A model of rationality

Question 1

Completeness

Answer 1

• an assumption by which the decision maker, given two choices in their set of alternatives, can always compare between them
• they can be indifferent between the two, or prefer one over the other, but cannot simply not choose between a given set of alternatives

Question 2

Transitivity

Answer 2

• assume that if an individual prefers a to b, and b to c, that they must prefer a to c

Question 3

Continuity

Answer 3

• technical assumption
• don’t need to know

Question 4

why use the assumptions of completeness, transitivity and continuity?

Answer 4

• so that preferences can be represented using a utility function

Question 5

non-satiation

Answer 5

• a consumer always prefers more of a good to having less of a good, all else equal
• if du/dx1>0 and du/dx2>0, then increasing x1 and/or x2, increases utility and non-satiation is therefore staisfied
• a consumer must strictly prefer a bundle for which they can consume more of both goods
• key implication: indifference curves are downwards sloping, and preferred set is above the indifference curve

Question 6

convexity

Answer 6

• given non-satiation, convexity is satisfied if the preferred set (shaded area) is a convex set
• a set is convex if the straight line joining any two points in the set, lies in the preferred set
• key implication - preference for averages

Question 7

why do we need to assume non-satiation and convexity

Answer 7

• guarantee interior solutions exist

Question 8

exogenous

Answer 8

• variables that are fixed in our model
• income and the price tends to be fixed

Question 9

endogenous

Answer 9

• variables that we are trying to solve for
• trying to make predictions on these variables
• the demand is the endogenous variable in most models of an individual’s decisions

Question 10

if the price of the good on the y axis increases, describe the Hick income and substitution method for decomposing this change

Answer 10

• Neutralising the income effect by bringing the new budget constraint curve up to where it first hits the indifference utility curve, so that even after the price change, the consumer gets the same utility
• New point of consumption would be where the indifference curve is tangent to the line. Move from A to A’ is a substitution effect – they have the same level of utility from A to A’, therefore the income effect has been neutralised.
• Between A to A’, the bundle of goods that you are consuming has changed – getting same utility from different combination of goods – substitution effect
• Move from A’ to B is the income effect – no price ratio changes, but just an income effect – taking money away from the student

Question 11

if the price of the good on the y axis increases, describe the Slutsky income and substitution method for decomposing this change

Answer 11

Slutsky
* Wants to decompose the move from A to B, neutralising the income effect
* Starting with new budget line, taking this line up to the original point A, where the consumer can buy the same bundle as before (A)
* Consumer would reoptimize, and would have a new indifference curve to maximise their utility
* Substitution effect will always drive the consumer to buy more of the good that is relatively cheaper
* Income effect – depending on whether the good is inferior/normal, will affect how the consumer acts, as their income changes
* The location of B will depend on which force is stronger, the income effect or the substitution effect, whether the goods are normal/inferior

Question 12

what is the difference between the slutsky method and the hicks method

Answer 12

• Hicks method brings new budget constraint curve up to where it is tangent to the indifference curve allowing the consumer to achieve the same utility as before, while the Slutsky method raises the line even higher, so that the consumer can consume the same bundle it was previously consuming

Question 13

income effect when good is normal

Answer 13

• increase in income –> increase in consumption of the good
• decrease in income –> decrease in consumption of the good

Question 14

income effect when good is inferior

Answer 14

• increase in income –> decrease in consumption of the good
• decrease in income –> increase in consumption of the good

Question 15

how can we measure the effect of a price change on the consumer?

Answer 15

1. Compensating variation: compensate the individual, give them money such that they will be exactly as well off as before the price change
2. Equivalent variation: how much would the consumer be willing to pay, to avoid the price change
3. Consumer surplus: quickest and easiest way

Question 16

what is the compensated demand

Answer 16

• abstract concept
• dotted line we draw for income and substitution effect of hicks
• minimises the cost of obtaining a certain level of utility
• e.g., fixing the indifference curve, and finding the lowest budget constraint such that it still touches the indifference curve - giving the individual the least amount of money such that they can still enjoy a certain level of utility

Question 17

uncompensated demand function?

Answer 17

• maximises utility given prices p1 and p2 and income m
• fixed budget line - choosing the indifference curve with the highest utility, but which still touches the line, and so is therefore tangent to the budget constraint

Question 18

giffen good

Answer 18

• Goods for which, as the price of the good increases, its demand also increases.
• this is where the income effect outweighs the substitution effect

Question 19

how can we evaluate these ways of measuring how price changes affect utility

Answer 19

• IF there is no income effect, or IF the price change is small, then the consumer surplus, compensating variation and equivalent variation are the same
• Consumer surplus – in between the two other measures – whether CV or EV are bigger depends on whether the good is normal or inferior

Question 20

If income changes in line with the base weighted index, and we assume that all consumers consume the same consumption bundle then:
A) consumer is neither better off nor worse off
B) consumer cannot be worse off, but may be better off
C) Consumer cannot be better off, but may be worse off
D) consumer is definitely better off

Answer 20

D - if income changes in line with the base weighted index, then the consumer cannot be worse off, because this means that you can still consume the same consumption bundle as before - sum of basket of goods changes to p1Bx1A + p2Bx2A, but so does your income
- but if consumers can substitute, then the new budget constraint will allow consumers to reoptimise to obtain a higher utility, because the gradient of the line will be different

Question 21

explain how for giffen goods, an increase in prices leads to an increase in demand for that good
- using hicks decomposition explanation

Answer 21

• Hicks method. Move the second budget constraint parallel to this curve, so that it intersect point A. New optimal point of consumption will be A’
• This is the substitution effect – moves the consumer to buying more of X, since price of Y goes up
• Move from A’ to B is unusual – consumption of x decreases, and consumption of Y increases.
• Individual experiences a fall in their income – therefore, naturally the consumption of X will decrease (consistent with x being a normal good). But they buy more of Y (consistent with Y being an inferior good)
• For an increase in the price of Y to lead to an increase in the consumption of Y, Y must be inferior, and the income effect must be greater than the substitution effect, since the substitution effect leads to a decrease in the consumption of Y, and the Income effect leads to an increase in consumption of Y
• Giffon goods

Question 22

first degree price discrimination

Answer 22

• Charge each citizen according to their willingness to pay for the good
• Problems: enforcement, and fact that you need to know what other people’s willingness to pay is
• Different price to each individual based off their willingness – corresponding point on the demand curve

Question 23

second degree

Answer 23

• special offers, cheaper if bought in bulk
• different price for different quantities – based on MR=MC in market for each group

Question 24

third degree price discrimination

Answer 24

• separated by membership – different price for different people
• market for members, market for non-members
• by segmenting the market, profits will be higher than a simple monopolist. Able to produce more, making use of what was perhaps previously spare capacity, allowing the firm to be more efficient with its factors of production. Leads to lower long run average costs.

Question 25

substitution and income effect - applied to labour supply
- what happens when leisure is inferior compared to when leisure is normal

Answer 25

If leisure is normal, then for a wage rise, the income effect will be positive, so the individual will work less according to the income effect

if leisure is inferior, then for a wage rise, the income effect shows how the individual will work more.

Question 26

effects of Robots and AI on wages and employment
- productivity effect
- displacement effect

Answer 26

Displacement effect: negatively by directly
displacing workers from tasks they were
previously performing

Productivity effect: positively because other
industries and/or tasks increase their demand
for labour