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Results tagged with microeconomics
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user 11824
Microeconomics is a branch of economics that studies the market behavior of individual actors (usually firms and consumers) and the aggregation of their actions in different institutional frameworks (usually the market).
2
votes
Destruction in Exchange Economies
Consider another example:
Consider a pure exchange economy with two goods X and Y and two consumers A and B.
Suppose utility functions are $$u_A(x_A, y_A) = \min(x_A, y_A)$$ and $$u_B(x_B, y_B) = \m …
- 9,842
4
votes
Accepted
How to derive Hicksian demand?
Expenditure minimization problem in the question is as follows :
\begin{eqnarray*} \min_{x\geq 0, y\geq 0} & \ \ p_Xx + p_Yy \\ \text{s.t.}& \ \ x + 3y \geq U \end{eqnarray*}
where $p_X > 0$, $p_Y > 0 …
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1
vote
Core-Equivalence Theorem (Debreu-Scarf Theorem) Intuition
I can try and explain how the core shrinks using an example:
Consider a pure exchange economy with two consumers $A$ and $B$ and two goods $X$ and $Y$. $A$ has an endowment of $1$ unit of $X$ and $B$' …
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1
vote
Example of an economy where Equilibria may not be efficient, where one agent is altruistic
Consider a one commodity, two consumer world with
Preferences: $u_1(x_1, x_2) = x_1$ and $u_2(x_1, x_2) = x_1 + x_2$, where $x_i$ is $i$'s consumption of the good.
Endowment: Both consumers have 10 u …
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2
votes
Accepted
Consumer theory with lump sum fee
Consumer's problem in default scenario:
\begin{eqnarray*} \max_{x_1, x_2} & \ \frac{x_2}{(1+x_1)^2} \\ \text{s.t.} & \ x_1 + x_2 \leq 10 \\& \ 0 \leq x_2 \leq x_1 \end{eqnarray*}
We can easily …
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1
vote
Meaning of equation in pure exchange economy
There is a mistake in the answer you posted. When $u_i = x_i^2 + y_i$ for $i\in \{A, B\}$, set of efficient allocations (along the contract curve) does not satisfy MRS$_A$ = MRS$_B$. This is because t …
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3
votes
How to derive a cost function when a firm takes over another firm to form a monopoly
Assuming that the firm is a price-taker in the input market, we can determine the cost function associated with plant 1 and 2 by solving the cost minimisation problem in the routine way, and we get:
…
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2
votes
How do you solve this problem
(a) To find the competitive equilibrium, we first find the demands. Utility maximisation problem of consumer $i$ is
\begin{eqnarray*} \max_{x_i\geq 0, y_i\geq 0} & \sqrt{x_i} + y_i\\ \text{s.t. } & px …
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4
votes
Accepted
Why is the budget correspondence lower hemicontinuous?
I think you need to recheck the definition you provided for lhc. This is because the definition you provided is always true for any correspondence at any point $(a,b)$ satisfying $b\in F(a)$. To see t …
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3
votes
Finding Optimal Consumption Bundle
In this case the optimal choice is $(x^*, y^*) = (3, 1)$. Here is the picture :
- 9,842
3
votes
Can anyone solve this indifference curve question?
Consider the utility function $u(x, y)= -|x-5|-|y-5|$.
Indifference map for $u$ is as follows :
- 9,842
1
vote
Walrasian Demand and Indirect Utility Function
Walrasian demand $(x_1^d,x_2^d)$ solves the following problem:
\begin{eqnarray*} \max_{x_1\geq 0,x_2\geq 0} & \min(2x_1+x_2,x_1+2x_2) \\ \text{s.t.} & p_1x_1+p_2x_2\leq m\end{eqnarray*}
where $p_1>0$, …
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3
votes
Accepted
Equilibrium allocation 'reachable' and 'existence'
Since this is just a picture and it does not specify the utility functions and the endowments, we have incomplete data and we cannot derive the competitive equilibrium with this much information. Whet …
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5
votes
Quasi-linear microeconomics problem
Here is the utility maximisation problem:
\begin{eqnarray*}\max_{(x_1,x_2)\in\mathbb{R}^2_+} & x_1+x_2^\beta \\ \text{s.t. } & p_1x_1+p_2x_2\leq M\end{eqnarray*}
where $p_1>0, p_2>0, M\geq 0, \beta\in …
- 9,842
2
votes
Accepted
Homogeneity of degree zero and normalization
Demand $x(p, m)$ is the solution to the utility maximization problem:
$\max\limits_{x\in\mathbb{R}^n_+} \ \ u(x) \\ \text{s.t.} \ \ p\cdot x \leq m$
where $p\in\mathbb{R}^n_{++}$ is price vector, a …
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