Microeconomics Lecture 4 PDF

Decomposition of the Total Effect into Substitution and Income Effects and Application of Consumer Theory Lecture 4 Lecturer: Priscilla T. Baffour (PhD) Priscilla T. Baffour (PhD) 1  Income and Substitution Effects In a demand relationship...

Decomposition of the Total Effect into Substitution and Income Effects and Application of Consumer Theory Lecture 4 Lecturer: Priscilla T. Baffour (PhD) Priscilla T. Baffour (PhD) 1  Income and Substitution Effects In a demand relationship the quantity consumed changes with price but what does the quantity change actually consist of? Substitution Effect - substitute other goods for A as Price of A rises Income Effect - as price of A falls, real income rises and so spend more on all goods Priscilla T. Baffour (PhD) 2  Application to Different Types of Goods Direction and size of effects varies with type of good Normal Good - as price falls, consumption rises - as income rises, consumption rises Inferior Good - as price falls, consumption rises - as income rises, consumption falls Giffen Good - as price falls, consumption rises - as income rises, consumption falls Priscilla T. Baffour (PhD) 3 Other Goods Normal Good U2 Subs: 1 to 3 or A to C (-ve) U1 Income: 3 to 2 or C to B (-ve) Price effect: A to B or 1 to 2 B A C BC2 1 3 2 BC1 BC3 QA Priscilla T. Baffour (PhD) 4 Other Inferior Good Goods Subs: 1 to 3 or A to C (-ve) Income: 3 to 2 or C to B (+ve) Price effect: A to B or 1 to 2 B A C U2 U1 BC2 QA 1 2 3 BC1 BC3 Priscilla T. Baffour (PhD) 5  Giffen Good Other Goods Subs: 1 to 3 or A to C (-ve) Income: 3 to 2 or C to B (+ve) Price effect: A to B or 1 to 2 B A U2 C U1 BC2 2 1 3 BC1 BC3 QA Priscilla T. Baffour (PhD) 6  Income and Substitution Effects Slutsky equation Total effect of price change = SE + IE Slutsky’s theorem states that the substitution effect of a price change (relative to quantity) is negative. We isolate the substitution effect by taking away from (giving) the consumer enough money to put her at the same level of satisfaction as before the price change. Priscilla T. Baffour (PhD) 7  Income and Substitution Effects Total effect of a price change for: – normal good is negative. Because the negative IE reinforces the already negative SE. For price fall, quantity DD increases. – Inferior good is still negative, but –SE > +IE. Quantity DD increases but less than the case for normal goods – Giffen good is positive because –SE < +IE. Quantity DD falls. Priscilla T. Baffour (PhD) 8  Labor-Leisure Choice Leisure - all time spent not working. The number of hours worked per day, H, equals 24 minus the hours of leisure or nonwork, N, in a day: H = 24 − N. – The price of leisure is forgone earnings. The higher your wage, the more an hour of leisure costs you. Priscilla T. Baffour (PhD) 9  Labor-Leisure Choice: Example Jackie spends her total income, Y, on various goods.  The price of these goods is $1 per unit. Her utility, U, depends on how many goods and how much leisure she consumes: U = U(Y, N) Jackie’s earned income equal: wH And her total income, Y, is her earned income plus her unearned income, Y*: Y = wH + Y* Priscilla T. Baffour (PhD) 10  (a) Indifference Curves and Constraints Time constraint Y , Goods per day Figure 5.8 Demand for Leisure I1 Budget Line, L1 L1 Y = w1H –w1 1 e1 Y1 0 N1 = 16 24 N, Leisure hours per day Y = w1(24 − N). 24 (b) Demand Curve H1 = 8 0 H, Work hours per day Each extra hour of leisure w, Wage per hour she consumes costs her w1 goods. w1 E1 0 N1 = 16 N, Leisure hours per day H1 = 8 H, Work hours per day Priscilla T. Baffour (PhD) 11  (a) Indifference Curves and Constraints Y, Goods per day I2 Time constraint Figure 5.8 Demand for L2 Leisure –w2 1 I1 e2 Y2 Budget Line, L1 L1 Y = w1H –w1 1 e1 Y1 0 N2 = 12 N1 = 16 24 N, Leisure hours per day Y = w1(24 − N). 24 (b) Demand Curve H 2 = 12 H1 = 8 0 H, Work hours per day w, Wage per hour Budget Line, L2 E2 w2 Y = w2H Y = w2(24 − N). w1 E1 Demand for leisure w2 > w1 0 N2 = 12 N1 = 16 N, Leisure hours per day H 2 = 12 H1 = 8 H, Work hours per day Priscilla T. Baffour (PhD) 12 Supply Curve of Labor Priscilla T. Baffour (PhD) 13 Income and Substitution Effects of a Wage Change (Increase) Y , Goods per d ay I2 Time const raint L2 Since income effect is I1 positive, leisure is a normal good. L* e2 e* L1 e1 0 N* N1 N2 24 N, Leisure hours per d ay 24 H* H1 H2 0 H , Work hours per d ay Substitution effect Total effect Income effect Priscilla T. Baffour (PhD) 14  Backward Bending Labor Supply Curve (a) Labor-Leisure Choice (b) Supply Curve of Labor Supply curve of labor Y , Goods per d ay w, Wage per hour L3 I3 Time const raint E3 I2 E2 I1 e3 L2 e2 E1 L1 e1 24 H2 H H1 0 0 H1 H3 H2 24 3 H , Work hours per d ay H , Work hours per d ay butlow At at high wages, wages, an increase an increase in the in the wage causes the worker to work more…. less…. Priscilla T. Baffour (PhD) 15  Ordinary curve vrs Compensated demand curve Compensating variation ensures that the consumer remains on the same IC. DDc is steeper than ordinary DDo curve. The slope of the DDc curve is higher in value for a normal good. The Hicksian demand function. Ordinary DDo curve considers both the Substitution and Income effects. The DDo is flatter. The slope of the DDo curve is smaller. The Marshallian demand function. The Marshallian demand function is the ordinary market demand function we have been discussing all along. Priscilla T. Baffour (PhD) 16 Other Goods Normal Good U2 Derive the Ordinary and Compensated Demand curves from this diagram U1 B A C BC2 1 3 2 BC1 BC3 QA Priscilla T. Baffour (PhD) 17 Ordinary curve vrs compensated demand curves Compensating variation ensures that the consumer remains on the same IC. DDc is steeper than ordinary DDo curve. The slope of the DDc curve is larger for a normal good. This is the Hicksian demand function. Ordinary DDo curve considers the effect of IE. The DDo is flatter. The slope of the DDo curve is smaller. This is the Marshallian demand function. The Marshallian demand function is the ordinary market demand function we have been discussing all along. Priscilla T. Baffour (PhD) 18  Marshallian and Hicksian demand functions Marshal: maximize utility subject to income constraint. D=f(P, I) Hicks: minimize budget constraint subject to utility. D=f(P, U) Given U=f(XaYb), and I = PxX + PyY, Try and derive both demand functions Priscilla T. Baffour (PhD) 19  Gross substitutes and gross complements If goods X and Y are both normal goods and if Px falls, the IE and SE would both encourage the consumer to buy more of X, but the gross (combined) effect on Y is ambiguous. IE encourages the consumer to buy more of Y SE encourages the consumer to buy less of Y If SE > IE, he will buy less of Y = X & Y are gross substitutes If SE < IE, he will buy more of Y = X & Y are gross complements Priscilla T. Baffour (PhD) 20  Application of Consumer Theory Cont. Compensating variation (CV) measures welfare loss to the consumer as a result of an increase in price by estimating the amount of money needed to compensate the consumer by restoring him/her to his/her initial utility before the price change. Simply, CV measures the amount of money a consumer will need to accept a price change. Equivalent variation (EV) on the other hand measures the amount of money needed to be taken away from the consumer to reduce his/her welfare just as would have resulted from the increase in price. In other words, the EV measures the amount of money a consumer is willing to sacrifice to avoid a price change. Priscilla T. Baffour (PhD) Slide 21  Compensating Variation CV is positive when there is a price increase, it tells the amount of money to be given to restore consumers to their initial utility level. Thus, the CV measures how much a consumer is made worse off as a result of the increase in price. CV is negative when there a price decrease, it tells the amount of money to be taken from the consumer to restore him or her to his or her original utility. Here, CV measures how much the individual is made better off due to the decrease in price. This is equivalent to EV of an increase in price. Priscilla T. Baffour (PhD) Slide 22  Compensating Variation Graphical representation of CV (Increase in Price) Y CV P1 > P0 B2 B1 B0 E2 E0 E1 U0 U1 P0 P1 X Priscilla T. Baffour (PhD) Slide 23  Compensating Variation Where; 𝑈 0 , 𝑃0 , 𝐸 0 , and 𝐵0 are the initial utility, price, equilibrium, and budget line respectively. With the increase in price, the new price (𝑃0 ) shifts the budget line inwards ( 𝐵1 ). The new equilibrium and utility are represented by 𝐸1 and 𝑈1 respectively. For the consumer to enjoy the same utility (𝑈 0 ), another budget line (𝐵2 ), tangential to the initial indifference curve (𝑈 0 ) and parallel to the new budget line (𝐵1 ) is drawn. Priscilla T. Baffour/ F.K. Agyire-Tettey Slide 24  Equivalent Variation EV is positive when there is a decrease in price. This is equivalent to CV of an increase in price. Similarly, EV is negative when there is an increase in price. It is equivalent to CV of a decrease in price. Although utilities are ordinal, it does not affect the value of the compensating variation. Priscilla T. Baffour (PhD) Slide 25  Equivalent Variation Graphical representation of EV (Increase in Price) Y EV P1 > P0 U0 U1 P0 P1 X Priscilla T. Baffour (PhD) Slide 26  Equivalent Variation Where; 𝑈 0 , 𝑃0 , 𝐸 0 , and 𝐵0 are the initial utility, price, equilibrium, and budget line respectively. With the increase in price, the new price (𝑃0 ) shifts the budget line inwards ( 𝐵1 ). The new equilibrium and utility are represented by 𝐸1 and 𝑈1 respectively. Get know how much to take from the consumer to make him/her equally worse off as the price increase does, , another budget line (𝐵2 ), tangential to the new indifference curve (𝑈1 ) and parallel to the initial budget line (𝐵0 ) is drawn. The difference between the old budget line 𝐵0 and the new budget line 𝐵2 is Equivalent variation. Priscilla T. Baffour (PhD) Slide 27  Comparison Between EV and CV Y CV P1 > P0 EV U0 U1 P1 P0 X Priscilla T. Baffour (PhD) Slide 28  Comparison Between EV and CV Properly drawn, we expect that the EV and the CV will not be the same. Hence, the EV and CV provide varying estimates of the cedi value between the two curves. The difference between the EV and CV is due to the fact that the two measures use different sets of relative prices to estimate the welfare loss. Priscilla T. Baffour (PhD) Slide 29  Application of EV and CV Let’s suppose; – The government in an attempt to encourage agriculture, subsidizes an agricultural input (x) by s per each unit of x. This implies an outward shifting of budget line since the subsidy reduces the price of input x. – In addition to consuming commodity x, individuals consume other commodities (y). – Input x is plotted on the horizontal axis and other commodities consumed on the vertical axis. This is shown by the figure in the next slide. Priscilla T. Baffour (PhD) Slide 30  Application of EV and CV Y EV P1 < P0 B2 B0 Yb B1 Ya E2 E1 E0 U1 U0 P1 P0 Xa X1 X Priscilla T. Baffour (PhD) Slide 31  Food subsidy or supplementary income? Food subsidy enables the consumer to buy at half the market price. The budget line rotates outward. The consumer ends up buying more than at the initial equilibrium. Supplementary income shifts the budget line to the right to touch a higher IC. The consumer buys more quantities than at the initial equilibrium The cost of food subsidy is greater than the cost of supplementary income. The quantity of goods bought under food subsidy is greater than supplementary income. Choosing one of these policies depends on the other goals of government and the indirect effects of each policy. Priscilla T. Baffour (PhD) 32 Edgeworth Box (Efficiency of Exchange) Priscilla T. Baffour (PhD) 33 The End Priscilla T. Baffour (PhD) 34