1. Questions 1 & 2 Individual A Perfect 1:1 substitutes
x-axis: one particular good
p1 = 0.8
y-axis: all other goods
money, given that p2 = 1
M = 120
Therefore, can consume (at extremes) 150 units of good 1, costing 0.8 per unit, or 120 units of “all other goods”/money
or any combination along budget line

2. Purple lines – indifference curves
Budget constraint: M = 120, p1 = 0.8
Qmoney
Qgood

3. Questions 3 & 4 Mostly the same as before
Individual A has perfect 1:1 substitutes as prefs
x-axis: one particular good
p1 = 1.2
y-axis: all other goods
money, given that p2 = 1
M = 120
Therefore, can consume (at extremes) 100 units of good 1, costing 1.2 per unit, or 120 units of “all other goods”/money
or any combination along budget line

4. Purple lines – indifference curves
Budget constraint: M = 120, p1 = 0.8
Qmoney
Budget constraint: M = 120, p1 = 1.2
Qgood

5. Why is the new IC lower than the old IC?
In general terms:
Increase in price of one good reduces feasible set
Perfect 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?

7. 30 Budget constraint: M = 120, p1 = 0.8 Qmoney
Qgood

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 bundle
Consider 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?

10. 24 Budget constraint: M = 120, p1 = 0.8 Qmoney
Qgood

11. Area ≈ ( ) * ( * 30)
≈ 0.2 * 135
≈ 27 6
Price Q1

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 P
CV and EV both positive
Individual is better off at old price
CV > EV and |CV| > |EV|
Fall in P
CV and EV both negative
Individual is better off at new price
CV > 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 = 0
If 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 good
p1original = 0.8, then p1new = 1.2
y-axis: all other goods
money, given that p2 = 1
M = 120
Q consumed of either good = M/(p1 + p2)
At original prices, 120/( ) =
At new prices, 120/( ) =

15. Budget constraint: M = 120, p1 = 0.8
Qmoney
Budget constraint: M = 120, p1 = 1.2
Qgood

16. CV=
Qmoney
Qgood

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 proportions
Therefore no substitution effect
Total effect = income effect
CV uses new prices => CV = increased cost

18. Qmoney
EV=
Qgood

19. EV < CV
Perfect 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 * ( )
≈ 24.2
Price
Change in surplus again between CV and EV Q1

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) ( )
≈ 51
As before!
D for Perfect substitutes
D for Perfect complements
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: Which is approximately 51