All Questions
11 questions
1
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1
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37
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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
2
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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 ...
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
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
0
answers
103
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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
0
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1
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2k
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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
1
vote
0
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375
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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)
$$\max_{\{c_t(s^t),a_{t+1}(s^t,s_{t+1})\}_{t=0}^{\infty}}\...
- 121
2
votes
2
answers
3k
views
Show that First order conditions are necessary and sufficient for utility maximization
I have a budget set
$$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
1
vote
1
answer
227
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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
3
votes
0
answers
387
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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
8
votes
1
answer
6k
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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