Linear Demand curve with Negative Slope

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-4

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y-intercept

x-intercept

Linear Demand curve with zero slope

Linear Demand curve with undefined slope

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-2

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x=a

(a,0)

Linear Supply curves with positive slope

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SS

S

Linear Supply curve with zero slope

S

Linear Supply curve with undefined slope

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x=a

(a,0)

S

Given the following linear equations, each

representing either a SUPPLY or DEMAND curve:

X-6y+9= 0 and 2x+3y-12= 0

Where, x represents the QUANTITY in hundreds of units

y represents the UNIT PRICE in tens of pesos

a) Identify which represents a demand

curve and which represents a supply

curve.

Given the following linear equations, each

representing either a SUPPLY or DEMAND curve:

X-6y+9= 0 and 2x+3y-12= 0

Where, x represents the QUANTITY in hundreds of units

y represents the UNIT PRICE in tens of pesos

b) Determine the market equilibrium point

algebraically.

c) Sketch the curves on the same coordinate

axes and indicate the market equilibrium

point.

The BREAK-EVEN CHART is a graphical

representation showing the relationship

among the TOTAL REVENUE (R), TOTAL COST

(Yc), and FIXED COST (FC) equations.

SOME IMPORTANT FEATURES IN THE BREAK-EVEN

ANALYSIS ARE THE FOLLOWING:

1. The FIXED COST LINE (FC) is parallel to the x-axis (hence, the

slope is zero) with y-intercept equal to the FIXED COST. Fixed costs

include all indirect costs and these exist regardless of whether

production takes place or not. These include overhead expenses

such as RENT, SALARIES OF PERSONNEL or ADMINISTRATIVE

SALARIES, PROPERTY TAXES, UTILITIES, INSURANCE, INTEREST ON

BORROWED CAPITAL, MAINTENANCE and DEPRECIATION OF OFFICE

EQUIPTMENT and MACHINERY. The fixed cost equation is Y= FC.

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FC

The TOTAL COST LINE slopes upward to the

right ( slope is positive) with its y-intercept

equal to the fixed cost. The total cost for

the production of a particular commodity in

a specified period of time has two distinct

components: FIXED COST and VARIABLE COST.

VARIABLE COSTS are directly proportional to the level of

production, that is, variable costs increase as quantity of

production increases. These include expenses for WAGES

or direct labor, raw materials and all others directly

related to the production or manufacturing process.

The TOTAL COST LINE equation is given by

Yc = total variable costs + fixed costs

OR

Yc = (variable cost per unit) X + fixed costs

where X pertains to the quantity of

production and Yc, to the toal cost. The

graph shows the relationship among FIXED

COST and VARIABLE COST and TOTAL COST.

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TOTAL COSTfixed cost

variable cost

Yc

FC

The TOTAL REVENUE LINE has a positive slope

and always passes through the origin (0,0)

since NO OUTPUT or NO SALES means NO

INCOME or NO REVENUE. The total revenue

equation can be stated as:

R= (selling price per unit) X

where X is the quantity of commodity

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R

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R

Yc

FC

Based from the figure, there is a point A where the REVENUE LINE intersects the FIXED COST LINE or where R=FC. Thus, solving the REVENUE and FIXED COST equations simultaneously will yield the value of X where revenue is just enough to recover fixed costs.

There is also a point in the graph where R=Yc. Thus, solving the revenue and total cost equations simultaneously will yield the value of x necessary for the producer to earn just enough revenue to recover total costs, or to BREAK-EVEN. This X value is called the BREAK-EVEN quantity and the corresponding y-value either in the total revenue or total cost equation is the BREAK-EVEN PRICE. These X and Y values are the coordinates of the BREAK-EVEN point.

In the region to the left of BREAK-EVEN POINT, Yc>R, is the LOSS and LOSS= Yc-R.

To the right of BREAK-EVEN POINT is R>Yc, is the PROFIT. PROFIT = R-Yc.

The BREAK-EVEN analysis also includes the concept of CONTRIBUTION MARGIN, C.M. is the difference between the SELLING PRICE PER UNIT and the VARIABLE COST PER UNIT.

Therefore, C.M. (in pesos) = S.P. per unit- V.C. per unit

To express C.M. as a percentage of the selling price per unit: (C.M. in %)(S.P. per unit)= S.P. per unit – V.C. per unit

C.M. in % =[(S.P. per unit-V.C. per unit)/(S.P. per unit)] (100%)

CONTRIBUTION MARGIN is also known as MARK-UP or GROSS PROFIT.

Another method to find the x and y

coordinates of BREAK-EVEN POINT is as

follows:

At the BREAK-EVEN POINT,

R= Yc

(S.P. per unit)x= (V.C. per unit)x+FC

(S.P. per unit- V.C. per unit)x= FC

(Contribution Margin in pesos)x=FC

OR

X or BEP per unit=FC/c.m. in pesos

The Y-coordinate of the BREAK-EVEN POINT,

or the BREAK-EVEN PRICE can be determined

from the preceding formula:

X= FC/ (C.M. in pesos)

X=FC/ (C.M. in %)(S.P. per unit)

X (S.P. per unit) = FC/ (C.M. in %)

THEREFORE, Y or BEP = FC/ (C.M. in %)

The production levels to attain the desired profit, both in units and in pesos, can be obtained by using the contribution margin method.

P= R-Yc

P= (S.P. per unit)X-[(V.C. per unit)X+FC]

P= [(S.P. per unit)X-(V.C. per unit)X]-FC

P+FC=(S.P. per unit- V.C. per unit)X

P+FC=(C.M. in pesos)X

Finally, X= (P+FC)/ (C.M. in pesos)

Where X is the sales volume or production level in units to attain profit.

PESO sales volume to attain P= (P+FC)/ C.M. in %

A practicum group of students in the College of

Business and Economics, majoring in Business

Management and enrolled in the subject

Entrepreneurial research, submits a feasibility study

on the production of garment bags. A summary

report reveals the following projected data analysis

for a particular month:

Rent, administrative salaries, maintenance and

depreciation of industrial sewing machines

amount to P2,160. Material and labor costs

amount to P180 per bag. Mark up is set at 40%.

a) Determine the selling price per unit.

A practicum group of students in the College of

Business and Economics, majoring in Business

Management and enrolled in the subject

Entrepreneurial research, submits a feasibility study

on the production of garment bags. A summary

report reveals the following projected data analysis

for a particular month:

Rent, administrative salaries, maintenance and

depreciation of industrial sewing machines

amount to P2,160. Material and labor costs

amount to P180 per bag. Mark up is set at 40%.

b) How many bags must be sold by the group for

the month in order to break-even.

c) How much will be the revenue or sales at

break-even point?

A practicum group of students in the College of

Business and Economics, majoring in Business

Management and enrolled in the subject

Entrepreneurial research, submits a feasibility study

on the production of garment bags. A summary

report reveals the following projected data analysis

for a particular month:

Rent, administrative salaries, maintenance and

depreciation of industrial sewing machines

amount to P2,160. Material and labor costs

amount to P180 per bag. Mark up is set at 40%.

d) How many bags must be sold to recover fixed

costs?

e) What should be the sales volume in units and

in pesos to obtain a profit of P3,000?

A practicum group of students in the College of

Business and Economics, majoring in Business

Management and enrolled in the subject

Entrepreneurial research, submits a feasibility study

on the production of garment bags. A summary

report reveals the following projected data analysis

for a particular month:

Rent, administrative salaries, maintenance and

depreciation of industrial sewing machines

amount to P2,160. Material and labor costs

amount to P180 per bag. Mark up is set at 40%.

f) Draw the break-even chart.

In each of the equations given below where X

represents quantity and Y as the unit price,

determine which corresponds to a demand curve and

which corresponds to a supply curve, which

corresponds to neither a demand nor a supply curve:

a) 3x+7y+2100=0 d) x-8= 0

b) 8x-5y-400= 0 e) y-5= 0

c) 2x-3y+60= 0 f)(1/2)x+(1/4)y-25 =0

Dynamic Sales Center will supply 50

pocket calculators at Php100 each. The

supply is increased to 80 pieces when

the unit price is increased by 20%. (a)

Set up the supply function. (b) How

many calculators will be supplied if the

unit price is P150? (c) Find the lowest

price at which this item would be

supplied.

The record of sales for Hi-Quality Ware

Products Corporation, which sells plastic

canisters at P50 each, shows a sales volume

of 400 units. The company decides to reduce

the unit price by P15 which consequently

results to sales of 150 more canisters.

(a) Set up the demand function.

(b) What is the highest price to be paid for this

item?

(c) How many canisters would be demanded if

they were free?

Millie’s footwear sells ladies shoes at

P800 a pair. Fixed costs are P120,000 and

variable costs amount to 50% of the total

revenue:

(a) Set up the total revenue, fixed cost, and

total cost functions.

(b) How many pairs of shoes must be sold to

recover fixed costs?

(c) Find the break-even point.

(d) Draw the break-even chart.

For the following equations, where X

represents quantity in thousands of units and

Y represents unit price in hundreds of pesos:

x-y+1 = 0 and 6x+10y-42 = 0

(a) Determine which represents the demand

curve and which represents the supply

curve.

(b) Find the market equilibrium point

algebraically.

(c) Draw the figure.