Revealed Preferences

Question 1

Revealed preferences - assumptions made (2)

Answer 1

Preferences do not change overtime
Monotonic & convex - preferred affordable bundle is unique

Question 2

Directly revealed preferred formula

Answer 2

If
P₁x₁ + p₂x₂ >= p₁y₁ + p₂y₂

Then (x₁,x₂) is revealed preferred to (y₁,y₂) since it means we have more of X than Y, and by monotonicity it is preferred.

Question 3

Indirectly revealed preferred example pg20

Answer 3

If X is directly revealed preferred to Y and Y is directly revealed preferred to Z, then by TRANSITIVITY X is revealed indirectly preferred to Z.

Question 4

Two axioms of revealed preferences

Answer 4

WARP

SARP

Question 5

What is the WARP condition

Answer 5

Necessary condition for economic rationality

If bundle X is directly revealed preferred to Y, then Y cannot be directly revealed preferred to X. (Sounds obvious)

Question 6

SARP

Answer 6

Necessary and sufficient condition

If bundle X is directly OR indirectly revealed preferred to Y, then Y cannot be directly or indirectly revealed preferred to X

(So same as warp but just adds indirectly revealed preferred)

Question 7

Example there WARP is violated (pg23)

Answer 7

They’re both under each others BC curves, so no direct revealed preference.

Question 8

Warp verified example (pg24) shows bundle X is better, as on a higher IC, thus is directly revealed preferred.

Question 9

When prices are (p₁, p₂) = (1,2) consumer Gardd demands 𝑥₁, 𝑥₂ = (1,2) and when prices are (𝑠₁, 𝑠₂) = (2,1) consumer Gardd demands 𝑦₁, 𝑦₂ = (2,1). Is this behavior consistent with economic rationality?

Answer 9

No. It violates WARP.

Using P prices, X costs 5, Y costs 4. So Y is affordable but he demanded bundle X, so X is directly revealed preferred. (Using FC2 formula)

But then using S prices, X costs 4, Y costs 5. X is affordable but he demands Y. So Y is directly preferred.

But this cannot be as it contradicts his choice earlier, so WARP is violated!!!

Question 10

When prices are (𝑝₁, 𝑝₂) = (2,1) consumer Mefus demands 𝑥₁, 𝑥₂ = (1,2) and when prices are (s₁, s₂) = (1,2) consumer Mefus demands y₁, y₂ = (2,1). Is this behavior consistent with economic rationality?

Finally, which one is better?

Answer 10

Yes.

At prices (𝑝₁, 𝑝₂) bundle X costs 4 and bundle Y costs 5; X is chosen when Y is not affordable.

At prices (𝑠₁, 𝑠₂) bundle X costs 5 and and bundle Y costs 4; Y is chosen when X is not affordable.

We found no contradiction (and we cannot say which bundle is “better”).

Question 11

Pg29 - checking WARP in data tables

Answer 11

Circled = directly revealed preferred.
Here we can see at prices 1 (1,2) shown by table above, the bundle that costs 5 is demanded. This means bundle 3 (6) is not affordable. Bundle 2 (4*) is affordable but wasn’t demanded, so bundle 1 is directly preferred to bundle 2.

Question 12

Pg30 checking SARP

Answer 12

Diagonal represents bundles chosen at the different price levels.

Looking at price 1, bundle 1 (costing 20) chosen. Meaning bundle 3 (22*) is unaffordable, and bundle 2 is affordable but wasn’t chosen, hence bundle 1 is directly revealed preferred.

Looking at price 2, bundle 2 is chosen. Bundle 1 is unaffordable in this instance, bundle 3 is affordable but not chosen, and so bundle 2 is directly revealed preferred to bundle 3.

By transitivity, as 1>2 and 2>3, 1>3 so we give bundle 3 (*)

Question 13

How to work out hypothetical income M’

Answer 13

M’ = M + ΔM = m + ΔPaA

ΔPaA is the change in prices (e.g used to be Pa=1 now Pa=6)
And A is the original quantity of A demanded.

Question 14

Sluy’s substitution effect formula

Answer 14

Difference between hypothetical consumption and initial consumption.

Hyp C - Initial C