Week 2/3 - Consumer Theory pt. 2 Flashcards
Finding demand (the primal)
- We are finding how much we consume/demand of each good in optimal bundle.
- To do this we maximse utility subject to our budget constraint.
Where is the optimal consumption point?
Where the highest indifference curve meets the budget constraint.
How might we find demand
- Langrange
- equi marginal principle - where the MRS is equal to the price ratio.
- unconstrained optimisation - rearrange budget constraint in terms of x2, differentiate, and equal to zero, to solve for x1.
Corner solutions
- Corner solutions includes goods which must me consumed together - complementary goods.
- We cannot always use the equi-marginal principle as this requires that indifference curve be
tangential to the budget line. In other words, the MRS must be equal to the price ratio.
What does it mean when the MRS is greater than the price ratio and vice versa?
When the MRS is greater than the price ratio, it means that the consumer derives more satisfaction from consuming good x than good y. Therefore they begin to consume more of good y and less of good x in order to reach maximising bundle where the BC and IC are tangent.
How do we know when utility functions represent the same taste?
Two conditions must be met for utility functions to represent the same tastes
- (i)
the ICs they give rise to must have the same shapes and
- (ii) the numbering on the
ICs needs to have the same order.
- To check if they have the same shape, we check
the MRS for those utility functions are the same
Quasilinear preferences
Utility for one variable is linear, and non linear in the other.
For example, U(x,y) = Y^1/2 + 2x
Quasilinear preferences
Utility for one variable is linear, and non linear in the other.
For example, U(x,y) = Y^1/2 + 2x
Giffen Good
Optimal demand for a good decreases when its price decreases.
- Income effect is negative
- income effect is greater than the substitution effect
Substitution Effect
-The rate at which you can exchange one good for another changes.
- That is, the MRS.
Income effect
The change in demand due to having more or less purchasing power.
How much does income need to change when the price of good x/y changes? (slutsky)
∆m = x1(∆p1)
Change in income = X1 multiplied by the price.
Income offer curve
- Depicts the optimal choice of two goods at different levels of income at constant prices.
- The shape changes based on the type of good. That is, normal, inferior. giffen ect.
Engel Curve
Represents the quantities demanded of the goods at various levels of income, when prices and preferences are held constant
Hicksian substitution effect
- We find optimal consumption bundle, at new prices, and keeping utility fixed.
- Utility fixed = Keep IC cruve fixed and move budget constraint line.
-Therefore to find the value of the substitution effect, we find the difference between optimal consumption at original budget line and new budget line (at new prices) - How can we minimise expenditure, subject to a fixed utility.
- The change in demand resulting from the change in opportunity costs with no change in real income.
- what is the change in income required to keep utility constant.
Hicksian income effect
Effect of change of price of a good on consumption.
- The effect of a price change is a function of two things. Namely, the substitution effect and the income effect.
The substitution effect will reflect the change in our tradeoff between the two goods. (pivot of budget line as price ratio changes)
The income effect will reflect the change in our purchasing power (shift in budget line as overall income and budget increases.)
Slutsky Substition effect
- Adjusting the consumer’s income following the price change such that the consumer’s original consumption bundle is affordable.
∆m = x1(∆p1) - Slutsky substitution effect keeps purchasing power constant.
- Both substitution effects (hick and slut) work in the same direction, but can lead to different amounts of ‘compensation’.
Slutsky identity (law of demand)
law of demand
if it is a normal good then, the change in X over the change in P is negative <0
That is, as the p increases x decrease
Compensating variation
- How much money would the government have to give the consumer after the price change to make him just as well off as he was before the price change?
- How far should we shift the new budget line so that it is just tangential to the original
indifference curve?
Equivalent Variation
How much money would have to be taken
away from the consumer before the price
change to leave him as well off as he would be
after the price change?
− What is the maximum amount you are willing to pay to avoid the price change?
− How far must we shift the original budget
line so that it is just tangential to the new
indifference curve?
