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Important Formulas in Microeconomics | Class 11

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  • Last Updated : 07 Feb, 2023
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Chapter: Introduction

1. Marginal Rate of Transformation

Marginal~Rate~of~Transformation~(MRT)=\frac{\Delta{Units~Sacrificed}}{\Delta{Units~Gained}}

2. Marginal Opportunity Cost (MOC)

Marginal~Opportunity~Cost~(MOC)=\frac{\Delta{Units~Sacrificed}}{\Delta{Units~Gained}}

Chapter: Consumer’s Equilibrium

1. Total Utility (TU)

TUn = U1 + U2 + U3 + ……………..+ Un

Where,

TUn = Total Utility from n units of a given commodity

U1, U2, U3, …………….., Un = Utility from the 1st, 2nd, 3rd, …………., nth unit

n = Number of units consumed

OR

TU= ∑MU

2. Marginal Utility (MU)

MUn = TUn – TUn-1

Where,

MUn = Marginal Utility from nth unit

TUn = Total Utility from n units

TUn-1 = Total Utility from n-1 units

n = Number of units consumed

OR

Marginal~Utility~(MU)=\frac{Change~in~Total~Utility}{Change~in~Number~of~Units}=\frac{\Delta{TU}}{\Delta{Q}}

3. Marginal Utility in terms of Money (Consumer’s Equilibrium in Single Commodity Case)

Marginal~Utility~in~terms~of~Money=\frac{Marginal~Utility~in~utils}{Marginal~Utility~of~one~rupee~(MU_M)}

4. Equilibrium Condition in case of Single Commodity 

Let’s say, the consumer is in consumption of a single commodity ‘x’.

  • The consumer will be in equilibrium if MUx = Px
  • The consumer will not be in equilibrium if MUx > Px
  • The consumer will not be in equilibrium if MUx < Px

5. Equilibrium Condition in case of Two Commodities

Let’s say, the consumer is in consumption of two commodities ‘x’ and ‘y’.

  • The consumer will be in equilibrium if 

\frac{MU_x}{P_x}=\frac{MU_y}{P_y}=MU_M

and MU falls as consumption increases

  • The consumer will not be in equilibrium if \frac{MU_x}{P_x}>\frac{MU_y}{P_y}
  • The consumer will not be in equilibrium if \frac{MU_x}{P_x}<\frac{MU_y}{P_y}

6. Marginal Rate of Substitution (MRS)

MRS_{AB}=\frac{Units~of~B~willing~to~sacrifice}{Units~of~A~willing~to~gain}

OR

MRS_{AB}=\frac{\Delta{B}}{\Delta{A}}

7. Algebraic Expression of Budget Line

M = (PA x QA) + (PB x QB)

Where,

M = Money Income

QA  Quantity of Apples (A)

QB = Quantity of Bananas (B)

PA = Price of each Apple

PB = Price of each Banana

8. Algebraic Expression of Budget Set

M ≥ (PA x QA) + (PB x QB)

Where,

M = Money Income

QA  Quantity of Apples (A)

QB = Quantity of Bananas (B)

PA = Price of each Apple

PB = Price of each Banana

9. Slope of Budget Line

Slope~of~Budget~Line=\frac{Units~of~B~willing~to~Sacrifice}{Units~of~A~willing~to~Gain}=\frac{\Delta{B}}{\Delta{A}}

10. Price Ratio

Price~Ratio=\frac{Price~of~X~(P_X)}{Price~of~Y~(P_Y)}=\frac{P_X}{P_Y}

11. Condition of Consumer’s Equilibrium by Indifference Curve Analysis

  • MRS_{XY}=Ratio~of~Prices~or~\frac{P_X}{P_Y}=Market~Rate~of~Exchange~(MRE)  OR Slope of Indifference Curve = Slope of Budget Line
  • MRS continuously falls

Chapter: Demand

1. Individual Demand Function

Dx = f(Px, Pr, Y, T, F)

Where,

Dx = Demand for Commodity x

f = Functional Relationship

Px = Prices of the given Commodity x

Pr = Price of Related Goods

Y = Income of the Consumer

T = Tastes and Preferences

F = Expectation of Change in Price in future

2. Market Demand Function

Dx = f(Px, Pr, Y, T, F, Po, S, D)

Where,

Dx = Demand for Commodity x

f = Functional Relationship

Px = Prices of the given Commodity x

Pr = Price of Related Goods

Y = Income of the Consumer

T = Tastes and Preferences

F = Expectation of Change in Price in future

Po = Size and Composition of population

S = Season and Weather

D = Distribution of Income

3. Market Demand Schedule

Dm = DA + DB + ……….

Where,

Dm = Market Demand

DA + DB + ………. = Individual Demands of Household A, Household B, and so on.

4. Slope of Demand Curve

Slope~of~Demand~Curve=\frac{Change~in~Price~(\Delta{P})}{Change~in~Quantity~(\Delta{Q})}

5. Cross Demand

Dx = f(Py)

Where,

Dx = Demand for the given Commodity

f = Functional Relationship

Py = Price of Related Commodity (Substitute or Complementary)

Chapter: Elasticity of Demand

1. Elasticity of Demand

i) Percentage Method:

Elasticity~of~Demand=\frac{Percentage~Change~in~Demand~for~X}{Percentage~Change~in~a~factor~affecting~the~Demand~for~X}

ii) Geometric Method:

Elasticity~of~Demand~(E_d)=\frac{Lower~Segment~of~Demand~Curve~(LS)}{Upper~Segment~of~Demand~Curve~(US)}

2. Price Elasticity of Demand

i) Percentage Method:

Elasticity~of~Demand~(E_d)=\frac{Percentage~change~in~Quantity~Demanded}{Percentage~change~in~Price}

Where,

Percentage~change~in~Quantity~Demanded=\frac{Change~in~Quantity~(\Delta{Q})}{Initial~Quantity~(Q)}\times{100}

Change~in~Quantity~(\Delta{Q})=Q_1-Q

Percentage~change~in~Price=\frac{Change~in~Price~(\Delta{P})}{Original~Price~(P)}\times{100}

Change~in~Price~(\Delta{P})=P_1-P

ii) Proportionate Method:

E_d=\frac{\Delta{Q}}{\Delta{P}}\times{\frac{P}{Q}}

Where,

Q = Initial Quantity Demanded

Q1 = New Quantity Demanded

\Delta{Q}  = Change in Quantity Demanded

P = Initial Price

P1 = New Price

\Delta{P}  = Change in Price

3. Degrees of Elasticity of Demand

Perfectly Elastic Demand

Ed = ∞

Perfectly Inelastic Demand

Ed = 0

Highly Elastic Demand

Ed > 1

Less Elastic Demand

Ed < 1

Unitary Elastic Demand

Ed = 1

Chapter: Production Function: Returns to a Factor

1. Production Function

Ox = f(i1, i2, i3 …………… in)

Where,

Ox = Output of Commodity x

f = Functional Relationship

i1, i2, i3 …………… in = Inputs needed for Ox 

2. Total Product (TP)

Total Product (TP) = AP x Units of Variable Factor

OR

TPn = MP1 + MP2 + MP3 +…………….MPn

OR

TP = ∑MP

3. Average Product (AP)

Average~Product~(AP)=\frac{Total~Product~(TP)}{Units~of~Variable~Factor~(n)}

4. Marginal Product (MP)

MPn = TPn – TPn-1

Where,

MPn = Marginal Product of nth unit of variable factor

TPn = Total products of n units of variable factor

TPn-1 = Total product of n-1 units of variable factor

n = Number of units of variable factor

OR

Marginal~Product~(MP)=\frac{Change~in~Total~Product}{Change~in~units~of~Variable~Factor}=\frac{\Delta{TP}}{\Delta{n}}

5. Relationship between TP and MP

  • MP increases when TP increases at an increasing rate
  • MP starts declining when TP increases at a diminishing rate
  • MP is zero when TP is maximum
  • MP is negative when TP decreases

6. Relationship between AP and MP

  • AP increases when MP>AP
  • AP is constant and at its maximum point when MP = AP
  • AP falls when MP<AP
  • MP becomes negative, and AP remains positive

Chapter: Concepts of Cost and Revenue 

1. Cost Function

C = f(q)

Where,

C = Cost of Production

f = Functional Relationship

q = Quantity of Output

2. Total Cost (TC)

Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)

3. Average Fixed Cost (AFC)

Average~Fixed~Cost~(AFC)=\frac{Total~Fixed~Cost~(TFC)}{Quantity~of~Output~(Q)}

4. Average Variable Cost (AVC)

Average~Variable~Cost~(AVC)=\frac{Total~Variable~Cost~(TVC)}{Quantity~of~Output~(Q)}

5. Average Cost (AC)

Average~Cost~(AC)=\frac{Total~Cost~(TC)}{Quantity~(Q)}

OR

AC = AFC + AVC

6. Marginal Cost (MC)

MCn = TCn – TCn-1

Where,

n = Number of Units Produced

MCn = Marginal Cost of the nth unit

TCn = Total Cost of n units

TCn-1 = Total Cost of n-1 units

OR

Marginal~Cost~(MC)=\frac{Change~in~Total~Cost}{Change~in~units~in~Output}=\frac{\Delta{TC}}{\Delta{Q}}

7. Relationship between AC and MC

  • AC falls when MC < AC
  • AC is constant and at its minimum point when MC = AC
  • AC rises when MC>AC
  • MC increases at a faster rate as compared to AC

8. Relationship between AVC and MC

  • AVC falls when MC<AVC
  • AVC is constant and at its minimum point when MC = AVC
  • AVC rises when MC>AVC
  • MC increases at a faster rate as compared to AVC

9. Relationship between TC and MC

  • MC decreases when TC rises at a diminishing rate
  • MC is at its minimum point when the rate of increase in TC stops diminishing
  • MC increases when TC rises at an increasing rate

10. Relationship between TVC and MC

  • Area under the Curve MC= TVC

11. Total Revenue (TR)

Total Revenue = Quantity x Price

OR

TRn = MR1 + MR2 + MR3 +…………….MRn

OR

TR = ∑MR

12. Average Revenue (AR)

Average~Revenue=\frac{Total~Revenue}{Quantity}

13. Marginal Revenue (MR)

MRn = TRn – TRn-1 

Where,

MRn = Marginal Revenue of nth unit

TRn = Total Revenue of n units

TRn-1 = Total Revenue of n-1 units

n = Number of Units Sold

OR

Marginal~Revenue~(MR)=\frac{Change~in~Total~Revenue}{Change~in~number~of~Units}=\frac{\Delta{TR}}{\Delta{Q}}

14. Relationship between AR and MR

  • When Price remains Constant: AR = MR and both curves coincide with each other in a horizontal line parallel to the X-axis

15. Relationship between TR and MR

  • When Price remains Constant: TR increases at a constant rate, and the slope of the TR curve is a positive straight line because of constant MR

16. Relationship between TR and Price Line

  • Area under the curve MR = Area under the Price Line = TR

17. Relationship between AR and MR

  • When Price falls with rise in Output: Slope of AR and MR curve is downward from left to right, but MR falls at a rate twice the fall rate in AR

18. Relationship between TR and MR (When Price falls with rise in Output)

  • TR increases as long as MR is positive
  • TR is at its maximum point when MR = 0
  • TR starts falling when MR becomes negative

19. Break-even Point

  • Break-even Point is determined when TR = TC or AR = AC

20. Shut-down Point

  • Shut-down Point is determined when TR = TVC or AR = AVC

Chapter: Producer’s Equilibrium

1. Conditions for Producer’s Equilibrium (MR-MC Approach)

  • MC = MR
  • MC > MR after MC = MR Output Level

2. Conditions for Producer’s Equilibrium (TR-TC Approach)

  • Difference between TR and TC is positively maximised
  • Total profits fall after that output level

Chapter: Theory of Supply

1. Individual Supply Function

Sx = f(Px, Po, Pf, St, T, G)

Where,

Sx = Supply of the given Commodity x

f = Functional Relationship

Px = Price of the given Commodity x

Po = Price of other Goods

Pf = Price of Factors of Production

St = State of Technology

T = Taxation Policy

G = Goals of the firm

2. Market Supply Function

Sx = f(Px, Po, Pf, St, T, G, N, F, M)

Where,

Sx = Supply of the given Commodity x

f = Functional Relationship

Px = Price of the given Commodity x

Po = Price of other Goods

Pf = Price of Factors of Production

St = State of Technology

T = Taxation Policy

G = Goals of the firm

N = Number of firms

F = Future expectations regarding Px

M = Means of transportation and communication

3. Market Supply Schedule

Sm = SA + SB + ……………..

Where,

Sm = Market Supply

SA + SB + …………….. = Individual Supply of Supplier A, Supplier B and so on

4. Slope of Supply Curve

Slope~of~Supply~Curve=\frac{Change~in~Price~(\Delta{P})}{Change~in~Quantity~(\Delta{Q})}

5. Price Elasticity of Supply

i) Percentage Method:

Elasticity~of~Supply~(E_s)=\frac{Percentage~change~in~Quantity~Supplied}{Percentage~change~in~Price}

Where,

Percentage~change~in~Quantity~Supplied=\frac{Change~in~Quantity~Supplied~(\Delta{Q})}{Initial~Quantity~Supplied~(Q)}\times{100}

Change~in~Quantity~(\Delta{Q})=Q_1-Q

Percentage~change~in~Price=\frac{Change~in~Price~(\Delta{P})}{Original~Price~(P)}\times{100}

Change~in~Price~(\Delta{P})=P_1-P

ii) Proportionate Method:

E_s=\frac{\Delta{Q}}{\Delta{P}}\times{\frac{P}{Q}}

Where,

Q = Initial Quantity Supplied

Q1 = New Quantity Supplied

\Delta{Q}  = Change in Quantity Supplied

P = Initial Price

P1 = New Price

\Delta{P}  = Change in Price

6. Kinds of Elasticities of Supply

Perfectly Elastic Supply

Es = ∞

Perfectly Inelastic Supply

Es = 0

Highly Elastic Supply

Es > 1

Less Elastic Supply

Es < 1

Unitary Elastic Supply

Es = 1


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