Volume 1: Quantitative Methods
Formula Sheet
Level I 2015

FinQuiz


Formula Sheet

Volume 1: Quantitative Methods

Reading 5: The Time Value of Money
1. Interest Rate
•

Interest Rate = Real Risk Free Interest Rate + Inflation Premium + Default Risk
Premium + Liquidity Premium + Maturity Premium.

•

Nominal Risk Free Interest rate = Real Risk Free Interest Rate + Inflation Premium

•

Interest rate as a growth rate = g =

-1

2. PV and FV of Cash Flow =
•

PV =

•

PV of Perpetuity =

•

PV (for more than one Compounding per year) = PV= FVN 1 +
ℎ

=

! "" #$%"



•

FVN = &' 1 +

•

FV (for more than one Compounding per year) = FVN = 1 +

•

FV (for Continuous Compounding) = FVN = &'

•


Solving for Number of periods = N =

(

)(

)(

*+
,+

(where LN = natural log)

-./.012334/563.0 0 .7/.0

•

Periodic Interest Rate =

•

Effective (or Equivalent) Annual Rate (EAR = EFF%) =

•

(4 80 9:;9 <9431=3> 0 =91 =3?30@0/

D


×

×(

4. Stated & Effective Rates

1 + & %A!%BC"

×

−1

EAR (with Continuous Compounding) = EAR =

−1


Formula Sheet

Volume 1: Quantitative Methods

5. PV & FV of Ordinary Annuity
•

PVOA = ∑3.H

•

FVOA = ∑3.H O&IJ. 1 +


•

Size of Annuity Payment = PMT =

•

G

= &IJ K

PV of Annuity Factor =

P

LM

( .

Q L

N

= &IJ Q

R

9:2334=.S /T.9

M U×
R

U
M
U

6. PV & FV of Annuity Due
•

PVAD = &IJ K

•

FVAD = &IJ Q

LM

N + PMT at t = PVOA + PMT
R 1+

= FVOA ×(1+r)

Reading 6: Discounted Cash Flow Applications
3. Net Present Value = ∑3.H

; G

G

− BVW
X;XXX


4. IRR (when project’s CFs are perpetuity) = NPV = - Initial Investment + 677 = 0
5. Holding Period Yield (HPR) =

YZ Y[ \Z
Y[

6. Money Weighted Rate of Return (MWR) = ∑=HW

;

677 G

= 0 (IRR represents the MWR)

7. Time Weighted Rate of Return (TWR):
^

•

TWR (when no external cash flows) = rTWR = HPR = rt =

•

TWR (for more than one periods) = rTWR = [(1+rt,1)× (1+rt,2)×… (1+rt,n)] -1

•

Annualized TWR (when investment is for more than one year)

^


= _ 1 + D O1 + D` … + 1 + D3 Pbc _1
•

TWR (for the year) = rTWR = [(1+R1)× (1+R2)×… (1+R365)] -1 where R1 =

^

^


Formula Sheet

Volume 1: Quantitative Methods

8. Bank Discount Yield = BDY = rBD =
9. Holding Period Yield = HPY =

efW
3



/

/

=T0

therefore Price = Par 1 −


3× gh
efW

YZ Y[ \Z
Y[

10. Effective Annual Yield = EAY = 1 + i&j

efk/.

− 1 (Rule: EAY > BDY)

11. Money Market Yield (or CD equivalent Yield) rMM:
•

rMM = HPY ×

•

rMM = (rBD) ×

•

rMM =

efW
.

/T0 /5409:.m0

4 Tm/ 0

efW gh
efW . gh

0/ 4 Sn=55
=T0

(Rule: rMM> rBD)

12. Bond Equivalent Yield = BDY = Semiannual Yield × 2

Reading 7: Statistical Concepts and Market Returns
1. Range = Maximum Value – Minimum Value
2. Class Interval = i ≥
•

o )
p

where

i = class interval, H = highest observed value, L = lowest observed value, k = number of
classes.

3. Absolute Frequency = Actual number of observations in a given class interval
4. Relative Frequency =

qrstuvwxyzx{vx|}~


•tw€u v rxzt•‚rsxzƒ€w„t|s

5. Cumulative Absolute Frequency = Add up the Absolute Frequencies
6. Cumulative Relative Frequency = Add up the Relative Frequencies
7. Arithmetic Mean =

…v t•trsxzƒ€w„t|s„|w†x‡€w€r€sx
t.t•trsxzƒ€w„t|s„|w†x‡€w€r€sx


Formula Sheet

Volume 1: Quantitative Methods

8. Median = Middle number (when observations are arranged in ascending/descending order)
3

•

For Even number of observations locate median at `

•

For Odd number of observations locate median at

3

`

9. Mode = observation that occurs most frequently in the distribution

|
XXXX
10. Weighted Mean = ‰
Š = ∑„HZ

„ ‰„

= (w1X1+ w2X2+….+ wnXn)

where X1, X2… Xn = observed values and w1, w2… wn = corresponding weights, sum to 1
11. Geometric Mean = GM = c‹‰ ‰` … ‰3 with Xi≥0 for i = 1,2,…n.
XXXX
12. Harmonic Mean = H.M = ‰
o =
∑c
Ž ‘Ž

13. Population Mean = µ =

(

3

∑c
Ž• Œ •
•Ž

with ‰= > 0 for i = 1,2,.,.,n.

where Xi = ith observation & N = number of observations in entire population

c

∑
14. Sample Mean = ‰X = Ž

‘Ž

3

where n = number of observation in the sample

15. Measures of Location:
•

Quartiles =

“= . =84.=93

•

Quintiles =

“= . =84.=93

•

Deciles =

•


Percentiles = Ly = " + 1

”
k

“= . =84.=93
W

,
S

WW

where Ly is location of percentile, y = % point at which distribution is being divided and
n= number of observations.
16. Mean Absolute Deviation = MAD =
17. Population Variance = σ2 =

X
∑c
Ž• |‘G ‘ |

∑Ž• ‘Ž – —
(

3


Formula Sheet


Volume 1: Quantitative Methods

18. Population Standard Deviation = √™ ` = š
19. Sample Variance = s2 =

∑Ž• ‘Ž – —
(

X —
∑c
Ž• ‘Ž ‘
3

20. Sample Standard Deviation (S.D) = s = š
21. Semi-variance = ∑ytz€uu‘„ ›‘X

X —
∑c
Ž• ‘Ž ‘
3

‘„ ‘X —
3

22. Semi-deviation (Semi Standard Deviation) = √ œ%•
23. Target Semi-variance = ∑ytz€uu‘„ ›ž
24. Target Semi-Deviation = ‹

3


Ÿ œ%•

25. Coefficient of Variation = CV =
26. Sharpe Ratio =

‘„ n —

‘X

x€|Ytzw•tu„t¡xwvz|

% "B = š∑ytz€uu‘„›‘X

‘„ ‘X —
3

where B = Target Value
% "B = š∑ytz€uu‘„ ›ž

‘„ n —
3

where s= sample S.D and ‰X = sample mean
x€|¡„s¢•zxx¡xwvz|

….\t•Ytzw•tu„t¡xwvz|

27. Excess Kurtosis = Kurtosis – 3
28. Geometric Mean return ≈ £ % ℎœ %BI


"D # " −

/ =/3T09:70.4 3
`

Reading 8: Probability Concepts
1. Empirical Probability of an event E = P(E) =
2. Odds for event E =

Yztr€r„u„w~t•xƒx|w¤
•tw€uYztr€r„u„w~

Yztr€r„u„w~t•¤

Z Yztr€r„u„w~t•¤

3. Odds against event E =

Z Yztr€r„u„w~t•¤
Yztr€r„u„w~t•¤

4. Conditional Probability of A given that B has occurred = P(A\B) =

2n
n

→ P(B) ≠ 0.


Formula Sheet


Volume 1: Quantitative Methods

5. Multiplication Rule (Joint probability that both events will happen):
P(A and B) = P(AB) = P(A\B) × P(B)
P(B and A) = P(BA) = P(B\A) × P(A)
6. Addition Rule (Probability that event A or B will occur):
P(A or B) = P(A) + P(B) – P(AB)
P(A or B) = P(A) + P(B) (when events are mutually exclusive because P(AB) = 0)
7. Independent Events:
•

Two events are independent if: P(B\A) = P(B) or if P(A\B) = P(A)

•

Multiplication Rule for two independent events = P(A & B) = P(AB) = P(A)× P(B)

•

Multiplication Rule for three independent events = P(A and B and C) = P(ABC) =
P(A) × P(B) × P(C)

8. Complement Rule (for an event S) = P(S) + P(SC) = 1 (where SC is the event not S)
9. Total Probability Rule:
P(A) = P(AS) + P(ASC) = P(A\S)×P(S) + P(A\SC)×P(SC)
P(A) = P(AS1) + P(AS2) +….+ P(ASn) = P(A\S1)×P(S1) + P(A\S2)×P(S2)… P(A\Sn)×P(Sn)
(where S1, S2, …,Sn are mutually exclusive and exhaustive scenarios)
10. Expected Return = E(wiRi) = wiE(Ri)
where (wi is weight of variable i and Ri is random variable i)

11. Covariance (between two random variables Ri and Rj):
Cov (Ri Rj) = ∑3=H O¥ D= − ¦D= POD§ − ¦D§ P
Cov (Ri Rj) = Cov (Rj Ri)
Cov (R, R) = σ2 (R)


Formula Sheet

Volume 1: Quantitative Methods

12. Portfolio Variance = 2 (Rp) = 3=H 3ĐH

2

D

` `

2 (Rp) =
e ăA

+

D , De + 2

` `
`
`

D` +


` `
e

D= +

`
` D`

e ăA

13. Standard Deviation (S.D) =

= Đ ăAOD= DĐ P

`

D` , De

De + 2
+

` ăA

D , D` +

`
e De
;9ôO7 7ơ P


14. Correlation (between two random variables Ri, Rj) = êOD= DĐ P =
15. Bayes Formula = & Ư " \

C"VA %A" =

(063:9

-7 ì-7ơ

/.=93\ô03.

(063:9

/.=93

ì

& & %A Ơ A. AVƯ "

16. Multiplication Rule of Counting = n factorial = "! = n (n-1)(n-2)(n-3)1.
17. Multinomial Formula (General formula for labeling problem) =
18. Combination Formula (Binomial Formula) = 3ă = O3P =

3

3!

3!

3 !3 !3 !


! !

where n = total number of objects and r = number of objects selected.
19. Permutation = 3& =

3

3!

!

Reading 9: Common Probability Distributions
1. Probability Function (for a binomial random variable) p(x) = p(X=x) = O3àPƠà 1 &
=

3!

3 à !à!<ả

< cãả

2. Probability Density Function (pdf) = f(x) = á 8 / VA =
0
à /

8 /

=


(for x = 0,1,2.n) where x = success out of n trials, n-x = failures out of

n trials, p = probability of success, 1-p = probability of failure, n= number of trials.

F(x) =

3 à

VA < <


Formula Sheet

Volume 1: Quantitative Methods

3. Normal Density Function = V º = -

√`¼

º¥

µ – —
`- —

for − ∞ < º < +∞

4. Estimations by using Normal Distribution:
`

•


Approximately 50% of all observations fall in the interval Á ± ™

•

Approximately 68% of all observations fall in the interval Á ± ™

•
•
•

e

Approximately 68% of all observations fall in the interval Á ± 2™
Approximately 68% of all observations fall in the interval Á ± 3™

More precise intervals for 95% of the observations are Á ± 1.96™ and for 99% of the

observations are Á ± 2.58™.

5. Z-Score (how many S.Ds away from the mean the point x lies)
É=

"!

!"A œ $

"!Aϥ

% ²$ =


6. Roy’s Safety-Frist Criterion = SF Ratio =
7. Sharpe Ratio = =

_± 7,

-,

‘ –
-

(when X is normally distributed)

ʱ 7, 7Ë Ì
-,

7Í b

8. Value at Risk = VAR = Minimum loss (in money terms e.g. $) expected over a specified
period at a specified probability level.
9. Mean (µL) of a lognormal random variable = exp (µ + 0.50σ2)
10. Variance (σL2) of a lognormal random variable = exp (2µ+ σ2) × [exp (σ2) – 1].
11. Log Normal Price = ST = S0exp (r0,T)
Where, exp = e and r0,t = Continuously compounded return from 0 to T
12. Price relative = Ending price / Beginning price = St+1/ St=1 + Rt, t+1
where,
Rt, t+1 = holding period return on the stock from t to t + 1.


Formula Sheet


Volume 1: Quantitative Methods

13. Continuously compounded return associated with a holding period from t to t + 1:
rt, t+1= ln(1 + holding period return) or
rt, t+1 = ln(price relative) = ln (St+1 / St) = ln (1 + Rt,t+1)
(The continuously compounded return < associated holding period return)

14. Continuously compounded return associated with a holding period from 0 to T:
R0,T= ln (ST / S0) or

W,

=

,

+

`,

+ ⋯+

W,

Where,
rT-I, T = One-period continuously compounded returns
15. When one-period continuously compounded returns (i.e. r0,1) are IID random variables
with mean µ and variance σ2, then
¦O

'

W,

P = ¦O

% "B = ™ ` O

,

P + ¦O
W,

`,

P = ™ `J

P + ⋯ + ¦O

W,

P = ÁJ And

S.D. = σ (r0,T) = σ√J
16. Annualized volatility
= sample S.D. of one period continuously compounded returns × √J
where, T = Number of trading days in a year = 250.


Formula Sheet


Volume 1: Quantitative Methods

Reading 10: Sampling and Estimation
1. Variance of the distribution of the sample mean =

-—
3

2. Standard deviation of the distribution of the sample mean = š

-—
3

3. Standard Error of the sample mean:
•

When the population S.D (σ) is known = ™‘
Ï =

•

When the population S.D (σ) is not known =
s=‹

œ¥$ •

% "B = √ ` ℎ




`

=

Ï
‘

-

√3

=

√3

where s = sample S.D estimate of

X —
∑c
Ž• ‘Ž ‘
3

4. Finite Population Correction Factor = fpc = šQ

( 3
(

R where N= population


5. New Adjusted Estimate of Standard Error = (Old estimated standard error × fpc)
6. Construction of Confidence Interval = Point estimate ± (Reliability factor × Standard
error)
•

Confidence interval for the normally distributed population with known variance =
º̅ ± É//`

•

-

√3

Confidence interval for the normally distributed population with unknown variance =
º̅ ± É//`

-

√3

where S = sample S.D.

7. Student’s t distribution
µ = ‰X ±

//` √3

(where t = critical value of t-distribution with df = n-1 and area of /2 in each tail)
(used when population variance is not known for both small and large sample sizes)



Formula Sheet

Volume 1: Quantitative Methods

8. Z-ratio = Z =

9. t-ratio = t =

x−µ
σ/ n

x −µ
s/ n

Reading 11: Hypothesis Testing
1. Test Statistic =

…€ Ñux…w€w„sw„} Ò~Ñtw†xs„Óx‡Ô€uvxt•ÑtÑvu€w„t|Ñ€z€ xwxz
sw€|‡€z‡xzztzt•s€ Ñuxsw€w„sw„}∗

-

when population S.D is unknown, the standard error of sample statistic is give by Ö‘
Ï =

√3

when population S.D is unknown, the standard error of sample statistic is give by ™‘

Ï =

√3

*

*

-

2. Power of Test = 1-Probability of Type II Error
3. Ó =

Ï Ø[
×

(when sample size is large or small but population S.D is known)

4. Ó =

Ï Ø[
×

(when sample size is large but population S.D is unknown where s is sample S.D)

5. w|

=

Z


Ù
√|
s
√|

Ï Ø[
×
s
√|

(when sample size is large or small and population S.D is unknown and

population sampled is normally or approximately normally distributed)
6. Test Statistic for a test of the difference between two population means (normally
distributed populations, populations variances unknown but assumed equal)
t=

XXXX XXXX
‘—
‘
Ú

–

—
Û—
Ü ÛÜ
Ý
c

c—

–—

/—

where Ö<` = pooled estimator of common variance =

3

3

- — 3—

3— `

where !V = " + "` − 2.
7.

Test Statistic for a test of the difference between two population means (normally
distributed populations, unequal and unknown populations variances unknown)

-——


Formula Sheet

t=

Volume 1: Quantitative Methods


XXXX XXXX
‘—
‘
Ú

!V =

Û—

c

–—

–

/—

Û—
—Ý
c—

In this case modified degree of freedom is used, which is calculated as

—
Û— Û—
—Ý
c
c—
—

—
—
Û—
Û
Ú Ý
Ú —Ý
c
c—
c
c—

Ú

8. Test Statistic for a test of mean differences (normally distributed populations, unknown
population variances)
=

•

1X –Þ^
-1X

•

XXX = ∑3=H !=
sample mean difference = !

•

sample variance = Ö1` =


•

sample S.D = ‹Ö1`

•

3

∑c
Ž•^ 1
3

1X —

sample error of the sample mean difference = XXX
! = Þ
3
√

8. Chi Square Test Statistic (for test concerning the value of a normal population variance)
‰` =

3

-^—

-—

where " − 1 = !V "!Ö ` =


œ¥$ •

% "B =

9. Chi Square Confidence Interval for variance
Lower limit = L =

3

-—

—
‘ß/—

and Upper limit = U = =

3

-—

‘ —·ß/—

X —
∑c
Ž•^ ‘Ž ‘
3


Formula Sheet


Volume 1: Quantitative Methods

10. F-test (test concerning differences between variances of two normally distributed
populations) F =
Ö` =

Ö` =

-—
-——

œ¥$ •
œ¥$ •

where

% "B AVV%



% "B AV BA"!

!V = " − 1"#œ

A ! Ÿ

!V` = "` − 1! "Aœ%" A ! Ÿ

œ¥$ % ℎ" A²


œ¥$ % ℎ"` A²

AVV

AVV

!Aœ

!Aœ

• %A"

• %A"

‘ —á

11. Relation between Chi Square and F-distribution = à = ‘ —

—á

•
•

3

where:

‰ ` is one chi square random variable with one m degrees of freedom


‰`` is another chi square random variable with one n degrees of freedom

12. Spearman Rank Correlation =

=1−

—
f ∑c
Ž• 1

3 3—

•

For small samples rejection points for the test based on are found using table.

•

For large sample size (e.g. n>30) t-test can be used to test the hypothesis i.e.
" − 2 /`
=
1 − ` /`


Formula Sheet

Volume 1: Quantitative Methods

Reading 12: Technical Analysis
1. Ratio (Relative Strength Analysis) =


Yz„}xt•€|€ssxww†€w„srx„|â€|€u~Óx‡
Yz„}xt•w†xžx|}† €z¢qssxw

2. Price Target for the
•

Head and Shoulders = Neckline – (Head – Neckline)

•

Inverse Head and Shoulders = Neckline + (Neckline– Head)

3. For the Double Tops Pattern:
•

Height = Highest high – Lowest Low

•

Price target = Lowest Low – Height of the pattern

4. For the Double Tops Pattern:

5.

•

Height = Highest high – Lowest Low


•

Price target = Highest High + Height of the pattern

Height of a Triangle = Price at the start of the downward slopping trend line – Price at the
start of the upward sloping trend line

6. Flags and Pennants Pattern
•

Flag Price Target = Price level at which the flag ends – (Price level at which the trend
starts – Price level at which the flag starts to form)

•

Pennant Price Target = Price level at which the pennant ends – (Price level at which the
trend starts – Price level at which the pennant starts to form)


Formula Sheet

Volume 1: Quantitative Methods

7. Simple Moving Average =

YZ Yã Yä …. Y|

8. Momentum Oscillator (or Rate of Change Oscillator ROC):
91/S å ;m/3>0–;m/3>03<0 =91 />9


× 100

•

ROC =

•

Momentum Oscillator Value M = (V-Vx)× 100

;m/3>03<0 =91 />9

(where V = most recent closing price and Vx = closing price x days ago)
•

Alternate Method to calculate M =

9. Relative Strength Index = RSI = 100 −

¶

× 100
WW

7-

where

∑ ç<Tm/3>0 :9 .m0<0 =914310 T93 =10 /.=93


RS = ∑ |“9°3Tm/3>0

:9 .m0<0 =914310 T93 =10 /.=93|

10. Stochastic Oscillator (composed of two lines %K and %D):
•

%é = 100

; ) ”

o ” ) ”

where:

C = latest closing price, L14 = lowest price in last 14 days, H14 is highest price
in last 14 days
•

%D = Average of the last three %K values calculated daily.

11. Put/Call Ratio (Type of Sentiment Indicators) =

Ôtuv xt•Yvw‚Ñw„t|s•z€‡x‡

Ôtuv xt•ê€uu‚Ñw„t|s•z€‡x‡

12. Short Interest Ratio (Type of Sentiment Indicators) =

…†tzwë|wxzxsw


qƒxz€âx\€„u~•z€‡„|âÔtuv x

13. Arms Index TRIN i.e. Trading Index (Type of Flow of funds Indicator) =
£ œC"! ºA JDC¯ =

(9.9:21«/3T=3>6 40 ÷(9.9:“0T5=3=3>6 40

954 09:21«/3T=3>6 40 ÷ 954 09:“0T5=3=3>6 40


Volume 2: Economics
Formula Sheet
Level I 2015

FinQuiz


Formula Sheet

Volume 2: Economics

Reading 13: Demand and Supply Analysis: Introduction
1. Slope of the demand curve =

2. Slope of the supply curve =














3. Consumer Surplus = Value that a consumer places on units consumed – Price paid to buy
those units
•

Area (for calculating Consumer Surplus) = ½ (Base × Height) = ½ (Q0 × P0)

4. Producer Surplus = Total revenue received from selling a given amount of a good – Total
variable cost of producing that amount
•

Total revenue = Total quantity sold × Price per unit

•

Area (for calculating Producer Surplus) = ½ (Base × Height) = ½ {(Q0) × (P0 – intercept
point on y-axis**)}
**where supply curve intersects y-axis

5. Total Surplus = Consumer surplus + Producer surplus
6. Total Surplus = Total value – Total variable cost
7. Society Welfare = Consumer surplus + Producer surplus

8. Price Elasticity of Demand =
Q2 − Q1
(Q1 + Q2 )
%∆Q
=
P2 − P1
%∆P
1
2 ( P1 + P2 )
1
2












Formula Sheet

Volume 2: Economics



9. Income Elasticity of Demand =












=

Q2 − Q1
(Q1 + Q2 )
%∆Q
=
I 2 − I1
%∆I
1
2 ( I1 + I 2 )
1
2



10. Cross Elasticity =


















Reading 14: Demand and Supply Analysis: Consumer Demand
1. Marginal Utility =
2.









Equation of Budget Constraint Line = (Price of Good X × Quantity of Good X) + (Price
of Good Y × Quantity of Good Y)





3. Slope of Budget Constraint Line =

4. Marginal Rate of Substitution =


















=

=





Reading 15: Demand and Supply Analysis: The Firm
1. Profit = Total revenue – Total cost
2. Accounting Profit = Total Revenue – Explicit Costs(or Accounting costs)
3. Economic Profit
•

= Total Revenue – Explicit Costs – Implicit Costs or

•

= Accounting Profit – Implicit Costs or

•

= Total Revenue – Total Economic Costs


















Formula Sheet

Volume 2: Economics

4. Economic costs = Explicit costs + Implicit costs
5. Normal Profit = Accounting Profit – Economic Profit
6. Accounting profit = Economic Profit + Normal Profit
7. Economic rent = (New “Higher” Price after increase in Demand – Previous Price before
increase in Demand) × Quantity supplied before increase in Demand
8. Total Revenue (TR):
•

= Price × Quantity or

•

= Sum of individual units sold × Respective prices of individual Units sold = Σ (Pi × Qi)

9. Average Revenue (AR) =



!







10. Marginal Revenue (MR) =

!

11. Total Variable Cost = Variable Cost per unit × Quantity Produced
12. Total Cost = Total Fixed + Total Variable


13. Average total cost (ATC) =

14. Marginal cost (MC) =

15. Marginal Variable Cost =










= Avg. Fixed Cost + Avg. Variable Cost



"




#

16. Marginal revenue (When there is perfect competition) = Avg. Revenue = Price = Demand
17. Profit can be increased by increasing output when MR> MC
18. Profit can be increased by decreasing output when MR< MC
19. Break-even price: P = ATC
Revenue = Average Total Cost

Output level where Price = Average Revenue = Marginal
where, Total Revenue = Total Cost.

20. Firms earn Economic Profits when Price > Average Total Cost


Formula Sheet

Volume 2: Economics

21. Profits occur when Total Revenue (TR) ≥ Total Cost (TC) AND when Price = Marginal
Cost

firm will continue operating.

22. Losses are incurred when there are Operating profits (Total Revenue ≥ Variable Cost) but
Total Revenue < Total Fixed Cost + Total Variable Cost AND when Price = Marginal Cost
while losses are < fixed costs

firm will continue operating.


23. Losses are incurred when there are Operating losses (Total Revenue ≤ Variable Cost) AND
when losses ≥ fixed costs

firm will shut down.


24. Average Product =

$ #




25. Marginal Product =



$ #



&

=

#

%


'

(

26. Least-cost optimization Rule:


$ #

$ #







=









27. Profit is maximized when: MRP = Price or cost of the input for each type of resource that is
used in the production process
28. Marginal Revenue product = Marginal Product of an input unit × Price of the Product =

Price of the input =









!



29. Surplus value or contribution of an input to firm’s profit = MRP – Cost of an input


Formula Sheet

Volume 2: Economics

Reading 16: The Firm and Market Structures
1. When there is perfect competition, Marginal revenue = Avg. Revenue = Price = Demand
2. Marginal Revenue = Price × 01 −


3. Concentration Ratio =

3


4

!





(





5
36

4. Herfindahl-Hirshman Index = Sum of the squares of the market shares of the top N
companies in an industry

Reading 17: Aggregate Output, Prices, and Economic Growth
1. Nominal GDP t = Prices in year t × Quantity produced in year t
2. Real GDP t = Prices in the base year × Quantity produced in year t
3. Implicit price deflator for GDP or GDP deflator =
!

!
















#









× 100

4. Real GDP = [(Nominal GDP / GDP deflator) ÷ 100]
5. GDP deflator =

&








× 100

6. GDP = Consumer spending on final goods and services + Gross private domestic investment
+ Government spending on final goods and services + Government gross fixed investment +
Exports – Imports + Statistical discrepancy
7. Net Taxes = Taxes – Transfer payments
8. GDP = National income + Capital consumption allowance + Statistical discrepancy


Formula Sheet

Volume 2: Economics

9. National Income = Compensation of employees (i.e. wages) + Corporate and government
enterprise profits before taxes + Interest income + unincorporated business net income
(proprietor’s income) + rent + indirect business taxes les subsidies
10. Total Amount Earned by Capital = Profit + Capital Consumption Allowance
11. PI = National income – Indirect business taxes – Corporate income taxes – Undistributed
corporate profits + Transfer payments
12. Personal disposable income (PDI) = Personal income – Personal taxes OR GDP (Y) +
Transfer payments (F) – (R/E + Depreciation) – direct and indirect taxes (R)
13. Business Saving = R/E + Depreciation
14. Household saving = PDI - Consumption expenditures - Interest paid by consumers to
business - Personal transfer payments to foreigners
15. Business sector saving = Undistributed corporate profits + Capital consumption allowance

16. Total Expenditure = Household consumption (C) + Investments (I) + Government spending
(G) + Net exports (X-M)
17. Private Sector Saving = Household Saving + Undistributed Corporate Profits + Capital
Consumption Allowance
18. GDP = Household consumption + Private Sector Saving + Net Taxes
19. Domestic saving = Investment + Fiscal balance + Trade balance
20. Trade Balance = Exports - Imports
21. Fiscal balance = Government Expenditure – Taxes = (Savings – Investment) – Trade
Balance
22. Average propensity to consume (APC) =

8






Formula Sheet

Volume 2: Economics

23. Quantity theory of money equation: Nominal Money Supply × Velocity of Money = Price
Level × Real Income or Expenditure
24. Percentage change in unit labor cost = % change in nominal wages - % change in
productivity
25. Economic growth = Annual % change in real GDP
26. Total Factor Productivity growth = Growth in potential GDP – [Relative share of labor in
National Income × (Growth in labor) + [Relative share
of capital in National Income × (Growth in capital)]

27. Growth in potential GDP = Growth in technology + (Relative share of labor in National
Income × Growth in Labor) + (Relative share of capital in
National Income × Growth in capital]
28. Capital share =Corporate profits + net interest income + net rental income + (depreciation/
GDP)
29. Labor share =

4





Reading 18: Understanding Business Cycle
1. Price index at time t2 =
Inflation Rate = 0

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× 100

9:;<=>?@A=B>GD<CE@F>GH:DI=@:@@FC=@K

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5−1

KXX

2. Fisher Index = YZ[ × Z\ (where, IL = Laspeyres index and Ip = Paasche Index)


3. ]GF@;:^>_`>D@(]bB)FGdF`:@>_ =
4. fPghONVihjWhRPi =

&





#



%











e




(

e

(




Formula Sheet

Volume 2: Economics

Reading 19: Monetary and Fiscal Policy
1. Total amount of money created = New deposit/ Reserve requirement
2. Money Multiplier =



!

k

3





!




3. Narrow money = M1= currency held outside banks + checking accounts + traveller’s check
4. Broad money = M2 = M1 + time deposits + saving deposits
5. M3 = M2 + deposits with non-bank financial institution
6. Quantity Theory of Money = M × V = P × Y where,
M = Quantity of money
V = Velocity of circulation of money
P = Average price level
Y = Real output
7. Neutral Rate = Trend Growth + Inflation Target
8. Impact of Taxes and Government Spending: The Fiscal Multiplier
The net impact of the government sector on AD:
•

G – T + B = Budget surplus or Budget deficit
where, G = government spending , T =taxes, B =transfer benefits

•

Disposable income = Income – Net taxes = (1 – t) Income
where, Net taxes = taxes – transfer payments, t = net tax rate

9. Fiscal Multiplier (in the absence of taxes) = 1/(1 - MPC)
where, MPC = Marginal propensity to consume
MPS = Marginal propensity to save and is estimated as MPS = 1 – MPC.
•

Total increase in income and spending = Fiscal multiplier × G