All Questions
11 questions
8
votes
1
answer
6k
views
Leontief preferences
I can solve most utility maximization problems using my mathematical knowledge .... but not when it comes to Leontief preferences. I do not have a book to lean on (am self-studying), so would really ...
- 81
3
votes
2
answers
678
views
setting of Lagrangian function
Consider a simple consumer's problem:
Max $u(X)$ s.t. $\sum_i^l p_i x_i\leq \sum_i^l p_i w_i$
$w$ is initial endowment.
We can set the Lagrangian function to solve this problem.
$L=u(X)+\lambda ( \...
- 245
3
votes
0
answers
387
views
Constrained optimization for $u(x_1,x_2,x_3,x_4)=\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \}$ [duplicate]
Suppose preferences are represented by the following utility function
\begin{equation}
u(x_1,x_2,x_3,x_4)=\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \}
\end{equation}
Write the
...
- 189
2
votes
2
answers
120
views
Do standard consumer theory axioms rule out corner solutions?
By standard consumer theory axioms I mean (1) completeness, (2) transitivity, (3) continuity, (4) non-satiation, and (5) strict convexity of the indifference curves.
If these axioms are not sufficient ...
2
votes
2
answers
3k
views
Show that First order conditions are necessary and sufficient for utility maximization
I have a budget set
$$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$
where $y>0$ is income.
Assuming the preferences are strictly monotonic and convex, I want to show that first order ...
- 63
2
votes
1
answer
71
views
When the global optimal is outside of the constraint set, what will be the demand?
$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex.
$a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that ...
- 2,084
1
vote
1
answer
227
views
Find Indifference curve/s and Marginal Rate/s of Substitution given only one point
Arka likes fries. She wants to consume as much as possible. She consumes either regular (1 oz) or large sizes (5 oz).
Draw her indifference curve through $(x_R, x_L) = (10,0)$ and her indifference ...
- 370
1
vote
1
answer
37
views
Under what conditions would a quasilinear utility function in a function form exhibit diminishing marginal rate of substitution?
Let the utility function be: $U(x_1,x_2) = x_1 + x_2^\alpha$.
Diminishing MRS requires $\frac{dMRS}{dx_1} <0$, however, taking this derivative results in 0, as $MRS = \frac{1}{\alpha x_2^{\alpha -1}...
- 11
1
vote
0
answers
103
views
On demand functions and Engel curves
A consumer has utility function $U(x,y)=(x−2)y$, where $x≥2$ and $y≥0$. The price of $x$ is $P_x$, the price of $y$ is $P_y$ and the consumer's income is $I>2P_x$. ($x$ and $y$ do not have to be ...
- 161
1
vote
0
answers
375
views
Natural borrowing/debt limit and other borrowing constraints
When confronted with the simple household consumption maximization problem under uncertainty (and with Arrow security sequential trading)
$$\max_{\{c_t(s^t),a_{t+1}(s^t,s_{t+1})\}_{t=0}^{\infty}}\...
- 121
0
votes
1
answer
2k
views
Budget Constraint in Utility Maximisation Problem with Lagrange Multipliers
Lets say we have a utility function $U: \mathbb{R}^{2} \to \mathbb{R}$ given by $U(x,y)$ and a binding budget constraint $p_{x} x + p_{y} y = m$, where $p_{x}, p_{y}$ are prices of goods $x,y$ and $m$ ...
- 131