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Questions 1 & 2

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- 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

Purple lines – indifference curves

Budget constraint: M = 120, p1 = 0.8

Qmoney

Qgood

- 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

Purple lines – indifference curves

Budget constraint: M = 120, p1 = 0.8

Qmoney

Budget constraint: M = 120, p1 = 1.2

Qgood

- 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

- “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?

Budget constraint: M = 120, p1 = 0.8

30

Qmoney

Budget constraint: M = 120, p1 = 1.2

Qgood

- “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?

- 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?

Budget constraint: M = 120, p1 = 0.8

Qmoney

24

Budget constraint: M = 120, p1 = 1.2

Qgood

Area ≈ (1 - 0.8) * (120 + 0.5 * 30)

≈ 0.2 * 135

≈ 27

6

Price

Q1

- 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|

- 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).

- CV = EV = ΔCS if and only if p > a for both original and new prices.

- 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/(0.8 + 1) = 66.66...
- At new prices, 120/(1.2 + 1) = 54.5454...

Budget constraint: M = 120, p1 = 0.8

Qmoney

Budget constraint: M = 120, p1 = 1.2

Qgood

CV=26.66...

Qmoney

Qgood

- “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 66.6666… equals 26.666….) 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

Qmoney

EV=21.818...

Qgood

- 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.

Area ≈(1.2 - 0.8) * (54.54... + 0.5 * (66.66... - 54.54...))

≈0.4 * (54.54... + 6.06...)

≈24.2

Price

Change in surplus again between CV and EV

Q1

- Summed (“aggregate”) demand looks like this:

- Loss of surplus:

Area ≈(0.2)(54.54)+(0.2)(0.5)(60-54.54)+(0.2)(180)+(0.2)(0.5)(216.67-180)

≈ 51

As before!

D for Perfect substitutes

D for Perfect complements