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EC2204
3- Consumer Choice
Learning Outcomes
Upon completing this section, the student should be able to:
• Describe and illustrate the assumptions of indifference curve
analysis• Illustrate and determine utility functions• Determine utility maximisation subject to budget constraint • Distinguish between income and substitution effects• Apply consumer choice theory to changing prices• Derive Engel Curves and Compensated demand Curves• Distinguish between Slutsky and Hicks in terms of their
approach to compensation variation in income.
Consumer Choice
• This section examines consumer decision-making.
• Decisions made at individual level are important.
• How much consumers spend on certain goods and services is of prime interest to business planners who want to anticipate future demand levels, but also to governments considering the imposition of a new tax.
• The approach taken will mainly use the neo-classical framework. This assumes that individuals are utility maximisers, something that is often criticised for being unrealistic.
• The theory is not meant to be an accurate description of every situation that an individual faces.
• What it does provide is an approach that can be used to make predictions when individual circumstances change.
• First we introduce the analytical tools, indifference curves to represent the preferences of individuals and 'budget' lines to represent the constraint of a given amount of income.
Consumer Choice
• We start with a simple way in which we can represent the preferences of individuals between different combinations of goods that they might buy.
• We limit ourselves to decisions concerning only two goods.
• One particular individual, Kate, who spends her time drinking coffee.
• She likes both Cappuccino and Espresso, both of which give her satisfaction or, in the language of economics, utility.
• Figure 5.1 shows alternative combinations that she might drink over a particular period of time, say each week. Point A shows three cups of cappuccino and two cups of espresso, points B and C show other possible combinations.
• The preferences she has in relation to Cappuccino and Espresso can be represented by an indifference curve.
• This is a graphical way of showing alternative combinations of two goods that yield a particular level of utility, or satisfaction, to an individual.
Figure 5.1: Indifference Curve
The completeness assumption: The consumer has preferences between all possible combinations of goods, and these preferences may be ordered. If the individual is presented with two alternative combinations of goods then he or she can state which one is preferred (or whether he or she is indifferent between them).
B
A
C
Number of Expressos
Number of Cappuccinos
6
5
4
3
2
1
0
0 1 2 3 4 5 6
Kate would be willing to
give up 1 cappuccino
In exchange for 2 expressosIC0
Figure 5.2: Indifference Map
The assumption of non-satiation: The wants of the consumer are insatiable. Intuitively the consumer is assumed to prefer-more of a good to less of it. It follows that indifference curves that are further away from the origin represent a higher level of satisfaction or utility.
E
C
D
Number of Expressos
Number of Cappuccinos
6
5
4
3
2
1
00 1 2 3 4 5 6
IC0
IC1
IC2
Fig 5.4: Diminishing Marginal Rate of Substitution (DMRS).
The rate at which the consumer is willing to exchange one good for another decreases the more the individual has of the second good. In terms of our example, the more cappuccino drunk, the greater the willingness to exchange a. cup for an espresso drink. This is illustrated below where the changing slope of the indifference curve shows the diminishing marginal rate of substitution.
Number of Expressos
Number of Cappuccinos
6
5
4
3
2
1
00 1 2 3 4 5 6
Starting at 5 Cappuccinos Kate
would be willing to give up 3 cappuccinos for 1 additional expresso
IC0
Starting at 3 Cappuccinos Kate
would be willing to give up 1 cappuccinos for 2 additional expresso
Figure 5.5: The Assumption of Transitivity
The assumption of transitivity: The assumption that consumers' preferences are transitive. This means that consumers are taken to be rational in the sense that their preferences are consistent. For example, in Figure 5.2, if the individual prefers the combination of goods associated with point E to that at point D, and also prefers (the combination associated with) point D to that at point C, then we can say that point E is preferred to point C.
Number of Expressos
Number of Cappuccinos
6
5
4
3
2
1
0
0 1 2 3 4 5 6
IC0
IC0
A
B
C
Note: if indifference curves intersect the assumption of transitivity is violated.
Utility Functions
•Another way of representing consumer preferences is with utility functions. In the case where the consumer buys just two goods a utility function can be written as:
•U = U(X,Y) where U stands for utility, X and Y represent the quantities of the two goods.
X Y U = XY X Y U = XY
25 4 100 50 8 400
20 5 100 40 10 400
10 10 100 20 20 400
5 20 100 10 40 400
4 25 100 8 50 400
X
Y
U = XY
U = f (10XY)
U = 3XY-100 25 4
100
1000 200
20
5
100
1000 200 10 10
100
1000 200
5 20 100 1000 200 4 25 100 1000 200
Table 3.2: Utility Function U = f (XY), U = f (10XY), U = f (3XY-100),
Figure 5.7: Indifference Curves for Perfect Substitutes / Complements
Good X
Good Y
Good X
Good Y
Both Good are Perfect Substitutes
Both Good are Perfect Complements
Figure 3.9: The Consumers’ Equilibrium
• Neo-classical theory assumes that consumers are utility maximisers. • To model this behaviour we need to bring together our representation of the
individual's preferences and the financial constraint faced. • The utility maximising consumer will attain the highest utility possible given his or her
budget constraint Figure 5.9 shows this as a point of tangency between the indifference curve, IC0, and the budget line, BL0, marked as point A- At the optimum point, the individual consumes the quantity Xo of good X, and the quantity Y0 of good Y.
Good X
Good Y
M/Py
0 0 X0 M/PX
Slope of the Budget line =
A
IC0
Y0
BL0
B
C
1y
x
P
P
Budget ConstraintBudget Constraint
Suppose student gets €60 per week of an allowance
S/he spends on food and/or entertainment
The Price of a typical basket of food is €10 and the price of the average entertainment unit (cinema) is €6.
DRAW THE STUDENTS BUDGET LINE
€60 = P(food)*Quantity of Food + P(entertainment * Quantity of entertainment) - Utility Function
Entertainment
Food
0 1 2 3 4 5 6 units
10 units
5
M/Pf = 60/10 =6
M/Pe = 60/6 = 10
Budget ConstraintBudget Constraint
Suppose a student gets €60 per week of an allowance.
Point A - S/he spends all income on entertainment
Point B - S/he spends all income on food
Typically the student will prefer some combination of Food/Entertainment
Point C - 5 units of entertainment and 3 units of food ( This will cost €60)
Entertainment
Food1 2 3 4 5 6
10
5
A
B
Budget Budget LineLine
C
Consumer Equilibrium - Assume Consumers are Utility MaximisersConsumer Equilibrium - Assume Consumers are Utility Maximisers
All points on the budget line represent combinations of food/entertainment that can be purchased for €60.
All Points on an IC represents equal levels of satisfaction of utility
WE CAN NOW MODEL INDIVIDUAL WE CAN NOW MODEL INDIVIDUAL PREFERENCES AND THE PREFERENCES AND THE FINANCIAL CONSTRAINTFINANCIAL CONSTRAINT
Entertainment
Food1 2 3 4 5 6
10
5
A
B
Budget Line
C
Consumer Equilibrium- Assume Consumers are Utility MaximisersConsumer Equilibrium- Assume Consumers are Utility Maximisers
The tangency between the IC and the budget line at Point C where the student can attain the highest possible utility give a budget constraint of €60
This is the highest possible utility given the income available.
This point is referred to as CONSUMER CONSUMER EQUILIBRIUMEQUILIBRIUM
Higher IC’s are desirable but not attainable for the given budget constraint
Lower IC’s do not maximise Utility
Entertainment
Food1 2 3 4 5 6
10
5
A
B
Budget Line
C
IF THE PRICE OF FOOD INCREASES T0 €12IF THE PRICE OF FOOD INCREASES T0 €12
M = Pf*Qf + Pe*Qe
€60 = €10*3 + €6*5 at Point C
Consumption Ration 3F:5EConsumption Ration 3F:5E
M = €60, Pf increases to €12, Pe remains constant at €6.
M/Pf = 60/12 = 5The Budget Line pivots from the Y axis inward as the student can only purchase 5 units of food after the price increase.
The Student cannot now maximise utility
at point C and moves to Point X, 4.5 units of E and 2.75 of Food (less of both goods)€60 = €12*2.75 + €6*4.5 at X
New consumption Ratio 2.75F:4.5ENew consumption Ratio 2.75F:4.5E
Entertainment
Food1 2 3 4 5 6
10
5
A
B
Budget Line
C
XICo
IC1
What if the PRICE OF FOOD INCREASES T0 €15What if the PRICE OF FOOD INCREASES T0 €15
M = PfQf + PeQe
M = €60, Pf increases to €15, Pe remains constant at €6.
M/Pf = 60/15 = 4 units of foodThe Budget Line pivots from the Y axis inward as the student can only purchase 4 units of food after the price increase.
The Student cannot now maximize utility at point X and moves to Point Y, 3.75 units of E and 2.5 of Food (less of both goods)
€60 = €15*2.5 + €6*3.75 at Y
New Consumption Ratio 2.5 F : 3.75 New Consumption Ratio 2.5 F : 3.75 E at point YE at point Y
Entertainment
Food1 2 3 4 5 6
10
5
A
B
Budget Line
CX
ICo IC1
Y
PCC
Price Consumption Curve
B1B2
Derive a Demand Curve for Food for Kaitlin from Indifferent CurvesDerive a Demand Curve for Food for Kaitlin from Indifferent Curves
Kaitlin has faced three prices for food. P = €10, P = €12 and P = €15
To Draw a Demand Curve you need Prices & QuantitiesYou’ve got both P & Q on your IC’s & Budget Constraint for
Kate
Derive Kaitlin’s Demand Curve for Food and her Price Consumption Curve
You Need only 2 Prices/2 Quantities to Draw a Demand Curve.
Q of Entertainment
Q of Food
M = €60, Pf = €10, Pe = €6
M/Pf @ €10
M/Pe @ €6
IC 1
If Pf €12
M/Pf @ €12
IC 2
If Pf €15
IF Pf €12
M/Pf @ €15
IC 3
PCC
Price
Q
P= 10
IC 2
P= 12
P= 15
Demand Curve for Food
at 3 different prices
Deriving the Demand Curve
Budget Line & Changes in IncomeBudget Line & Changes in Income
Quantity of Food
Entertainment
0 1 2 3 4 5 6 6.6
11
10
9
8
7
6
5
4
3
2
1
0
Budget Line when M = €60, Pfood = €10 ; PEnt = €6
Budget Line when M = €66, Pfood = €10 ; PEnt = €6
Income Consumption Curves (ICC) & Engel Curves
Q Good Y
Q Good X
Budget Line when M = €60, Pfood = €10 ; P ent = €6
If you get a 10% pay rise M = €66, Pfood = €10 ; P ent = €6
If you get a 20% pay rise M = €72, Pfood = €10 ; P ent = €6
ICC – Income Consumption Curve
Income
Q Good X
M = €60
M = €66
M = €72
The Relationship between the level of The Relationship between the level of demand for good and the level of demand for good and the level of income is known as an Engel curveincome is known as an Engel curve
Engel CurveEngel Curve
Income & Substitution EffectsIncome & Substitution Effects
A change in Price of a good effects a consumers income.
If Kate bought only food and food prices fell, the max. she can buy is the ratio of Money Income to the Price of Food - M/Pfood.
If the Pfood increased it led to a decrease in purchasing power or real income.
This income effect can lead to an increase, decrease or no change in the demand for food
The extent of the reduction in real income is affected by the proportion of income spent on food.
The income effect of a price change is the adjustment of demand to the change in real income alone. (Budget Line)
The substitution effect of a price change is the adjustment of demand to the relative price change alone. (IC’s)
This is the effect of a change in the relative price ratio on the demand for a good.
A rise in Pricefood changes the price ratio, reducing the demand for food, for the purchasing power available to the individual.
Income & Substitution EffectsIncome & Substitution Effects
The Income Effect: (p 78)There is an effect on a consumer's income when there is a change in the price of one or other of the goods. For example, suppose the consumer only bought good X and the price of it incresed. The maximum amount that he or she could buy is given by the ratio of money income to the price of good X, M/PX, which will drop giving an decrease in purchasing power or real income. The income effect can lead to an increase, decrease or no change in the demand for the good as the extent of the rise in real income arising from a fall in the price of good X is clearly affected by the proportion of the budget spent on good X.
The Substitution Effect: (p78) This is the effect of a change in the relative price ratio on the demand for a good. If a rise in the price of X lowers the price ratio and this will reduce the demand for X, for a given level of purchasing power available to the individual. The substitution effect is referred to as being ‘negative’ since the change in the price ratio and the effect on demand for X move in the opposite directions. (If the price goes up the quantity demanded goes down and vice versa)
Income & Substitution Effects
Good X (food)
Good Y - EntertainmentM/Py
90/25=3.6
0
0 X0= 2 M/PX=90/20 = 4.5
A
IC0
Y0 = 2
BL0
•Suppose a student gets €90per week of an allowanceS/he spends on food and/or entertainment. The Price of a typical basket of food is €20 and the price of the average entertainment unit (night out) is €25. The student’s budget line can be represented as follows: M = PXQx+ PYQY. The student can purchase either 4.5 units of food and zero entertainment, or have 3.6 units of entertainment and zero food, but they generally prefer combinations of both goods. Point A represents a student’s decision to consume 2 baskets of food and have 2 nights out. [€90 = €20*2+ 25*2] no savingThe students consumption ratio is 2 Food : 2 Entertainment (A)
Inflation increases the price of food
Following Budgetary changes, the price of food increased to €30 a basket, whereas the price of entertainment remained the same. So now, the maximum the student can consume is 3 baskets of food from the €90 allowance.
The student can no longer be in equilibrium at point A, they do not have enough income.
Good X (food)
Good Y - Entertainment
M/Py
90/25
0
0 X1= 1.5 X0= 2
A
IC0
Y0 = 1.8
BL0
B
The students consumption ratio is now1.5 units of Food : 1.8 units of Entertainment
Price effect of an increase in the price of Food
Price effect = Income + Substitution Effect
Good X (food)
Good Y - Entertainment
M/Py
90/25
0
0 X1= 1.5 X0= 2
A
IC0
Y0 = 1.8
BL0
B
The students consumption ratio is now 1.5 Food : 1.8 Entertainment
C
A-C = Substitution EffectC- B = Income Effect
A-B = Price Effect
BL2
BL1
The income effect of a price change is the adjustment of demand to the change in real income alone, measured along the Budget Line.
The substitution effect of a price change is the adjustment of demand to the relative price change alone, measured along the indifference curve. This is the effect of a change in the relative price ratio on the demand for a good.
B AC
10
9
8
7
6
5
4
3
2
1
0
Problem: Decompose a Price increase for food into and Income and Substitution Effect
Entertainment10
9
8
7
6
5
4
3
2
1
0
Food 0 1 2 3 4 5 6
M = €60
Pf = €10
Pe = €6
Pf up €15
IC1
IC2
A - B = Price Effect on Food
A
B
C
A - C = Substitution Effect
B - C = Income Effect
Draw a construction line parallel to new budget line
and at tangent to original indifference curve IC1The parallel line holds the consumption ratio constant
As it is at tangent to original IC – you get the same level of utility as you had before the price increase.
B1B2
Income and Substitution Effects
Food
Entertainment
0 1 2 3 4 5 6
10
9
8
7
6
5
4
3
2
1
0
Decompose a – b (price effect) into income & substitution effect
Draw a construction line parallel to B2 – new budget line and at tangent to original indifference curve IC1
b a
a to b = price effect on the quantity demanded of food as a result of an increase in price of food
c – b = income effect
IC1
IC2
A
C
B
The parallel line holds the consumption ratio constant
As it is at tangent to original IC – you get the same level of utility as you had before the price increase.
a – c = substitution effect cc
Hicks versus Slutsky
You are a Business Manager Manager –
The Consumer Price Index (CPI) indicates Prices Increase (Inflation) –
You want to know how much Money – Income must you compensate the workers for the price increase to keep them on their original level of Utility
Use Hicks Compensation Variation in Income
You are a Business Manager Manager –
The Consumer Price Index indicates Price Increases (Inflation) –
You want to know how much Money – Income must you compensate them for the price increase to keep them on their original Bundle of Goods
Use Slutsky Compensation Variation in Income
Compensation Variation in Income - Price Increase Good X
Slutsky vs HicksSlutsky vs Hicks
Y/PxY/Px1
How much do have to compensate money income so that you can attain original level of utility after price increase- Hicks?
IC0
B
C
IC1
Y/Py
Originally at point A on original IC maximising utility at Point A, Px increases, budget line pivots inward to Y/Px1 . Consumer moves to Point B consuming less of good x, and relatively more of good y. Draw new budget line parallel to new BL at tangent to original indifference curve IC0.
Slutsky Compensation Variation in Income = r – t, Hicks Compensation Variation in Income = s - t
rs
t
The Income decrease is called the welfare loss at the new relative prices
How much do have to compensate money income so that you can purchase original bundle after price increase - Slutsky?Slutsky
Hicks A
Hicksian Income Effect
Good X (food)
Good Y - Entertainment
M/Py
90/25
0
0 X1= 1.5 X0= 2
A
IC0
Y0 = 1.8
BL0
B
The students consumption ratio is now 1.5 Food : 1.8 Entertainment
C
A-C = Substitution EffectC- B = Income Effect
A-B = Price Effect
BL2
BL1
Hicksian Income Effect
Slutsky and Hicksian Income Effect
Good X (food)
Good Y - Entertainment
M/Py
90/25
0
0 X1= 1.5 X0= 2
A
IC0
Y0 = 1.8
BL0
B
The students consumption ratio is now 1.5 Food : 1.8 Entertainment
C
A-C = Substitution Effect
C- B = Income Effect
A-B = Price Effect
BL3
BL1
Hicksian Income Effect
Slutsky Income Effect
IC1
Sample Question
C2.A typical student maximises their utility function U = U (F,E) subject to an income constraint (M). M = PF QF + PE QE., where M = money income, F = Food and E = Entertainment, P = price and Q = Quantity. The student has an income of €60, the price of food is €10 per basket and the price of entertainment is €6 per unit.
(a)Illustrate the student’s budget line showing consumer equilibrium at 5 units of entertainment and 3 baskets of food.
(b) If the price of food increases to €12 per basket, illustrate a typical consumer equilibrium after the price increase. Identify both the income and substitution effect resulting from the increase in the price of food.
(c)Derive the student’s demand curve for food at both €10 and €12 per basket, while maximising utility subject to the budget constraint.
(d) You are the manager of a firm. The staff representative has cited the consumer price index (CPI) to demonstrate that prices have risen in excess of the recent pay increase in the document Towards 2016. The minimum the staff will accept is compensation that will allow then to purchase the bundle of goods that maximised their utility before the price increases. Demonstrate how you would determine the level of income necessary to compensate your staff for the price increase clearly differentiating between the Hicksian and Slutsky compensation variation in income.
Recall our Learning Outcomes
You should now be able to:
• Describe and illustrate the assumptions of indifference curve
analysis• Illustrate and determine utility functions• Determine utility maximisation subject to budget constraint • Distinguish between income and substitution effects• Apply consumer choice theory to changing prices• Derive Engel Curves and Compensated demand Curves• Distinguish between Slutsky and Hicks in terms of their
approach to compensation variation in income.
