ch3( Consumer Equilibrium)

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Chapter 3 Consumer Equilibrium:

Chapter 3 Consumer Equilibrium

Introduction:

How does a consumer determine the amount of a commodity that should be consumed ? Depends on: Level of satisfaction derived Level of income Constrains consumption Introduction

Basic Concepts:

Basic Concepts Utility is the satisfaction an individual derives from the consumption of a particular commodity Psychological phenomenon Marshall suggested - it can be measured Unit of measure - ‘ Utils ’

Basic Concepts:

Basic Concepts Total Utility (TU) Sum total of the satisfaction derived when a given number of units of a commodity are consumed Eg: the TU after 3 cups of ice-cream is the sum of the satisfaction from the 1 st , 2 nd and 3 rd cups Marginal Utility (MU) Additional satisfaction derived when one more unit of the commodity is consumed Eg: MU of the 3 rd cup of ice-cream is TU of 3 cups minus TU of 2 cups Utility

Total Utility and Marginal Utility:

Total Utility and Marginal Utility Cups of Ice-cream (N) TU (utils) MU (utils)= ∆TU/ ∆N 1 18 18 – 0 = 18 2 34 34 – 18 = 16 3 46 46 – 34 = 12 4 51 51 – 46 = 5 5 51 51 – 51 = 0 6 43 43 – 51 = -8 Cups of ice-cream (N) TU= Σ MU (utils) MU (utils) 1 18 18 2 18 + 16 = 34 16 3 34 + 12 = 46 12 4 46 + 5 = 51 5 5 51 + 0 = 51 0 6 51 - 8 = 43 -8

Total Utility Curve:

Number of units consumed Total Utility Number of Cups 0 1 2 3 4 5 6 TU 0 18 34 46 51 51 43 Total Utility Curve

Total Utility Curve:

Number of units consumed Total Utility TU Total Utility Curve

Relationship between TU & MU:

Number of units consumed Total Utility TU 0 MU No. of units consumed Marginal Utility Relationship between TU & MU

Relationship between TU & MU:

Number of units consumed Total Utility TU 0 MU No. of units consumed Marginal Utility Relationship between TU & MU

Relationship between TU & MU:

Number of units consumed Total Utility TU 0 MU No. of units consumed Marginal Utility When MU is decreasing and positive, TU increases at a decreasing rate When MU=0, TU is at its maximum point When MU is decreasing and is negative, TU starts declining Relationship between TU & MU

Law of Diminishing Marginal Utility:

Law of Diminishing Marginal Utility Statement of Law: As more and more units of a commodity are consumed, the level of satisfaction derived from every additional unit of the commodity eventually declines Implies that MU could increase initially, but will eventually decline Law highlights the behaviour of MU with units of the commodity consumed

Assumptions:

Assumptions Utility is measurable - ‘Utils’ Consumption takes place continuously over a stipulated time period Reasonable amount of the commodity forms a unit A grain of rice is NOT a reasonable amount Consumers are rational Marginal utility of money is held constant

Consumer Equilibrium - Single Commodity:

Consumer Equilibrium - Single Commodity Equilibrium is state of balance No reason to deviate from equilibrium At equilibrium, consumer ’ s satisfaction is maximum, subject to budget constraint Conditions for consumer equilibrium: Net benefit is maximised Net benefit is the difference between the TU in money terms and the expenditure made on consumption MU in money terms is equal to the price of the commodity

Consumer Equilibrium - Single Commodity:

Condition for Consumer Equilibrium: Net benefit is maximized Difference between the total utility in money terms and expenditure is maximized Assumptions: Marginal utility of the Rupee is equal to 1 Price per cup of ice cream is : Rs 12 Consumer Equilibrium - Single Commodity

Consumer Equilibrium - Single Commodity:

Total utility and expenditure on the consumption of ice creams Units Total utility TU in money Total expenditure Difference consumed (in utils) terms (TU/MU R ) (pxq) (in Rs) (net benefit) (in Rs) 1 18 18 12 6 2 34 34 24 10 3 46 46 36 10 Consumer Equilibrium - Single Commodity

Consumer Equilibrium - Single Commodity:

General Principle: MU of commodity MU of rupee = Price of commodity Consumer Equilibrium - Single Commodity MU x MU R = P x Where: MU X is the marginal utility of commodity x MU R is the marginal utility of rupee P X is the price of commodity x MU X is marginal utility of MU R commodity x in money terms

Consumer Equilibrium - Single Commodity:

General Principle: MU of commodity MU of rupee = Price of commodity Consumer Equilibrium - Single Commodity MUx 0 Units of the commodity Marginal Utility / Price E Px MU x MU R = P x

Consumer Equilibrium - Single Commodity:

General Principle: MU of commodity MU of rupee = Price of commodity Consumer Equilibrium - Single Commodity MUx 0 Units of the commodity Marginal Utility / Price Q’ E Px MU x MU R = P x

Consumer Equilibrium - Single Commodity:

General Principle: MU of commodity MU of rupee = Price of commodity Consumer Equilibrium - Single Commodity MUx 0 Q” Units of the commodity Marginal Utility / Price Q’ A E Px B MU x MU R = P x AQ ’’ : Marginal Utility BQ ’’ : Marginal Expenditure

Consumer Equilibrium - Single Commodity:

General Principle: MU of commodity MU of rupee = Price of commodity Consumer Equilibrium - Single Commodity MUx 0 Q” Units of the commodity Marginal Utility / Price Q’ A E Px B MU x MU R = P x Marginal Net Benefit AQ ’’ : Marginal Utility BQ ’’ : Marginal Expenditure

Consumer Equilibrium - Single Commodity:

General Principle: MU of commodity MU of rupee = Price of commodity Consumer Equilibrium - Single Commodity MUx 0 Q” Units of the commodity Marginal Utility / Price Q’ A E Px B MU x MU R = P x Marginal Net Benefit AQ ’’ : Marginal Utility BQ ’’ : Marginal Expenditure

Consumer Equilibrium - Single Commodity:

General Principle: MU of commodity MU of rupee = Price of commodity Consumer Equilibrium - Single Commodity MUx 0 Q” Units of the commodity Marginal Utility / Price Q’ Q’’’ A E C Px B D MU x MU R = P x DQ ’’’ : Marginal Utility CQ ’’’ : Marginal Expenditure

Consumer Equilibrium - Single Commodity:

Total utility and expenditure on the consumption of ice creams Units Total utility TU in money Total expenditure Difference consumed (in utils) terms (TU/MU R ) (pxq) (in Rs) (net benefit) 1 15 5 4 1 Consumer Equilibrium - Single Commodity Assumptions: MU of rupee is 3 and Price per ice cream is Rs 4

Consumer Equilibrium - Single Commodity:

Total utility and expenditure on the consumption of ice creams Units Total utility TU in money Total expenditure Difference consumed (in utils) terms (TU/MU R ) (pxq) (in Rs) (net benefit) 1 15 5 4 1 2 34 11.3 8 3.3 Consumer Equilibrium - Single Commodity Assumptions: MU of rupee is 3 and Price per ice cream is Rs 4

Consumer Equilibrium - Single Commodity:

Total utility and expenditure on the consumption of ice creams Units Total utility TU in money Total expenditure Difference consumed (in utils) terms (TU/MU R ) (pxq) (in Rs) (net benefit) 1 15 5 4 1 2 34 11.3 8 3.3 3 46 15.3 12 3.3 Consumer Equilibrium - Single Commodity Assumptions: MU of rupee is 3 and Price per ice cream is Rs 4

Consumer Equilibrium - Single Commodity:

Total utility and expenditure on the consumption of ice creams Units Total utility TU in money Total expenditure Difference consumed (in utils) terms (TU/MU R ) (pxq) (in Rs) (net benefit) 1 15 5 4 1 2 34 11.3 8 3.3 3 46 15.3 12 3.3 4 51 17 16 1 Consumer Equilibrium - Single Commodity Assumptions: MU of rupee is 3 and Price per ice cream is Rs 4

Consumer Equilibrium - Single Commodity:

Total utility and expenditure on the consumption of ice creams Units Total utility TU in money Total expenditure Difference consumed (in utils) terms (TU/MU R ) (pxq) (in Rs) (net benefit) 1 15 5 4 1 2 34 11.3 8 3.3 3 46 15.3 12 3.3 4 51 17 16 1 5 51 17 20 -3 Consumer Equilibrium - Single Commodity Assumptions: MU of rupee is 3 and Price per ice cream is Rs 4

Consumer Equilibrium - Single Commodity:

Total utility and expenditure on the consumption of ice creams Units Total utility TU in money Total expenditure Difference consumed (in utils) terms (TU/MU R ) (pxq) (in Rs) (net benefit) 1 15 5 4 1 2 34 11.3 8 3.3 3 46 15.3 12 3.3 4 51 17 16 1 5 51 17 20 -3 6 43 14.3 24 -9.7 Consumer Equilibrium - Single Commodity Assumptions: MU of rupee is 3 and Price per ice cream is Rs 4

Consumer Equilibrium - Single Commodity:

Total utility and expenditure on the consumption of ice creams Units Total utility TU in money Total expenditure Difference consumed (in utils) terms (TU/MU R ) (pxq) (in Rs) (net benefit) 1 15 5 4 1 2 34 11.3 8 3.3 3 46 15.3 12 3.3 4 51 17 16 1 5 51 17 20 -3 6 43 14.3 24 -9.7 Consumer Equilibrium - Single Commodity Assumptions: MU of rupee is 3 and Price per ice cream is Rs 4

Consumer Equilibrium - Two Commodities Case:

Equilibrium condition for commodity x: Consumer Equilibrium - Two Commodities Case Mu x Mu R Mu x P x = P x =Mu R ------------------ (i)

Consumer Equilibrium - Two Commodities Case:

Equilibrium condition for commodity x: Equilibrium condition for commodity y: Consumer Equilibrium - Two Commodities Case Mu x Mu R Mu x P x = P x =Mu R ------------------ (i) Mu y Mu R Mu Y P Y = P y = Mu R ------------------ (ii)

Consumer Equilibrium - Two Commodities Case:

Equilibrium condition for commodity x: Equilibrium condition for commodity y: (i) = (ii) Consumer Equilibrium - Two Commodities Case Mu x Mu R Mu x P x = P x =Mu R Mu y Mu R Mu Y P Y = P y = Mu R Mu x P x Mu Y P Y = Mu R = ------------------ (i) ------------------ (ii)

Consumer Equilibrium - Two Commodity Case:

Consumer Equilibrium - Two Commodity Case Equilibrium conditions for 2 commodities Ratio of the marginal utility to price of one commodity is equal to the ratio of the marginal utility to the price of the second commodity Expenditure on both commodities should be less than or equal to consumer’s income P x . Q x + P y . Q y < Y Mu x P x Mu Y P Y =

Consumer Equilibrium - Two Commodity Case:

Shyama has Rs 10 to spend on oranges and apples. Price of each fruit is Rs 2 per kg. Using the marginal utility schedule given below determine the extent to which Shyama should consume each of the fruits to maximize her satisfaction. Consumer Equilibrium - Two Commodity Case Quantity in Kgs MU of apples MU of oranges 1 16 14 2 14 12 3 12 10 4 10 8 5 8 6

Consumer Equilibrium - Two Commodity Case:

Quantity MU MU of MU of apples/ MU of oranges/ in Kgs of apples oranges price of apples price of oranges 1 16 14 8 7 2 14 12 7 6 3 12 10 6 5 4 10 8 4 3 5 8 6 4 3 Consumer Equilibrium - Two Commodity Case

Consumer Equilibrium - Two Commodity Case:

In the above table the ratios of marginal utilities to prices are equal for the following combinations of apples and oranges: 2 apples + 1 orange 3 apples + 2 oranges 4 apples + 3 oranges 5 apples + 4 oranges Consumer Equilibrium - Two Commodity Case

Consumer Equilibrium - Two Commodity Case:

The expenditure incurred on each of the above combinations is given in the table below: No. of No. of Price of Price of Expenditure Expenditure Total Apples oranges Apples Oranges on Apples on Oranges Expenditure (Rs) (Rs) (Rs) (Rs) (Rs) 2 1 2 2 4 2 6 3 2 2 2 6 4 10 4 3 2 2 8 6 14 5 4 2 2 10 8 18 Consumer Equilibrium - Two Commodity Case Shyama chooses 3 kg of apples and 2 kg of oranges as she maximises utility, subject to her budget of Rs 10