 26.42 66.00 200 700 5,100 5,800 3.50 25.50 29.00 78.00 210 700 6,010 6,710 3.33 28.62 31.95 91.00 220 700 7,060 7,760 3.18 32.09 35.27 105.00 230 700 8,260 8,960 3.04 35.91 38.96 120.00 240 700 9,620 10,320 2.92 40.08 43.00 136.00 250 700 11,150 11,850 2.80 44.60 47.40 153.00

d) The profit-maximizing price (P) = $27 and

the profit-maximizing output (Q) = 130 units At that P and Q combination MR = MC = 15

e) At this P and Q combination: TR = $3,510; TC = $2,510 and Π = $1,000 P = $27; AC = $19.31; AVC = $13.92 and MC = $15 unit profit (P-AC) = $7.69 f) The break/even point is at Q = 60, and P = $34, TR = TC = $2,040

g) The firm maximizes sales revenue (TR) without losing money at Q = 172

5.6 To find the break/even point solve for: TR = TC

TR = TC PQ = TC

1,200Q � 0.05Q2 = 35,000,000 + 300Q 0.05Q2 - 900Q + 35,000,000 = 0 (a) (b) (c) Entering these values into the quadratic formula yields two answers: Q1 = 56,833 and Q2 = 123,167 The lower of the two values is the break/even point

TR, TC TC TR B/E Point Q (Output)

0 Q1 = 56,833 Q2 = 123,167 5.7

a) To maximize sales (TR) revenue, you should solve for MR = 0 TR = PQ = (100 � 0.001Q) Q = 100Q - 0.001 Q2 MR = 100 - 0.002Q MR = 0

0 = 100 - 0.002Q 0.002 Q = 100 Q = 50,000

At this Quantity (Q) P = 100 - 0.001 (50,000) P = $50 TR = PQ = 50 x 50,000 = $2,500,000 TC = 1,200,000 + 20 (50,000) = $2,200,000 Π = TR � TC = $300,000 After-tax profit : Π (1-τ) = 300,000 (1 � 0.4) = $180,000 ROE = Π (1-τ) / I x 100 = 180,000 / 1,000,000 x 100 = 18%

b) To maximize profit (Π ), you should solve for MR = MC TR = PQ = (100 � 0.001Q) Q = 100Q - 0.001 Q2 MR = 100 - 0.002Q TC = 1,200,000 + 20Q MC = 20 To max profit solve for MC = MR

20 = 100 - 0.002Q 0.002 Q = 80 Q = 40,000

At this Quantity (Q) P = 100 - 0.001 (40,000) P = $60 TR = PQ = 60 x 40,000 = $2,400,000 TC = 1,200,000 + 20 (40,000) = $2,000,000 Π = TR � TC = $400,000 After-tax profit : Π (1-τ) = 400,000 (1 � 0.4) = $240,000 ROE = Π (1-τ) / I x 100 = 240,000 / 1,000,000 x 100 = 24% c) If the firm wants to maximize sales revenue (TR) subject to a profit constraint

of 21% on equity capital, first find out what the target for profit will be:

An after-tax profit of 21% on capital invested of $1,000,000 represents $210,000 of profit annually. Before-tax it is: (1 / (1-τ) ) = 1 / ( 1 � 0.4) x 21% = 21% / 0.6 = 35% on equity capital or $350,000 a year. To find the quantity that should be produced to satisfy this condition (constraint) solve for : TR - TC = Π* where Π* is the profit constraint: TR - TC = Π*

PQ - TC = 350,000 PQ - ( 1,200,000 + 20Q ) = 350,000 100Q � 0.001Q2 � 1,200,000 � 20Q � 350,000 = 0

- 0.001Q2 + 100Q � 20Q � 1,550,000 = 0 0.001 Q2 - 80 Q + 1,550,000 = 0 (a) (b) (c) Entering these values into the quadratic formula yields two answers:

Q1 = 32,930 and Q2 = 47,071

Choose the higher of the two values to maximize revenue. Thus firm should aim to produce Q = 47,071 units annually The price (P) it should set is: P = 100 - 0.001 (47,071) Or P = $52.93

TR = PQ = 52.93 x 47,071 = $2,491,468 TC = 1,200,000 + 20 (47,071) = $2,141,420 Π = TR � TC = $350,048 After-tax profit : Π (1-τ) = 350,048 (1 � 0.4) = $210,029 ROE = Π (1-τ) / I x 100 = 210,029 / 1,000,000 x 100 = 21%

d) If the market price drops to $40 per unit, the break/even point is found by solving for TR = TC at that price:

TR = TC PQ = TC 40Q = 1,200,000 + 20Q 20Q = 1,200,000 Q = 60,000 units

e) If the market price falls even further to $25 per unit, the firm should produce:

P = 100 - 0.001 Q 25 = 100 - 0.001 Q Q = 75 / 0.001 = 75,000 units

At this quantity TC = 1,200,000 + 20 (75,000) = $2,700,000 TR = PQ = 25 ( 75,000 ) = $1,875,000 And Π = TR � TC = $ - 825,000

The firm should continue to operate since the price (P) exceeds AVC (MC): Since P > AVC Or 25 > 20, the firm makes a contribution margin of $5 per unit which

can go towards covering part of its fixed cost, thus minimizing its loss.

f) If the market price falls even further to P = $15 per unit, there is no point in continuing production as the price does not even cover variable (or marginal) cost of $20 per unit. If it stays open the losses will exceed those if it shuts down completely. Since P < AVC, the firm should shut down.

P = 100 - 0.001 Q 15 = 100 - 0.001 Q Q = 85 / 0.001 = 85,000 units

At this quantity TC = 1,200,000 + 20 (85,000) = $2,900,000 TR = PQ = 15 ( 85,000 ) = $1,275,000 And Π = TR � TC = $ - 1,625,000 a) Perfect competition, Differentiated competition, Oligopoly & Monopoly

Perfect competition

Differentiated competition

Oligopoly Monopoly

i.

VERY MANY

MANY FEW ONE

ii.

STANDARDIZED

DIFFERENTIATED STD/DIFF UNIQUE

iii.

VERY LOW

LOW HIGH VERY HIGH

5.6.1 Price competition: Competing on the basis of the lowest price.

Promotional competition: Advertising, marketing & business development. Production competition: Best product or service available on the market. Involves research & development. Continuous product development in order to achieve product differentiation and become better than the competition. Strategic competition: mergers & acquisitions, vertical/horizontal integration, takeovers, outsourcing, foreign production & strategic alliances.