Research: Application to Business Problems

53
0 Table of Contents 1. Linear Demand Function 2. Linear Supply Function 3. Market Equilibrium 4. Break-even analysis 5. Product Transformation Curves

description

MATH 2163: Calculus Applied to BusinessResearch 1: APPLICATIONS TO BUSINESS PROBLEMS

Transcript of Research: Application to Business Problems

Page 1: Research: Application to Business Problems

0

Table of Contents

1. Linear Demand Function

2. Linear Supply Function

3. Market Equilibrium

4. Break-even analysis

5. Product Transformation Curves

Page 2: Research: Application to Business Problems

Linear Demand Function

Demand is a schedule or a curve that shows the various amounts of a product that

consumers are willing and able to purchase at each of a series of possible prices during a

specified period of time. Demand shows the quantities of a product that will be purchased at

various possible prices, other things equal.1

The Law of Demand states that, assuming consumers are rational, “the higher the price

(P) of a good, the lesser the quantity demanded (Qd),” or alternatively stated, “the lower the

price, the higher the quantity demanded all other things held equal or constant.” 2

Demand Function, Demand Schedule and Demand Curve

The Law of Demand which shows the negative or inverse relations between price and

quantity demanded can be illustrated in three different ways through a demand function,

demand schedule and a demand curve.

We can express the relationship between the market demand and price of a product in

the form of an equation- known as a linear demand function.

Qd= a – bPWhere ,Qd = quantity demanded

a = quantity demanded if price was zero

P = price

1 McConnell, Campbell R., Stanley L. Brue & Sean M. Flynn, “Economics Principles, Problems and Policies,” McGraw Hill 18th

edition, 2009, pg.46

2 Payumo, Casiana S., Jose R. Ronan, Norie L. Maniego & Aileen L. Camba, “Understanding Economics,” 2012, pg. 36

Page 3: Research: Application to Business Problems

2

b = slope of the curve (∆Qd∆ P

= +∆Qd−∆ P

or−∆Qd+∆ P

)

For an illustration, we expressed in terms of a mathematical equation as follows:

Qd= 500 – 10P

The demand function above shows the slope or coefficient of the price is -10 which

means that for every peso increase in price, quantity demanded decreases by 10 units. The

constant term 500 is the quantity demanded if the price was zero.

We can complete a demand schedule (which is simply a table showing the quantity

demanded for a product over a range of prices), if we have numerical values for ‘a’ and ‘b’.

Assume that a = 500 and b = 10.

Table 1.1

Demand Schedule

Point Price Calculation Quantity Demanded

A 0 Qd=500-10(0) 500

B 10 Qd=500-10(10) 400

C 20 Qd=500-10(20) 300

D 30 Qd=500-10(30) 200

E 40 Qd=500-10(40) 100

Page 4: Research: Application to Business Problems

The table shows that as price goes up from P1.00 to P50.00, quantity demanded

decreases from 490 to 0 units.

The inverse relationship between price and quantity demanded for any product can be

represented on a simple graph, in which, by convention, we measure quantity demanded on

the horizontal axis and p rice on the vertical axis. When we plotted the six price-quantity data

points listed in the accompanying table and connected the points with a smooth curve, labeled

D. Such a curve is called a demand curve.

The demand curve shows a downward slope indicating negative or inverse relations

between price and quantity demanded. At point E, the quantity demanded is 100 units and the

price is P40.00 and as price goes down to P30.00 at point D, quantity demanded increases from

100 to 200 units.

100 200 300 400 5000

10

20

30

40

50

E

D

C

B

A

Figure 1.1: Demand Curve

Qd

Price

Page 5: Research: Application to Business Problems

4

Now assume that the value of ‘a’ changes to 600. We will compute the new values for

the quantity demanded over the same price ranges.

Table 1.2

New Demand Schedule

Point Price Calculation Quantity Demanded

F 0 Qd=600-10(0) 600

G 10 Qd=600-10(10) 500

H 20 Qd=600-10(20) 400

I 30 Qd=600-10(30) 300

J 40 Qd=600-10(40) 200

On the same graph paper as before plot the new demand curve for the schedule above.

Page 6: Research: Application to Business Problems

You can see that there has been a parallel shift of the demand curve- in this case the

demand curve has shifted out. So changes in the value of ‘a’ are caused by changes in non-

price determinants of demand such as income, number of buyers, price expectation, etc. This is

what you called change in demand (ΔD). The demand curve will shift either to the left

(decrease) or the right (increase). This is shown in Figure 1.3.

Figure 1.3

The Change in Demand

Non-price Determinants of Demand

Price is one of many determinants of demand- others include changes in tastes and

preferences, income of consumers, price of substitute goods, price of complementary goods,

buyer’s expectations about future prices and numbers of buyers. 3

1. Income of the consumers. Has direct relation for normal goods but if the product is an

inferior good, its relationship to demand is inverse.

3 Payumo, Casiana S., Jose R. Ronan, Norie L. Maniego & Aileen L. Camba, “Understanding Economics,” 2012, pg. 38

Page 7: Research: Application to Business Problems

6

2. Tastes and preferences. Have direct relation to demand. If one’s taste is in favor of the

product, the higher will be the demand for it.

3. Prices of related goods and services. Has direct relation for substitute goods (like rice

and bread) but inverse for complementary goods (like bread and butter).

4. Buyer’s expectations about future prices. Has direct relation to demand. If price is

expected to increase, people tend to panic buy, hence, demand increases.

5. Number of buyers. Has direct relation to demand. The more the number of buyers, the

higher the demand.

Now, when there is a change in the price of the good itself is called change in quantity

demanded (ΔQd). A change in quantity demanded is a movement from one point to another

point—from one price-quantity combination to another—on a fixed demand schedule or

demand curve. For an example, a decline in the price of corn from P15 to P10 will increase the

quantity of corn demanded from 20 to 40 bushels.

Figure 1.4

A curve depicting a change in quantity demanded

Page 8: Research: Application to Business Problems

Figure 1.4 shows that decrease in price, results to increase in quantity demanded from q1 to q2

representing a movement along a given demand curve from point A to point B.

Linear Supply Function

Supply refers to different quantities of good that sellers are willing and able to sell at

any given time at various possible prices other things equal.4

The Law of Supply demonstrates the quantities that will be sold at certain prices. This

means that “the higher the price, the higher the quantity supply ( Qs).” Producers supply more

at a higher price because it will mean higher revenue. 5

Supply Function, Supply Schedule and Supply Curve

The Law of Supply which shows the positive or direct relations between price and

quantity supplied can be illustrated in three different ways through a supply function, supply

schedule and a supply curve.

We can express the relationship between the quantity supplied and price of a product in

the form of an equation- known as a linear supply function.

Qs=c+dPWhere, Qs= Quantity supplied

P= price of the product

c= minimum quantity supply when the price is zero

4 5McConnell, Campbell R., Stanley L. Brue & Sean M. Flynn, “Economics Principles, Problems and Policies,” McGraw Hill 18 th

edition, 2009, pg.51

5

Page 9: Research: Application to Business Problems

8

d= slope of the curve (∆Qs∆P

= +∆Qs+∆P

or−∆Qs−∆ P

)

For an illustration given the supply function as follows:

Qs=-10+2PThe function shows the coefficient or the slope of the price is 2 and a constant term -10.

The slope means that for every peso increase in price, quantity supplied will increase by 2 units

while the constant term -10 implies that no one will supply the good if the price is below P5.00.

Table 2.1

Supply Schedule

Point Price Calculation Quantity Supplied

A 5 Qs=-10+2(5) 0

B 10 Qs=-10+2(10) 10

C 15 Qs=-10+2(15) 20

D 20 Qs=-10+2(20) 30

E 25 Qs=-10+2(25) 40

Using a supply schedule, we will determine the corresponding quantity supplied as the

price increases. As we can see, the price increases by P5.00, the quantity supplied increase also

Page 10: Research: Application to Business Problems

by 10 units. The schedule shows the positive or direct relationship of the price and the quantity

supplied.

0 10 20 30 400

5

10

15

20

25

A

B

C

D

EFigure 2.1: Supply Curve

Figure 2.1 Supply curve corresponds with the price–quantity supplied data in the

accompanying table. The upward slope of the curve reflects the law of supply—producers offer

more of a good, service, or resource for sale as its price rises.

Change in Quantity Supplied vs. Change in Supply

Figure 2.2

A curve depicting a change in quantity supplied

Page 11: Research: Application to Business Problems

10

Figure 2.2 shows the movement along the supply curve means that the supply

relationship remains consistent. Therefore, a movement along the supply curve will occur when

the price of the good changes and the quantity supplied changes in accordance to the original

supply relationship.

A change in quantity supplied(∆Q¿¿ s)¿ occurs when is caused only by a change in

price of the good itself all other things constant or equal.

Figure 2.3

Shift in the supply of beer

Figure 2.3 shows that the if the price for a bottle of beer was $2 and the quantity

supplied decreased from Q1 to Q2, then there would be a shift in the supply of beer. A shift in

the supply curve would occur if, for instance, a natural disaster caused a mass shortage of hops;

beer manufacturers would be forced to supply less beer for the same price.

Page 12: Research: Application to Business Problems

A change in supply (∆S) occurs whenever any of the non-price determinants of supply

changes. An increase in supply is represented by a shift of the supply curve to the right.

Alternatively, a decrease in supply is represented by a shift of the curve to the left. This is

shown in Figure 2.4

Figure 2.4

The Change in Supply

Non-price Determinants of Supply

Aside from price of the product there are several factors that will cause a shift in good’s

supply curve.6

1. Price of other goods. The supply of one good may decrease if the price of another good

increases, causing producers to reallocate resources to produce larger quantities of the

more profitable good.

2. Number of Sellers. More sellers result in more supply, shifting the supply curve to the

right.

6 NetMBA, http://www.netmba.com/ (accessed May 11, 2014)

Page 13: Research: Application to Business Problems

12

3. Prices of relevant inputs. If the cost of resources used to produce a good increase,

sellers will be less inclined to supply the same quantity at a given price, and the supply

curve will shift to the left.

4. Technology. Technological advances that increase production efficiency shift the supply

curve to the right.

5. Expectation. If sellers expect prices to increase, they may decrease the quantity

currently supplied at a given price in order to be able to supply more when the price

increases, resulting in a supply curve to shift to the left.

Page 14: Research: Application to Business Problems

Market Equilibrium

When supply and demand are equal (i.e. when the supply function and demand function

intersect) the economy is said to be at equilibrium. At this point, the allocation of goods is at its

most efficient because the amount of goods being supplied is exactly the same as the amount

of goods being demanded. Thus, everyone (individuals, firms, or countries) is satisfied with the

current economic condition. At the given price, suppliers are selling all the goods that they have

produced and consumers are getting all the goods that they are demanding.

Qd=Qs

Two Approaches to Market Equilibrium

Graphical Approach

To find market equilibrium, we combine the two curves onto one graph. The point of

intersection of supply and demand marks the point of equilibrium. Unless interfered with, the market

will settle at this price and quantity. At this point of intersection, buyers and sellers agree on both price

and quantity. For instance, in the graph below, we see that at the equilibrium price p*, buyers want to

buy exactly the same amount that sellers want to sell.

Figure 3.1

Market Equilibrium

Page 15: Research: Application to Business Problems

14

As you can see on the chart, equilibrium occurs at the intersection of the demand and

supply curve, which indicates no allocative inefficiency. At this point, the price of the goods will

be P* and the quantity will be Q*. These figures are referred to as equilibrium price and

quantity. In the real market place equilibrium can only ever be reached in theory, so the prices

of goods and services are constantly changing in relation to fluctuations in demand and supply.

Disequilibrium

Excess Supply (Surplus)

If the price is set too high, excess supply will be created within the economy and there will

be allocative inefficiency.

Figure 3.2

Excess Supply (Surplus)

At price P1

the quantity of goods that the producers wish to supply is indicated by Q2. At P1, however, the

quantity that the consumers want to consume is at Q1, a quantity much less than Q2. Because

Q2 is greater than Q1, too much is being produced and too little is being consumed. The

Page 16: Research: Application to Business Problems

those consuming the goods will find the product less attractive and purchase less because the

price is too high.

Excess Demand (Shortage)

Excess demand is created when price is set below the equilibrium price. Because the

price is so low, too many consumers want the good while producers are not making enough of

it.

Figure 3.3

Excess Demand (Shortage)

In this situation, at price P1, the quantity of goods demanded by consumers at this price

is Q2. Conversely, the quantity of goods that producers are willing to produce at this price is Q1.

Thus, there are too few goods being produced to satisfy the wants (demand) of the consumers.

However, as consumers have to compete with one other to buy the good at this price, the

demand will push the price up, making suppliers want to supply more and bringing the price

closer to its equilibrium.

Page 17: Research: Application to Business Problems

16

Algebraic Approach

Mathematically, we will determine the market equilibrium by setting the two equations

equal. Consider the demand function:

Qd=20−P

And supply function:

Qs=10+4 P

Then to find the equilibrium point, we set the two equations equal. Notice that quantity is on

the left-hand side of both equations. Because quantity supplied is equal to quantity demanded

at equilibrium, we can set the right-hand sides of the two equations equal.

Qs=Qd10+ 4P= 20-PP+4P=20-10

5P5

=105

P*=2At equilibrium, the price is P5. To find out the equilibrium quantity, we can just plug the

equilibrium price into either equation and solve for Q.

Qd=20−(2)=18Qs=10+4 (2 )=18Q*=18 units

Shifts up and down supply and demand curves are represented by plugging different prices into

the supply and demand equations: different prices yield different quantities. Using tabular form

we can find the equilibrium price and quantity.

Page 18: Research: Application to Business Problems

Quantity Demanded

(Q¿¿d )¿

Price Quantity Supplied

(Q¿¿ s)¿

Qd−Qs

20 0 10 (10)

18 2 18 0

16 4 26 10

14 6 34 20

Table 3.1

Table 3.1 is the result of the combining the demand schedule and supply schedule. At

any price above P2.00 will have a surplus; alternatively any price below the equilibrium price

will result to shortage in the market.

IMPACT OF CHANGE IN DEMAND AND SUPPLY ON MARKET EQUILIBRIUM

1. Change in Demand

Suppose that the supply of some good (for example, health care) is constant and the

demand for the good increases. As a result, the new intersection of the supply and demand

curves is at higher values on both the price and the quantity axes.

a) An increase in demand raises both equilibrium price and equilibrium quantity.

b) A decrease in demand reduces both equilibrium price and equilibrium quantity.

Page 19: Research: Application to Business Problems

18

2. Change in Supply

Suppose that the demand for some good (for example, cell phones) is constant but the

supply increases. The new intersection of supply and demand is located at a lower equilibrium

price but at a higher equilibrium quantity.

a) An increase in supply reduces equilibrium price but increases equilibrium quantity.

b) If supply decreases, equilibrium price rises while equilibrium quantity declines.

3. Supply Increase; Demand Decrease

a) Equilibrium price: Both changes

decrease price, so the net result

is a price drop greater than that

resulting from either change

alone.

b) Equilibrium quantity:

i. The increase in supply

increases equilibrium quantity, but the decrease in demand reduces it.

The direction of the change in equilibrium quantity depends on the

relative sizes of the changes in supply and demand. If the increase in

Page 20: Research: Application to Business Problems

supply is larger than the decrease in demand, the equilibrium quantity

will increase

ii. But if the decrease in demand is greater than the increase in supply, the

equilibrium quantity will decrease.

4. Supply Decrease; Demand Increase

a) Equilibrium price: A decrease in supply and an increase in demand for some

good (for e x ample, gasoline) both increase price. Their combined effect is an

increase in equilibrium price greater than that caused by either change

separately.

b) Equilibrium quantity:

i. If the decrease in supply is larger than the increase in demand, the

equilibrium quantity will decrease.

ii. If the increase in demand is greater than the decrease in supply, the

equilibrium quantity will increase.

5. Supply Increase; Demand Increase

a) Equilibrium price: A supply increase drops equilibrium price, while a demand

increase boosts it. If the increase in supply is greater than the increase in

demand, the equilibrium price will fall. If the opposite holds, the equilibrium

price will rise. If the two changes are equal and cancel out, price will not change.

b) Equilibrium quantity: The increases in supply and in demand both raise the

equilibrium quantity. Therefore, the equilibrium quantity will increase by an

amount greater than that caused by either change alone.

6. Supply Decrease; Demand Decrease

a) Equilibrium price: If the decrease in supply is greater than the decrease in

demand, equilibrium price will rise. If the reverse is true, equilibrium price will

fall. If the two changes are of the same size and cancel out, price will not change.

Page 21: Research: Application to Business Problems

20

b) Equilibrium quantity: d e creases in supply and demand both reduce equilibrium

quantity, we can be sure that equilibrium quantity will fall.

Page 22: Research: Application to Business Problems

Breakeven Analysis

Firms use breakeven analysis, also called cost-volume-profit analysis:

(1) To determine the level of operations necessary to cover all costs and

(2) To evaluate the profitability associated with various levels of sales.

Break-even analysis is a supply-side analysis; that is, it only analyzes the costs of the

sales. It does not analyze how demand may be affected at different price levels.

The firm’s operating breakeven point is the level of sales necessary to cover all

operating costs. At that point, earnings before interest and taxes (EBIT) equal $0. In other

words, break-even point (BEP) is the point at which cost or expenses and revenue are equal:

there is no net loss or gain, and one has "broken even." A profit or a loss has not been made,

although opportunity costs have been "paid," and capital has received the risk-adjusted,

expected return. In short, all costs that need to be paid are paid by the firm but the profit is

equal to 0.

The first step in finding the operating breakeven point is to divide the cost of goods sold

and operating expenses into fixed and variable operating costs.

a) Fixed costs are costs that the firm must pay in a given period regardless of the

sales volume achieved during that period. These costs are typically contractual;

rent, for example, is a fixed cost. Because fixed costs do not vary with sales, we

typically measure them relative to time. For example, we would typically

measure rent as the amount due per month.

b) Variable costs vary directly with sales volume. Shipping costs, for example, are a

variable cost. We typically measure variable costs in dollars per unit sold.

Page 23: Research: Application to Business Problems

22

Algebraic Approach

For single-product firm, using the following variables, we can recast the operating

portion of the firm’s income statement into the algebraic representation.

Equation 4.1: Operating breakeven point

Q= FCP−VC

VC = variable operating cost per unit

FC = fixed operating cost per period

Q = sales quantity in units

P = sale price per unit

As noted above, the operating breakeven point is the level of sales at which all fixed and

variable operating costs are covered—the level at which EBIT equals P0. Setting EBIT equal to

P0 and solving for Q which is the firm’s operating breakeven point.

For multiproduct firms, the operating breakeven point is generally found in terms of

peso sales, S. This is done by substituting the contribution margin, which is 100 percent minus

total variable operating costs as a percentage of total sales, denoted VC%, into the

denominator.

Equation 4.2: Multiproduct firm’s BEP

S= FC1−VC%

This multiproduct-firm breakeven point assumes that the firm’s product mix remains the

same at all levels of sales.

Page 24: Research: Application to Business Problems

Contribution Margin Approach

The contribution margin approach to calculate the break-even point (i.e. the point of

zero profit or loss) is based on the CVP analysis concepts known as contribution margin and

contribution margin ratio. Contribution margin ratio is the ratio of contribution margin to sales.

Contribution margin (CM) is the excess of sales (S) over the variable costs (VC) of the

product. It is the amount of money available to cover fixed costs (FC) and to generate profits.

CM=S−VC

When calculated for a single unit, it is called unit contribution margin (Unit CM). It is

the excess of the unit selling price (p) over the unit variable cost (v).

Unit CM=P−VC

EXAMPLE 4.1:

Consider the following data for company X:

Total Per Unit Percentage

Sales (2500 units) P75000 P30 100%

Less: Variable Costs 30000 12 40

Contribution Margin P45000 P18 60%

Less: Fixed Cost 15000

Net Income P30000

Breakeven point is computed as follows:

Q∈units= FCP−VC

=P1500030−12

=833.33units

Q∈pesos=833.33units×30=P25000 or

¿ P15000÷60%=P25000

EXAMPLE 4.2:

Page 25: Research: Application to Business Problems

24

Calculate the break-even output for TFC = P20, 000, P = P7, and AVC = P5

Q∈units= FCP−VC

=P200007−5

=10000units

EXAMPLE 4.3:

Suppose TFC = P10, 000, P = P5, AVC = P2. What is the output necessary to earn P5000 total

profit? What is the “average contribution margin”?

Q∈units= FCP−VC

=P10000+50005−2

=5000units

ACM=P−AVC=P5−2=P3

Break-even point for Multiple Products

Some company sells more than one product. To calculate break-even points for multiple

products we need to compute first the weighted average contribution margin per unit. Sales

mix is the proportion in which two or more products are sold.

EXAMPLE 4.3

Following information is related to sales mix of product A, B and C.

Product A B C

Sales Price per Unit P15 P21 P36

Variable Cost per Unit P9 P14 P19

Sales Mix Percentage 20% 20% 60%

Total Fixed Cost P40,000

Calculate the break-even point in units and in pesos.

1. Calculate the contribution margin per unit for each product:

Page 26: Research: Application to Business Problems

Product A B C

Sales Price per Unit $15 $21 $36

− Variable Cost per Unit $9 $14 $19

Contribution Margin per Unit $6 $7 $17

2. Calculate the weighted-average contribution margin per unit for the sales mix using the

following formula:

Product A CM per Unit × Product A Sales Mix Percentage

+ Product B CM per Unit × Product B Sales Mix Percentage

+ Product C CM per Unit × Product C Sales Mix Percentage

= Weighted Average Unit Contribution Margin

Product A B C

Sales Price per Unit P15 P21 P36

− Variable Cost per Unit P9 P14 P19

Contribution Margin per Unit P6 P7 P17

× Sales Mix Percentage 20% 20% 60%

P1.2 P1.4 P10.2

Sum: Weighted Average CM per

UnitP12.80

3. Calculate total units of sales mix required to break-even using the formula:

Break-even Point in Units of Sales Mix = Total Fixed Cost ÷ Weighted Average CM per Unit

Total Fixed Cost P40,000

÷ Weighted Average CM per Unit $12.80

Break-even Point in Units of Sales

Mix3,125

4. Calculate number units of product A, B and C at break-even point:

Page 27: Research: Application to Business Problems

26

Product A B C

Sales Mix Ratio 20% 20% 60%

× Total Break-even Units 3,125 3,125 3,125

Product Units at Break-even

Point625 625 1,875

5. Calculate Break-even Point in dollars as follows:

Product A B C

Product Units at Break-even Point 625 625 1,875

× Price per Unit P15 P21 P36

Product Sales in Dollars P9,375 P13,125 P67,500

Sum: Break-even Point in Dollars P90,000

Changing Costs and the Operating Breakeven Point

A firm’s operating breakeven point is sensitive to a number of variables: fixed operating cost

(FC), the sale price per unit (P), and the variable operating cost per unit (VC).

Page 28: Research: Application to Business Problems

Production Transformations Curve

Production Possibility Curve is a graphical representation of alternative production

possibilities facing an economy. A PPC is a graphical illustration of all combination of goods and

services that can be produced in a given economy at a given time, if all the available resources

in the economy are fully and efficiently employed.

As the total productive resources of the economy are limited the economy has to choose

between different goods. The productive resource can be employed for the production of

various alternative goods. It has therefore, to be decided which goods are to be produce more

and which ones less.

Assumptions:

1. Economy is produces two goods.

2. Full employment of resources is assumed.

3. Time period is given and constant.

4. Factors of productions are given and constant.

5. Production techniques are given and constant.

PPC Schedule

Production possibilities schedule shows the different combination of different goods

with the given technology and factors of production. Let us assume that the economy is

producing only two commodities: consumer goods and capital goods.

Page 29: Research: Application to Business Problems

28

PPC is a curve showing all possible combination of two goods that a country can produce

within a specified time period with all its resources fully or efficiently employed. It is always

concave to the origin.

The PPC also called transformation curve because in moving from one point to another

on it, one good is 'transformed' into another not physically but by transferring resources from

one use to the another.

Points Inside and Outside PPC

With the given resources being fully employed and utilized can lie anywhere on the PPC

but not inside or outside of it.

Outside Shift in PPC

If the productive resources expand or increase, the PPC will shift outward to the right

showing that more of both goods can be produce than before. Technological progress by

improving productive efficiency allows the society to produce more of the both goods with a

given and fix amount of resources. The PPC can shift outward with the growth of the economy

because of:

1. The increase in the amount of capital.

2. The increase in the amount of natural and human resources.

3. Progress in technology.

Page 30: Research: Application to Business Problems

EXAMPLE:

Mythica, which is a hypothetical economy, produces only two goods - textbooks and computers. When it uses all of its resources, it can produce five million computers and fifty five million textbooks. In fact, it can produce all the following combinations of computers and books.

Figure 5.1

Production Possibilities Curve Schedule

Figure 5.2

Production Possibilities Curve

Interpreting PPCs

Page 31: Research: Application to Business Problems

30

Firstly, we can describe the opportunity cost to Mythica of producing a given output of

computers or textbooks. For example, If Mythica produces 3m computers; the opportunity cost

is 5m textbooks. This is the difference between the maximum output of textbooks that can be

produced if no computers are produced (which is 70m) and the number of textbooks that can

be produced if 3m computers are produced (which is 65m). Similarly, the opportunity cost of

producing 7m computers is 31m textbooks - which is 70 - 39.

PPFs can also illustrate the opportunity cost of a change in the quantity produced of one

good. For example, suppose Mythica currently produces 3 million computers and 65m

textbooks. We can calculate the opportunity cost to Mythica if it decides to increase production

from 3 million computers to 7 million, shown on the PPF as a movement from point A to point

B. And textbooks are shown here.

The result is a loss

of output of 26 million textbooks (from 65 to 39m). Hence, the opportunity cost to Mythica of

this decision can be expressed as 26m textbooks. In fact, this is the same as comparing

the static opportunity cost of producing 3m computers (5m textbooks) and 7m computers (31m

textbooks).

Page 32: Research: Application to Business Problems

Pareto efficiency

Any point on a PPF, such as points 'A' and 'B', is said to be efficient and indicates that an

economy’s scarce resources are being fully employed. This is also called Pareto efficiency, after

Italian economist Vilfredo Pareto. Any point inside the PPF, such as point 'X' is said to be

inefficient because output could be greater from the economy’s existing resources. Any point

outside the PPF, such as point 'Z', is impossible with the economy’s current scarce resources,

but it may be an objective for the future. Pareto efficiency can be looked at in another way -

when the only way to make someone better off is to make someone else worse off. In other

words, Pareto efficiency means an economy is operating at its full potential, and no more

output can be produced from its existing resources.

Pareto efficiency is unlikely to be achieved in the real world because of

various rigidities and imperfections. For example, it is unlikely that all resources can be fully

employed at any given point in time because some workers may be in the process of training,

or in the process of searching for a new job. While searching for work, or being trained, they

are unproductive. Similarly, an entrepreneur may have wound-up one business venture, and be

in the process of setting-up a new one, but during this period, they are unproductive. Despite

this, Pareto efficiency is still an extremely useful concept.

Page 33: Research: Application to Business Problems

32

It is a useful concept for two reasons:

1. It can be an objective for an economy because it can set a direction towards which an

economy can move.

2. It can help highlight the imperfections and rigidities that exist in an economy and

prevent Pareto efficiency being achieved.

Increasing opportunity cost

Opportunity cost can be thought of in terms of how decisions to increase the production

of an extra, marginal, unit of one good leads to a decrease in the production of another good.

According to economic theory, successive increases in the production of one good will

lead to an increasing sacrifice in terms of a reduction in the other good. For example, as an

economy tries to increase the production of good X, such as cameras, it must sacrifice more of

the other good, Y, such as mobile phones.

This explains why the PPF is concave to the origin, meaning it is bowed outwards. For

example, if an economy initially produces at A, with 8m phones and 10m cameras (to 20m), and

then increases output of cameras by 10m, it must sacrifice 1m phones, and it moves to point B.

Page 34: Research: Application to Business Problems

If it now wishes to increase output of cameras by a further 10m (to 30m) it must sacrifice 2m

phones, rather than 1m, and it moves to point C; hence, opportunity cost increases the more a

good is produced. The gradient of the PPF gets steeper as more cameras are produced,

indicating a greater sacrifice in terms of mobile phones foregone.

Marginal analysis

Economic decisions are taken in a marginal way, which means that decisions to

produce, or consume, are made one at a time.

For example, a typical consumer does not decide to drink four cans of cola at the

beginning of each day, rather they make four individual decisions, one at a time. Similarly, a

baker does not decide to produce 5,000 loaves of bread in a year, but decides each day or week

what to produce. Economic decisions are marginal because conditions are constantly changing,

and consumers and producers would be highly irrational if they did not consider this. Hence,

each production or consumption decision is assumed to be made one at a time so that changing

conditions can be assessed.

Page 35: Research: Application to Business Problems

34

Economic growth

Economic growth has two meanings:

1. Firstly, and most commonly, growth is defined as an increase in the output that an

economy produces over a period of time, the minimum being two consecutive quarters.

2. The second meaning of economic growth is an increase in what an economy can

produce if it is using all its scarce resources. An increase in an economy’s productive

potential can be shown by an outward shift in the economy’s production possibility

frontier (PPF).

The simplest way to show economic growth is to bundle all goods into two basic

categories, consumer and capital goods. An outward shift of a PPF means that an economy has

increased its capacity to produce.

What creates growth?

When using a PPF, growth is defined as an increase in potential output over time, and

illustrated by an outward shift in the curve. An outward shift of a PPF means that an economy

Page 36: Research: Application to Business Problems

has increased its capacity to produce all goods. This can occur when the economy undertakes

some or all of the following:

a) Employs new technology

Investment in new technology increases potential output for all goods and services

because new technology is inevitably more efficient than old technology. Widespread

'mechanization' in the 18th and 19th centuries enabled the UK to generate vast quantities of

output from relatively few resources, and become the world's first fully industrialized economy.

In recent times, China's rapid growth rate owes much to the application of new technology to

the manufacturing process.

An economy will not be able to grow if an insufficient amount of resources are allocated

to capital goods. In fact, because capital depreciates some resources must be allocated to

capital goods for an economy to remain at its current size, let alone for it to grow.

b) Employs a division of labor, allowing specialization

A division of labor refers to how production can be broken down into separate tasks,

enabling machines to be developed to help production, and allowing labor to specialize on a

small range of activities. A division of labor, and specialization, can considerably improve

productive capacity, and shift the PPF outwards.

c) Employs new production methods

New methods of production can increase potential output. For example, the

introduction of team working to the production of motor vehicles in the 1980s reduced wastage

Page 37: Research: Application to Business Problems

36

and led to considerable efficiency improvements. The widespread use of computer controlled

production methods, such as robotics, has dramatically improved the productive potential of

many manufacturing firms.

d) Increases its labor force

Growth in the size of the working population enables an economy to increase its

potential output. This can be achieved through natural growth, when the birth rate exceeds the

death rate, or through net immigration, when immigration is greater than emigration.

e) Discovers new raw materials

Discoveries of key resources, such as oil, increase an economy’s capacity to produce.

An inward shift of a PPF

A PPF will shift inwards when an economy has suffered a loss or exhaustion of some of

its scarce resources. This reduces an economy's productive potential.

Page 38: Research: Application to Business Problems

A PPF will shift inwards if:

a) Resources run out

If key non-renewable resources, like oil, are exhausted the productive capacity of an

economy may be reduced. This happens more quickly as a result of the application of ultra-

efficient production methods, and when countries over-specialize in producing goods from non-

renewable resources.

Sustainable growth means that the current rate of growth is not so fast that future

generations are denied the benefit of scarce resources, such as non-renewable resources, and a

clean environment.

b) Failure to invest

A failure to invest in human and real capital to compensate for depreciation will reduce

an economy's capacity. Real capital, such as machinery and equipment, wears out with use and

its productivity falls over time. As the output from real capital falls, the productivity of labor will

also fall. The quality and productivity of labor also depends on the acquisition of new skills.

Therefore, if an economy does not invest in people and technology its PPF will slowly move

inwards.

c) Erosion of infrastructure

A military conflict is likely to destroy factories, people, communications, and

infrastructure.

Page 39: Research: Application to Business Problems

38

d) Natural disaster

If there is a natural disaster, such as the 2005 boxing-day tsunami, or the Haiti

earthquake of 2010, an economy’s PPF will shift inwards.

Investment and economic growth

Allocating scarce funds to capital goods, such as machinery, is referred to as

real investment. If an economy chooses to produce more capital goods than consumer goods,

at point A in the diagram, then it will grow by more than if it allocated more resources to

consumer goods, at point B, below.

To achieve long run growth the economy must use more of its capital resources to

produce capital rather than consumer goods. As a result, standards of living are reduced in the

short run, as resources are diverted away from private consumption. However, the increased

investment in capital goods enables more output of consumer goods to be produced in the long

run. This means that standards of living can increase in the future by more than they would

have if the economy had not made such as short-term sacrifice. Hence economies face a choice

between high levels of consumption in the short run and the long run.

Investment

If an economy chooses to produce more capital goods than consumer goods, at point A

in the diagram, then it will grow by more than if it allocated more resources to consumer goods,

at point B.

Page 40: Research: Application to Business Problems

There is a trade-off between the short and the long run. In the short run, the economy

must use resources to produce capital rather than consumer goods. Standards of living are

reduced in the short run, as resources are diverted away from private consumption. However,

in the longer run the increased investment in capital goods enables more output of consumer

goods to be produced. This means that standards of living can increase by more than they

would have if the economy had not made the short-term sacrifice.

Asymmetric growth

An economy can grow because of an increase in productivity in one sector of the

economy - this is called asymmetric growth.

For example, an improvement in technology applied to industry Y, such as motor vehicles, but

not to X, such as food production, would be illustrated by a shift of the PPF from the Y-axis only

Factor mobility

If workers, or other resources, are moved from one sector to another, then the position

of the PPF will change, with an increase in the maximum output in the industry receiving the

resources, and a fall in the maximum output of the industry losing resources.

Page 41: Research: Application to Business Problems

40

Works Cited

Books

McConnell, Campbell R., Stanley L. Brue & Sean M. Flynn, “Economics Principles, Problems and

Policies,” McGraw Hill 18th edition, 2009

Gitman, Lawrence J. & Chad J. Zutter, “Principles of Managerial Finance,” The Prentice Hall

series of finance 13th edition, 2012

Payumo, Casiana S., Jose R. Ronan, Norie L. Maniego & Aileen L. Camba, “Understanding

Economics,” 2012

Websites

https://oldfieldeconomics.wikispaces.com/

http://www.investopedia.com/

http://www.netmba.com/

http://www.sparknotes.com/

http://economydetail.blogspot.com/

http://www.economicsonline.co.uk/

http://www.econport.org/