Week 2 Term 1 Flashcards
(20 cards)
What is the Expenditure Minimisation Problem (EMP)?
The minimum level of expenditure a consumer must make to achieve a certain utility level given a set of prices.
The consumer faces a price vector p = (p1, p2, …, pn) and wants to achieve a utility level u.
What is the Hicksian demand for good i?
x(p, u) is called the Hicksian demand for good i, also known as the compensated demand function for good i.
- It represents the quantity demanded when utility is held constant.
What is the definition of the expenditure function?
The minimum expenditure necessary at the given prices to achieve the given utility level.
Mathematically, it can be defined as e(p, u) = Σ pi xi(p, u) for i = 1 to n.
What does Shephard’s Lemma state?
If e(p, u) is differentiable in p, then the Hicksian demand functions can be recovered from the expenditure function.
This lemma links the expenditure function and the demand function directly.
What are the properties of the expenditure function?
- Continuous in prices (p) and utility (u)
- Strictly increasing in prices (p) and utility (u)
- Homogeneous of degree 1 in prices (p) - changing all prices int the expenditure fucntion by a common multiple, then expenditure changes by the same factor
- Concave in prices (p)
These properties help in understanding the behavior of consumer expenditure under different conditions.
What is a quasilinear utility function?
A utility function that is linear in one argument and non-linear in the other.
Example: u(x1, x2) = f(x1) + x2.
What does it mean for preferences to be quasilinear?
Preferences are linear in one good, leading to constant marginal utility with respect to that good.
This characteristic simplifies analysis, particularly for goods that constitute a small part of income.
Fill in the blank: The solution to the EMP can be obtained using the _______.
[Lagrangian method]
True or False: The expenditure function is strictly decreasing in prices.
False.
The expenditure function is strictly increasing in prices.
What does the term ‘Hicksian demand’ refer to?
The quantity of a good demanded when utility is constant while prices change.
It is derived from the expenditure minimization framework.
What is the relationship between Cobb-Douglas preferences and the EMP?
Cobb-Douglas preferences lead to specific forms of the EMP, allowing for straightforward calculation of Hicksian demands.
These preferences are characterized by constant elasticity of substitution.
What are quasilinear preferences?
Preferences where the marginal utility with respect to one good is constant. This applies to goods forming a small part of a consumer’s income.
How is the marginal rate of substitution (MRS) between goods x1 and x2 defined in quasilinear preferences?
MRS = MU1/MU2
MU1 = f′(x1), where MU stands for marginal utility.
What is a characteristic of indifference curves in quasilinear preferences?
Indifference curves are vertically parallel shifts of each other. => constant marginal utility of one good
This reflects the constant marginal utility of one good.
What is the income effect of consuming x1 (non-linear) in quasilinear preferences?
The consumption of x1 is independent of the consumer’s income if income is above a certain threshold. -> This means there is no income effect.
In the context of quasilinear preferences, what happens to the utility function when analyzing goods?
The good that enters the utility function is denoted as ‘all other goods’.
What does the term ‘marginal utility’ refer to in quasilinear preferences?
The additional satisfaction gained from consuming one more unit of a good. In this case, it remains constant with respect to the good forming a small part of income.
True or False: In quasilinear preferences, the consumption of x1 depends on the consumer’s income.
False.
Consumption of x1 is independent of income above a certain threshold.
With Quasilinear preferences , if high income then the solution is
Interiror Solution
With quasilinear preferences, if income is low, then the solution is
Corner Solution
