All Questions
Tagged with optimization self-study
11 questions
2
votes
0
answers
54
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Irrelevance of Heterogeneous Agent Modelling
This is a question from a previous year PhD entrance exam. I have outlined how I have tried to tackle the problem as well:
N.B. 1 This exam is of 100 points and this particular problem is of 25 points....
- 51
1
vote
0
answers
69
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Finding cost function
The production function is as follows
$$f(z)=(z_1+z_2)(z_3+z_4)$$
Find the cost function?
What I did is as follows. But I am not sure about my solution. How do you solve it?
*duplicated question
- 192
1
vote
0
answers
61
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Find the utility of each agent whenever the social welfare is maximized
Question:
Suppose that the utility possibilities curve of 2 people economy is given by the equation $u_1^2 + Au_2^2=20$ where $A\in R_+$ and the social welfare function of the economy is $W(u_1,u_2)=...
- 192
1
vote
1
answer
353
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Find Pareto optimal allocations and the core for the following economies
Find Pareto optimal allocations and the core for the following economies.
There are two consumers and two goods. Utility functions are $u_1(x_1,y_1)= 10x_1-(y_1-2)^2$ and $u_2(x_2,y_2) = 10y_2 − (x_2 −...
- 192
0
votes
2
answers
1k
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Corner solution of the maximization problem
Answer
Hello, I upload the actual question with my 8-pages answer. Please can you check it. Is there a corner dissolution for $c=\gamma$. Please share your ideas. Thanks.
- 192
1
vote
0
answers
150
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Revenue maximization problem
There are $N>0$ Households in an economy.
The government has aim to maximize a weighted average of income by imposing tax on the rich people and redistribute the tax revenue to the labor ones.
...
- 192
1
vote
1
answer
421
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Central bank loss function (I did a solution, but it doesn’t totally make sense I guess)
I have question on central bank loss function.
We know that the central bank loss function is
$$L(\pi, \bar{Y})= (\pi- \pi^e)^2+\beta \bar {Y}^2$$
And we know that fisher equation is $$i=r+\pi^e$$...
- 192
0
votes
1
answer
99
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Neoclassical model with proportional taxes
In a certain economy, time is discrete with periods $t=0,1,2,...$. The economy is populated by many households and identical firms. The utility of a household is:
$\displaystyle\sum^{\infty}_{t=0}\...
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-4
votes
1
answer
756
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Question about budget constraint and utility maximization [closed]
I have also following budget set
$$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$
where y is income.
Assume that there are two stories. The agent can shop in both of them. The first store ...
- 192
2
votes
2
answers
3k
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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
2
answers
3k
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Utility maximization question setting up.
Consider a consumer whose preferences can be represented by the following utility function: $$u(x_1,x_2)=\dfrac{x_2}{(1+x_1)^2}.$$
Assume the agent's income is $y=5$. The price of one unit ...
- 192