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Constant Elasticity of Substitution: Special Cases

Take an $n$-commodity constant elasticity of substitution utility function, $$U = \left[\sum^n_{i=1} \alpha_i x^\rho_i \right]^\frac{1}{\rho}$$ How do we show the following: Show that as $\rho \rightarrow 0$ that this utility function represents…
Kitsune Cavalry
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"Competitive equilibrium" vs. "General equilibrium"

What is the difference between the term "competitive equilibrium" and the term "general equilibrium"? Here in econ.SE, they are two different tags, so there is probably a difference between them, but I don't understand what exactly.
Erel Segal-Halevi
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Why is the percentage of Australian businesses that don't have any employees so high?

I'm trying to understand this Australian Bureau of Statistics release, which says: In June 2014, 61% of actively trading businesses in Australia had no employees, 27% had 1-4, 10% had 5-19, 2% had 20-199, and less than 1% had 200 or more. I…
Mike
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8
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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 maximization problem. My equations are: $$x_2-\lambda…
Übel Yildmar
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8
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Practical examples of fair division algorithms being used

Consider the problem of fairly sharing a homogeneous cake between two people. It is well-known that a fair division can be achieved through the divide and choose procedure: player 1 cuts the cake into two pieces and player 2 chooses a piece. This…
Ubiquitous
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8
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Autonomous or non-autonomous optimal control system?

I have a following system with endogeneous discounting. $c,k$ and $h(k)$ are consumption, capital and endogeneous discount function based on physical capital. (the properties of this function are not relevant with the question, so I don't write them…
optimal control
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Do welfare payments for children incentivise having children?

A common argument against safety net social welfare for people with children is that it can incentivise people without better options to have children. This could be considered a problem if it means people who aren't fit to be parents continue…
dwjohnston
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8
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Log-normality assumption in consumption based asset pricing

Consider a very basic discrete time representative consumer maximization problem with CRRA utility. There exist a risky asset with time $t$ price $p_t$ that pays time $t+1$ dividend $d_{t+1}$ , and a riskless asset with price $p_t^f$ that pays a…
vvv
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How and when is M0 money created?

The Federal Reserve Coin and Currency Service Website describes their currency order process thus: The 7.2 billion notes included in the FY 2015 order reflect the Board’s estimate of net demand for currency from domestic and international…
8
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1 answer

What is the percentage of announced Merger & Acquistion deals actaully completed?

I am assuming that not all M&A deals announced are completed. There are factors such as anti trust laws and consumer protection agencies that legally prohibit the two companies from completing the M&A. Statistically, what is the percentage of…
Bee Dev
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Why is Land not considered as a fixed capital?

As far as I know 'Fixed Capital' includes things which don't deteriorate or get used up upto a long, e.g. tools, machinery and building etc. My question is that since Land fulfills this criteria, why is it not considered as a Fixed Capital?
user31782
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8
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5 answers

Deriving the Euler Equation

I want to derive the Euler Equation for the following: $$max \sum\limits_{t=0}^{T} = \beta^{t}U(C_t)$$ $$s.t. C_t+K_{t+1} \leq f(K_t) , t=0,1,2,...,T-1$$ $$-K_{T+1} \leq 0$$ I'm a bit confused about why the F.O.C. have that:…
123
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What are the best books for developing a solid understanding of fundamentals of Economics?

Recently, Raghuram Rajan, a former chief economist at the International Monetary Fund and current Governor of central bank of India, while addressing undergraduate students of Economics, said: ... In this country there is a tremendous need for…
claws
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Real-life applications of repeated games theory

What are some scenarios in which the theory of repeated games have been applied? I am looking, for example, for scenarios in which a government, a firm or a person accepted a decision which relied upon a result such as the Folk theorem.
Erel Segal-Halevi
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8
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4 answers

Can higher working hours reduce productivity?

Are there studies about the impact on per-hour output (productivity) of increasing the number of hours worked each week by employees? If every employee works 3hrs/week longer (from 41 to 44hrs), does productivity increase or decrease? Edit About…
Sider
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