Chp 2 - Consumer choice

Question 1

What is the Walrasian budgetset?

Answer 1

B(p,w) = {x in R^L :px≤w}

Det här är alltså hela budgetsetet där budgetlinjen är själva kanten. Settet är allt på och under linjen.

Question 2

What are the three main restrictions for the consumer choice and so the main assumptions for walrasian demand function?

Answer 2

1. Walras law holds: The consumer always spends her entire budget.
2. Demand is homogeneous of degree zero: Only real opportunities matter.
3. Choice reveals information about stable preferences: WARP holds.

Question 3

What is Walras Law?

Answer 3

Studying Walras law: px(p,w) = w, we can conclude that an increase in $w$ will yield a proportional increase in consumption. This is because we exhaust all the budget. We also get that at least one good in the basket needs to be a normal good. The other conclusion we can draw is that an increase in $p$ will lead to both a wealth effect (we get porer and can consume less of everything) and a substitution effect where we will substitute away from the good from which $p$ increased, however, we will still exhaust all our budget.

Question 4

State WARP and explain what it mean

Answer 4

If px(p’w’) ≤ w and x(p,w) ≠ x(p’,w’), then p’x(p,w) > w’

If x is chosen over x’ in budget set B where both x and x’ are feasible bundles, but x’ is chosen over x when the consumer faces some other budget set B’, then x is not a feasible bundle in budget set B’.

Question 5

how that not all good can be (i) luxury goods, (ii) necessities or (iii) inferior goods.

Answer 5

See note and notion.

Question 6

What can be said regarding price-dispersion?

Answer 6

If nothing else is stated, we can assume that the indirect utility is quasi-convex in prices which implies that greater price dispersion will yield strictly greater utility. Intuitively, with price dispersion, the consumer can substitute substitute between goods and get higher utility than if all prices are fixed at some average price.

This is also true for firms profit. Here flexible prices are also better then fixed prices.

Question 7

What are the features of the Slutsky substitution matrix?

Answer 7

Symmetric
Satisfies s(p,w)p = 0 eller ps(p,w) = 0
Negative semi-definite