Learning OutcomesUpon 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 CurveThe 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). Number of Cappuccinos 6 C 5 4 3 A 2 Kate would be B willing to give up 1 cappuccino 1 IC0 In exchange for 2 expressos 0 0 1 2 3 4 5 6 Number of Expressos
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. Number of Cappuccinos E D 6 C 5 4 3 IC2 2 IC1 1 IC0 0 0 1 2 3 4 5 6 Number of Expressos
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 Cappuccinos 6 Starting at 5 Cappuccinos 5 Kate would be willing to give up 3 cappuccinos 4 for 1 additional expresso Starting at 3 Cappuccinos Kate would be willing to 3 give up 1 cappuccinos for 2 additional expresso 2 IC0 1 0 0 1 2 3 4 5 6 Number of Expressos
Figure 5.5: The Assumption of TransitivityThe 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 Cappuccinos 6 5 4 3 A 2 C 1 IC0 B IC0 0 0 1 2 3 4 5 6 Number of ExpressosNote: if indifference curves intersect the assumption of transitivity is violated.
Utility Functions•Another way of representing consumer preferences is with utility functions. In the casewhere 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 Table 3.2: Utility Function U = f (XY), U = f (10XY), U = f (3XY-100), X Y U = XY U = f (1 0XY) U = 3XY-1 00 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
Figure 5.7: Indifference Curves for Perfect Substitutes / Complements Good Y Good Y Both Good are Perfect Both Good are Perfect Complements Substitutes Good X Good X
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 individuals 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 Y Px Slope of the Budget line = = −1 M/Py Py B A Y0 C IC0 BL0 0 0 X0 M/PX Good X
Budget ConstraintSuppose student gets €60 per week of anallowance EntertainmentS/he spends on food and/or entertainment 10 units M/Pe = 60/6 = 10The Price of a typical basket of food is €10 andthe price of the average entertainment unit(cinema) is €6.DRAW THE STUDENTS BUDGET LINE M/Pf = 60/10 =6€60 = P(food)*Quantity of Food + P(entertainment 5* Quantity of entertainment) - Utility Function 0 1 2 3 4 5 6 units Food
Budget ConstraintSuppose a student gets €60 per weekof an allowance. EntertainmentPoint A - S/he spends all income 10 A Budgeton entertainment LinePoint B - S/he spends allincome on food C 5Typically the student will prefer somecombination of Food/EntertainmentPoint C - 5 units of entertainment and B3 units of food ( This will cost €60) 1 2 3 4 5 6 Food
Consumer Equilibrium - Assume Consumers are Utility MaximisersAll points on the budget line representcombinations of food/entertainment thatcan be purchased for €60. Entertainment AAll Points on an IC represents equal levels 10 Budgetof satisfaction of utility LineWE CAN NOW MODEL INDIVIDUALPREFERENCES AND THEFINANCIAL CONSTRAINT C 5 B 1 2 3 4 5 6 Food
Consumer Equilibrium- Assume Consumers are Utility MaximisersThe tangency between the IC and thebudget line at Point C where the studentcan attain the highest possible utility giveEntertainment abudget constraint of €60 10 A BudgetThis is the highest possible utility given the Lineincome available.This point is referred to as CONSUMEREQUILIBRIUM C 5Higher IC’s are desirable but not attainablefor the given budget constraintLower IC’s do not maximise Utility B Food 1 2 3 4 5 6
IF THE PRICE OF FOOD INCREASES T0 €12M = Pf*Qf + Pe*Qe€60 = €10*3 + €6*5 at Point C EntertainmentConsumption Ration 3F:5EM = €60, Pf increases to €12, Pe remains 10 A Budgetconstant at €6. LineM/Pf = 60/12 = 5The Budget Line pivots from the Y axis inwardas the student can only purchase 5 units offood after the price increase. C 5The Student cannot now maximise utility Xat point C and moves to Point X, ICo4.5 units of E and 2.75 of Food IC1(less of both goods) B€60 = €12*2.75 + €6*4.5 at XNew consumption Ratio 2.75F:4.5E 1 2 3 4 5 6 Food
What if the PRICE OF FOOD INCREASES T0 €15M = P f Q f + P eQeM = €60, Pf increases to €15, Pe remains Entertainmentconstant at €6. A 10 BudgetM/Pf = 60/15 = 4 units of food LineThe Budget Line pivots from the Y axis inward as PCCthe student can only purchase 4 units of food afterthe price increase. Price ConsumptionThe Student cannot now maximize utility at 5 C Curvepoint X and moves to Point Y, 3.75 units of E Xand 2.5 of Food (less of both goods) Y ICo€60 = €15*2.5 + €6*3.75 at Y IC1New Consumption Ratio 2.5 F : 3.75 B2 B1 BE at point Y 1 2 3 4 5 6 Food
Derive a Demand Curve for Food for Kaitlin from Indifferent CurvesKaitlin has faced three prices for food.P = €10, P = €12 and P = €15To Draw a Demand Curve you need Prices & QuantitiesYou’ve got both P & Q on your IC’s & Budget Constraint for KateDerive Kaitlin’s Demand Curve for Food and her Price Consumption CurveYou Need only 2 Prices/2 Quantities to Draw a Demand Curve.
Deriving the Demand CurveQ of Entertainment M = €60, Pf = €10, Pe = €6 PCC IF Pf ↑ €12 If Pf ↑ €12 M/Pe @ €6 If Pf ↑ €15 IC 1 IC 2 IC 2 IC 3 Q of Food Price M/Pf @ €15 M/Pf @ €12 M/Pf @ €10 P= 15 P= 12 P= 10 Demand Curve for Food at 3 different prices Q
Budget Line & Changes in IncomeEntertainment 11 Budget Line when M = €60, Pfood = €10 ; PEnt = €6 10 Budget Line when M = €66, Pfood = €10 ; PEnt = €6 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 6.6 Quantity of Food
Income Consumption Curves (ICC) & Engel Curves Q Good Y 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 = €72 Engel Curve M = €66 The Relationship between the level of demand for good and the level of M = €60 income is known as an Engel curve Q Good X
Income & Substitution EffectsA change in Price of a good effects a The income effect of a price changeconsumers income. is the adjustment of demand to the change in real income alone. (BudgetIf Kate bought only food and food prices Line)fell, the max. she can buy is the ratio ofMoney Income to the Price of Food - The substitution effect of a priceM/Pfood. change is the adjustment of demand to the relative price change alone. (IC’s)If the Pfood increased it led to a decreasein purchasing power or real income. This is the effect of a change in the relative price ratio on the demand forThis income effect can lead to an a good.increase, decrease or no change in thedemand for food A rise in Pricefood changes the priceThe extent of the reduction in real ratio, reducing the demand for food, for the purchasing power available toincome is affected by the proportion of the individual.income spent on food.
Income & Substitution EffectsThe Income Effect: (p 78) The Substitution Effect: (p78)There is an effect on a consumers income This is the effect of a change in thewhen there is a change in the price of one or relative price ratio on the demand for aother of the goods. For example, suppose the good. If a rise in the price of X lowers the price ratio and this will reduce theconsumer only bought good X and the price demand for X, for a given level ofof it incresed. The maximum amount that he purchasing power available to theor she could buy is given by the ratio of individual.money income to the price of good X, M/PX,which will drop giving an decrease in The substitution effect is referred to aspurchasing power or real income. being ‘negative’ since the change in theThe income effect can lead to an increase, price ratio and the effect on demand fordecrease or no change in the demand for the X move in the opposite directions. (Ifgood as the extent of the rise in real income the price goes up the quantity demandedarising from a fall in the price of good X is goes down and vice versa)clearly affected by the proportion of thebudget spent on good X.
Income & Substitution Effects •Suppose a student gets €90per week of an allowance S/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, Good Y - Entertainment or have 3.6 units of entertainment and zero food, but they generally M/Py prefer combinations of both goods. 90/25 =3.6 Point A represents a student’s decision to consume 2 baskets of food and have 2 nights out. [€90 = €20*2+ 25*2] no saving The students consumption ratio is 2 Food : 2 Entertainment (A) Y0 = 2 A IC0 BL0 0 0 X 0= 2 M/PX=90/20 = 4.5 Good X (food)
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. Good Y - Entertainment The student can no longer be in equilibrium at point A, they do not have enough income. M/Py The students consumption ratio is now 90/25 1.5 units of Food : 1.8 units of Entertainment AY0 = 1.8 B IC0 0 BL0 0 X1= 1.5 X0= 2 Good X (food) Price effect of an increase in the price of Food
Price effect = Income + Substitution Effect The income effect of a price change is the adjustment of demand to the change in real income alone, measured along the Budget Line. Good Y - Entertainment The substitution effect of a price change is The students consumption ratio is now 1.5 Food : 1.8 Entertainment the adjustment of demand to the relative M/Py price change alone, measured along the 90/25 indifference curve. This is the effect of a change in the relative price ratio on the demand for a good. C A Y0 = 1.8 B IC0 0 BL2 BL1 BL0 0 X1= 1.5 X0= 2 Good X (food) A-B = Price Effect A-C = Substitution EffectC- B = Income Effect
Problem: Decompose a Price increase for food into and Income and Substitution Effect Draw M construction line parallel to new budget line a = €60 Entertainment Pf up €15 and at= €10 to original indifference curve IC1 Pf tangent 10 10The parallel line 9 8 7 6 5 4 A - B = Price Effect on Food 3holds the Pe = €6 2 1 9 0consumption ratioconstant A - C = Substitution Effect 8As it is at tangent B - C = Income Effect 7to original IC – youget the same level 6 Cof utility as you Ahad before the 5price increase. 4 B IC1 3 2 IC2 1 0 B 0 1 2 C 3 A 4 5 6 Food
Income and Substitution Effects Entertainment Decompose a – b (price effect) into income & substitution effecta to b = priceeffect on the 10 The parallel line holds the Draw a construction line parallel to B2 –quantity new budget line and at tangent to constant consumption ratio original 9demanded of indifference curve it is at tangent to original As IC1food as a result 8 IC – you get the same level ofof an increase in utility as you had before theprice of food 7 price increase. 6 B A 5 C IC1 4 3 IC2 2 1a – c = substitution 0 b a B2 B1effect 0 1 2 c 3 4 5 6 Foodc – b = income effect
Hicks versus SlutskyYou are a Business Manager Manager – You are a Business Manager Manager – The Consumer Price Index indicatesThe Consumer Price Index (CPI) Price Increases (Inflation) –indicates Prices Increase (Inflation) –You want to know how much Money – You want to know how much Money – Income must you compensate them forIncome must you compensate the the price increase to keep them on theirworkers for the price increase to original Bundle of Goodskeep them on their original level ofUtility Use Slutsky Compensation Variation inUse Hicks Compensation Variation Incomein Income
Compensation Variation in Income - Price Increase Good X Slutsky r Y/Py vs Hicks The Income decrease is called the s welfare loss at the new relative prices How much do have to compensate money income so that you can purchase original bundle after price t increase - Slutsky? Slutsky How much do have to compensate money C income so that you can attain original level of utility after price increase- Hicks? Hicks A B IC0 IC1 Y/Px1 Y/PxOriginally at point A on original IC maximising utility at Point A, P x increases, budget line pivotsinward to Y/Px1 . Consumer moves to Point B consuming less of good x, and relatively more ofgood y. Draw new budget line parallel to new BL at tangent to original indifference curve IC 0.
Hicksian Income Effect Good Y - Entertainment The students consumption ratio is now 1.5 Food : 1.8 Entertainment M/Py 90/25 Hicksian Income Effect C A Y0 = 1.8 B IC0 0 BL2 BL1 BL0 0 X1= 1.5 X0= 2 Good X (food) A-B = Price Effect A-C = Substitution EffectC- B = Income Effect
Slutsky and Hicksian Income Effect Good Y - Entertainment The students consumption ratio is now 1.5 Food : 1.8 Entertainment M/Py 90/25 Hicksian Income Effect C Slutsky Income Effect A Y0 = 1.8 B 0 IC0 BL3 IC1 BL1 BL0 0 X1= 1.5 X0= 2 Good X (food) A-B = Price Effect A-C = Substitution EffectC- B = Income Effect
Sample QuestionC2.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 OutcomesYou 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.
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