Presentation on theme: "Questions 1 & 2 Individual A Perfect 1:1 substitutes"— Presentation transcript:
1 Questions 1 & 2 Individual A Perfect 1:1 substitutes x-axis: one particular goodp1 = 0.8y-axis: all other goodsmoney, given that p2 = 1M = 120Therefore, can consume (at extremes) 150 units of good 1, costing 0.8 per unit, or 120 units of “all other goods”/moneyor any combination along budget line
3 Questions 3 & 4 Mostly the same as before Individual A has perfect 1:1 substitutes as prefsx-axis: one particular goodp1 = 1.2y-axis: all other goodsmoney, given that p2 = 1M = 120Therefore, can consume (at extremes) 100 units of good 1, costing 1.2 per unit, or 120 units of “all other goods”/moneyor any combination along budget line
5 Why is the new IC lower than the old IC? In general terms:Increase in price of one good reduces feasible setPerfect substitute preferences imply all income is spent on one good (unless a = p1/p2 where 1:a is form of preferences)Shift in relative prices reduces consumption of good 1 => welfare effects will be negative
6 Compensating variation – new prices “This is the amount of money we need to give to the individual to restore him or her to the same level of happiness (the same indifference curve) as before the price rise.”Draw in parallel shift of new budget constraint until we hit the original indifference curve.What is the associated increase in income that this implies?
8 Why is this less than the increased cost of the originally purchased bundle of goods? “Originally the individual bought 150 units of the good – costing 120 at the original price and 180 at the new price”Individual substitutes away from good 1 and purchases good 2.Utility vs income, constrained to buy one bundleConsider case where budget constraint shifted out until it passes through original bundle of goods (Slutsky decomposition – Chapter 19.8)Pasty tax?
9 Question 5 – equivalent variation (old prices) Same problem as questions 1-4, only concentrating on equivalent variation rather than compensating variation.“Calculate the equivalent variation – this is the amount of money that we need to take away from Individual A at the original prices to have the same impact on his or her welfare as the price rise.”Draw in parallel shift of old budget constraint until we hit the new indifference curve.What is the associated decrease in income that this implies?
12 CV ≠ EV (generally...) Look at things from two different perspectives CV – new price (old level of utility)EV – old price (new level of utility)Rise in PCV and EV both positiveIndividual is better off at old priceCV > EV and |CV| > |EV|Fall in PCV and EV both negativeIndividual is better off at new priceCV > EV but |CV| < |EV|
13 What about QLP / PS? Ignore possibility of corner solutions with QLP shifting of budget constraint to calculate either CV or EV will always produce same value (D ⊥ Y).PS always (well...) has corner solutions.CV = EV = ΔCS if and only if p > a for both original and new prices.CV = EV = ΔCS = 0If p ≤ a for at least one price, we have different corner solutions (or multiple solutions if p = a).
14 Questions 8-9 Individual B Perfect 1:1 complements x-axis: one particular goodp1original = 0.8, then p1new = 1.2y-axis: all other goodsmoney, given that p2 = 1M = 120Q consumed of either good = M/(p1 + p2)At original prices, 120/( ) =At new prices, 120/( ) =
15 Budget constraint: M = 120, p1 = 0.8 QmoneyBudget constraint: M = 120, p1 = 1.2Qgood
17 CV = increased cost“Note that the compensating variation in this case is exactly equal to the increased cost of the originally purchased bundle of goods. (0.4 times … equals ….) Why?”Perfect complementarity means goods must be purchased in fixed proportionsTherefore no substitution effectTotal effect = income effectCV uses new prices => CV = increased cost
19 EV < CVPerfect complements => no substitution effect, so move between same two bundles when measuring CV and EV.Always consume positive quantity of each good.Because price of one good changes, cost of purchasing must be lower with lower prices.
20 Price Area ≈ (1.2 - 0.8) * (54.54... + 0.5 * (66.66... - 54.54...)) ≈ 0.4 * ( )≈ 24.2PriceChange in surplus again between CV and EVQ1
21 Question 10 Summed (“aggregate”) demand looks like this: p = 1.2; D = p = 1 ; D between 60 and 180 p = 0.8; D = Then it is quite simple to evaluate the surplus loss: (0.2)(54.54)+(0.2)(0.5)( )+(0.2)(180)+(0.2)(0.5)( ) Which is approximately 51
22 Question 10 Loss of surplus: Area ≈ (0.2)(54.54)+(0.2)(0.5)( )+(0.2)(180)+(0.2)(0.5) ( )≈ 51As before!D for Perfect substitutesD for Perfect complementsp = 1.2; D = p = 1 ; D between 60 and 180 p = 0.8; D = Then it is quite simple to evaluate the surplus loss: Which is approximately 51