All Questions
20 questions
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 ...
1
vote
2
answers
76
views
Does duality hold for u(x, y) = x^2 + y^2? (Corner solution)
Could you please help me evaluate this logic?
I've been told that "if preferences are strongly monotonic, duality holds."
In the case of utility u(x,y) = x^2 + y^2, we will get a corner ...
- 53
1
vote
1
answer
112
views
Existence and uniqueness of demand, and symmetry implies equal demands given equal prices
Encountered the following problem during self study:
My take on the problem is that if we can show that the equation of the income expansion path is $x_1=x_2$ for all such $U(x_1,x_2)$ then we have ...
- 667
3
votes
3
answers
636
views
The formula for expansion path
Is there a way how to precisely compute the expansion path?
I know a consumer's utility function $U(\boldsymbol{x})$, I know the budget constraint $\sum P_i x_i \leq M$, I am able to compute the ...
- 834
0
votes
1
answer
74
views
Looking for a term I'm pretty sure exists
Let me describe the situation:
Company is selling a product; they buy it at x, sell it at some % over for profit. Taken on a monthly scale, you can see the profit of that particular object by ...
1
vote
2
answers
1k
views
Conditions to use the Lagrangian method
I have seen that the prices and $\text{MU}_{i}$ are assumed to be positive (or, the preferences monotonic). This is always mentioned when a utility maximization problem is being solved with the ...
- 244
1
vote
3
answers
4k
views
Graphing indifference curves to visualize solutions?
I am having trouble with being able to graph indifference curves. This is a particularly important skill to have especially when trying to visualize corner solutions, and when the Lagrangian method ...
- 155
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
1
vote
1
answer
741
views
Generalizing demand for perfect substitutes utility function
I have the utility function:
$U(x_1,...,x_n)=a_0+\sum_{i=1}^{n}a_ix_i\;\;\;\;\;\;\;\;\;a_j\in\mathbb{R}_+ \;\;\forall j=\{0,...,n\}$ (maybe $a_0$ could be zero)
$\sum_{i=1}^{n}a_i\in (0,K)\;\;\;$ ...
- 943
2
votes
2
answers
456
views
In an intertemporal (2-period) consumption model, why is the investment rate independent of discount factor?
In lecture, my professor defined the following 2-period consumption model:
$c_i = $ consumption in period $i$.
$y =$ endowed income in period 1.
$r = $ interest rate in perfect credit markets.
$h = $ ...
- 21
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
0
votes
0
answers
284
views
Finding the optimal consumption bundle given the strictly concave utility function $v(x,y) = U(x) +y$?
I am also finding it difficult to understand what are the fundamental differences between analysing optimal bundles between concave and convex functions ?
Does it also happen that the optimal bundle ...
- 11
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
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
0
answers
78
views
Does this conditional increase in income affect a budget line in the same way as an unconditional increase in income would?
Note: It's been awhile since I've taken introductory microeconomics. I remember increases in income move budget line outward. What if the increases have some condition?
The problem:
Jill has $I$ to ...
- 370
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
8
votes
3
answers
2k
views
Does the Marshallian demand function always include prices and income?
I have the following utility function:
$$U(x_i)=x_1x_2+x_3$$
with budget constraint:
$$p_1x_1+p_2x_2+p_3x_3\leq I$$
I use the Kuhn-Tucker method to find the optimal choices of the Utility ...
- 1,044
2
votes
2
answers
2k
views
Intermediate macroeconomics: optimal bundle for quasilinear utility?
How would I go about solving this question:
Assuming consumer's utility function is $U(C,L)=c+2l^{0.5}$, consumer earns a wage of 0.5/hour, $h=24$ and there is no real dividend and tax is $T=11$. ...
- 133
2
votes
2
answers
1k
views
Editing formula for finding Marshallian Demand with Cobb-Douglas utility function
Suppose a utility function $u=x_1^ax_2^b$ with $a+b=1$. The following formula finds the values for $x$:
$x_1 = \frac{am}{p_1}\\
x_2 = \frac{bm}{p_2}$
But what if the utility function looks like $u=...
- 245
12
votes
2
answers
44k
views
Marshallian Demand for Cobb-Douglas
When trying maximize the utility having a cobb-douglas utility function $u=x_1^ax_2^b$, with $a+b = 1$, I found the following formulas (Wikipedia: Marshallian Demand):
$x_1 = \frac{am}{p_1}\\
x_2 = \...
- 245