Week 4 - Consumer theory Flashcards
Where does the demand curve come from?
consumers
Where does the supply curve come from?
producers
What are the 3 steps of what bundles of goods makes you best off?
- Preferences
- Budget constraints
- Put them together
What is a consumption bundle
(basket of goods) is a complete list of quantities for all available goods
What is the notation of a typical consumption bundle?
X = (x , x , x )
B C F
Eg A = (2, 5, 1) or A = (2 bananas, 5 coconuts, 1 fish)
What are the x and y axis of the consumption model eg?
eg
x = pizza
y = coke
What are the 3 ways of comparing a consumption bundle by any individual (preferences)?
If bundle A is strictly preferred to bundle B, then A>B
If bundle A is weakly preferred to bundle B, then A≥ B
If the individual is indifferent between A and B, then A~B
What are the three assumptions about individual preferences?
- Completeness
- Transitivity, Reflexivity
- Non-satiation, diminishing marginal utility
What is the completeness assumption?
for any pair of available consumption bundles X and Y, the individual can say whether X≥Y or Y≥X (or both)
What is the transivity assumption?
for any three consumption bundles, X, Y, Z
X≥Y and Y≥Z imply X≥Z
What is reflexivity?
(within transitivity)
for identical consumption bundles, there is no strong preference for either of them X~X
What is the non-satiation assumption?
more is better than less (at least more is no worse than less)
What does it mean if the bundle is further away from the axis on the preference graph
the ‘better’ they are, prefer those bundles (get more quantity)
What is the utility function?
it assigns each consumption bundle an index number of happiness (=total utility)
How can the utility function U(X) be used for any two consumption bundles?
for any two consumption bundles, X and Y, the utility function can be used to extract the individual’s preferences as follows:
if U(X) > U(Y) then the individual strictly prefers bundle X to Y
if U(X) = U(Y) then the individual is indifferent between consumption bundles X and Y
the utility function can take a variety of mathematical forms (to compare different assumption models)
What is the ordinal utility?
means that only the ranking of utility levels has a meaning - the difference between utility levels is meaningless
U(A) = 20 and U(B) = 40 does not mean that the individual prefers bundle B twice as much as A
What does it mean to be indifferent between X and Y?
if you neither prefer X to Y, nor Y to X, you are indifferent between X and Y, and you derive the same utility from both bundles:
U(X) = U(Y)
What shape are indifference curves?
always downward sloping
What is an example of axis on an indifference curve?
Pizza and coke
eg X1 = (3,4) and X2 = (4,3)
make a rectangle, both have utility of 12
all being utility of 12 means this individual is indifferent to all of these consumption models as they have the same utility
Where does the second indifference curve go when it has a greater utility than the other curve?
above, further away the better
higher utility levels lie further outwards (to the origin)
one indifference curve for each utility level
Why cant indifference curves cross example?
Eg
A and B on the same indifference curve A~B
B and C on the same indifference curve B~C
By transitivity A~C
But A is on a higher indifference curve than C
So A>C
What is marginal utility?
the additional utility generated by an additional unit of the good, holding the quantities of all other goods constant
How do you mathematically calculate the marginal utility of a good?
it is the partial derivative of U(x_1,…,x_n) with respect to x
MU_L = ∂U(x_1,…x_n) / ∂x_i
What is the diminishing marginal utility?
as an individual consumes more and more of some good, the additional utility gained from an additional unit of consumption decreases
What is the marginal rate of substitution?
how much of one good a consumer will give up to get a bit more of another good (trade off)
What does the marginal rate of substitution measure between any two goods 1 and 2 (MRS_1,2)?
measures how many units of good2 the individual is willing to give up (substitute) for 1 additional unit of good1, such that utility remains constant
What is the marginal rate of substitution equation?
MRS_1,2 = MU_1 / MU_2
Eg Q
Suppose that the additional utility Ted gains from an additional slice of pizza is 4. (Marginal utility of pizza is 4). The marginal utility of Coke is 3
How many cokes is Ted willing to give up to get an additional slice of pizza?
1 coke is 3 units of utility
1/3 of a coke is 1 unit of utility
1 and 1/3 of a coke is 4 units of utility
If you are giving up 1 and a 1/3 of coke, you will be losing 4 units of utility
So after the trade, gaining one slice of pizza (4 units of utility) and losing 1 and a 1/3 units of coke (4 units of utility), utility levels will be the same
Willing to give 4/3 cokes for 1 pizza slice
Pizza utility = 4 Coke utility = 3
MRS_p,c = MU_p / MU_c
(also the gradient of the indifference curve △y/△x
4/3 coke / 1 pizza)
What changes as you move along the indifference curve?
the marginal rate of substitution
How do we find the slope of the indifference curve?
draw a tangent at that point, find gradient
as you consume more and more pizza, coke is going to be more valuable so less willing to give up coke
Why is the MRS is typically decreasing?
If i have alot of coke, but little pizza, an additional slice of pizza is worth a lot of coke. MRS_p,c is large
If i few cokes, but a lot of pizza, then an additional slice of pizza isnt worth many cokes. MRS_p,c is small
What are budget constraints
individuals have money, income or a budget to finance consumption, denote this budget as m (assuming no savings), constraint individuals face stopping buying everything you want
What is an assumption budget constraints have on individuals?
assume the budget/ income an individual has, they want to spend all that money, no savings
What is the total expenditure for the consumption bundle?
Expenditures for consumption bundle X=(x_1 x_2)
Total expenditure of each consumption bundle depends on the price of each good and number of goods you consume
Total expenditure: E(X) = p1 x x1 + p2 x x2
(^price of good x no. you consume)
Eg p1 = £9 p2= £1 E(3, 4) = 27 + 4 = £31
How do individuals make a judgement whether they can afford this consumption bundle?
if the amount of money the individual has is greater or equal to the expenditure of the consumption model then you can afford it
so, any consumption plan X is feasible if its expenditure doesnt exceed the budget, ie m≥ E(X)
What is the budget set?
consists of all feasible consumption plans
consists of all bundles (x_p ; x_c) satisfying the budget constraint
ie m≥ (p_p) x (x_p) + (p_c) x (x_c)
What is the budget line?
represents all the consumption bundles that exhaust the consumers income (no saving and no borrowing)
ie m= (p_p) x (x_p) + (p_c) x (x_c)
or x_c = (m/p_c) - (p_p/p_c) x (x_p)
How do you visualise the budget set?
on a graph
number of consumptions of each good on the two axis
budget line is the line on the graph (downward sloping)
budget set is the area under the line
Budget set graph example
pizza x axis x_p
coke y axis x_c
p_p = £3
p_c = £1
m = £9
Budget set: 3x_p + x_c ≤ 9
or x_c ≤ 9 - 3x_p
Budget line x_c = 9 - 3x_p
(bundles below this line can afford)
How do you maximise utility according to the budget line?
you want to maximise utility, so the way to do that is to spend all you money (no savings, savings give you no utility)
What does the steepness of the budget line tell us?
-(p_p / p_c) = -3/1 = -3
relative prices of the two goods determine the slope of the budget constraint
What happens to the budget line when there is a change in income/ prices
Shift of the budget line
Shift of the budget line example income increase
Income increases to 12 from 9
x_c ≤ 12 - 3x_p
instead of x_c ≤ 9 - 3x_p
Shift of the budget line example price of coke triples to £3
x_c ≤ 3 - x_p
instead of x_c ≤ 9 - 3x_p
What is the constrained optimisation problem?
something you want to maximise -> utility
something that limits how much of the good you can get -> constraint is the budget
What is the optimal consumption bundle?
the feasible consumption bundle the maximises the consumer’s utility
What is the optimal/rational spending rule?
if consumption bundle (x_1, x_2) maximises the utility of an individual, given her budget set, then it satisfies the condition
optimal consumer bundle: MRS_1, 2 = p_1 / p_2
^MRS can also be MU_1/ MU_2
if MRS_1,2 > P_1/ P_2 then buy more of good 1 and less of good 2
if MRS_1,2 < P_1 / P_2 then buy more of good 2 and less of good 1
What does it mean if you are not at he optimal choice?
eg consuming many cokes and not many pizza, so we are willing to trade off alot of cokes to consume additional units of pizza
What is income elasticity of demand?
the percentage change in Qd associated with a 1% change in consumer income
describes how responsive demand is to income changes
positive for normal goods
negative for inferior goods
Budget variation: Eg as income rises, prices unchanged, the consumption of pizza falls why is this
the budget line has shifts right from income rising, point B (placed on new line) compared to point A is positioned where there is a reduction in pizza
so pizza is an inferior good, the income elasticity of demand for pizza is negative
Applying optimal choice: price variation eg a rise in the price of pizza
Line changes where the line crosses the pizza x axis is now closer to 0
marginal utility is reduced and the rise in price of pizza leads to decreased consumption of pizza (substituting away from pizza, substitution effect)
move to a lower indifference curve on the new pizza line, consumption change of pizza as a result of income change, known as income effect
Two effects (substitution + income) gives us the decrease of consumption of pizza as a result of price increase
consumers may consume more/ less burgers, depending on whether these goods are substitutes or complements
as long as the consumer derives utility from both goods, a price increase will lower her utility
but if pizza an inferior good, income and substitution effect will go right instead
Is the substitution effect always positive or negative?
negative
What is the giffen good?
the income effect of a inferior good swamp the substitution effect (overwhelms the substitution effect)
(a good people consumer more as the price rises)
What is the substitution effect?
consumers switching to cheaper products as prices increase
When there is an increase in price of a normal good what will the: substitution effect, income effect and total effect be?
Substitution effect: -
Income effect: -
Total effect: -
When there is an decrease in price of a normal good what will the: substitution effect, income effect and total effect be?
Substitution effect: +
Income effect: +
Total effect: +
When there is an increase in price of a inferior good what will the: substitution effect, income effect and total effect be?
Substitution effect: -
Income effect: +
Total effect: ?
When there is an decrease in price of a inferior good what will the: substitution effect, income effect and total effect be?
Substitution effect: +
Income effect: -
Total effect: ?
