# Questions tagged [elasticity-of-substitution]

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### Conceptually, what's the difference between the discount rate and the intertemporal elasticity of substitution?

Suppose I have a standard maximization problem with a CRRA utility function $$\max_{c_t} \sum_{t=0}^\infty \beta^t \frac{c^{1-\sigma}}{1-\sigma}$$ It seems to me that both $\beta$ and $\sigma$ control ...
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### Elasticity of Substitution of CRS Production Function

Suppose that $F(\cdot)$ has CRS in $K$ and $L$, the elasticity of Substitution is $\sigma_{K L} \equiv F_{L} F_{K} / F F_{L K}$. I once derived this equation but I remember that it takes me quite ...
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### How to compute elasticity of substituion in general?

We know that the elasticity of substitution is defined as $$e=\frac{d \ln(x_2/x_1)}{d \ln(MRS_{12})}=\frac{\frac{d(x_2/x_1)}{x_2/x_1}}{\frac{d(MU_1/MU_2)}{MU_1/MU_2}}$$ When we compute ES for CES ...
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### When do workers versus capital owners share of income increase?

The share of total income obtained by workers rather than capital owners is for obvious reasons of interest. Assuming that the economy can be desribed by an aggregate production function $$Y = F(K,L)$$...
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### How to compute elasticity of substitution in labor market of blacks and whites using experience-education groups?

I'm reading "Competition in the Promised Land – Black Migrants in Northern Cities and Labor Markets", by Leah Boustan, and I'm trying to understand her computation of black and white ...
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### Example of a (not quasi-linear) production function whose inputs are not perfect substitutes but are not asymptotic at the axes

I'm looking for an example of a family of production functions indexed by, say, rho, where the inputs become closer and closer to perfect substitutes as rho approaches 1, and yet, the marginal product ...
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### Contradictory FOC and maximizing solution

I have to maximize the following function - $\max_{x \in (0,1)} (((p_1x)^{2r} + (p_2(1-x))^{2r})/2)^{1/r}$ where, $p_1$ and $p_2$ are drawn from uniform distribution [0,1] and are considered to be ...
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### In the BLP paper, why interacting consumer characteristic with product characteristic can generate more desirable substitution pattern

Got a question about the famous BLP paper (http://people.stern.nyu.edu/wgreene/Econometrics/BLP.pdf). When there is no interaction between product characteristic and consumer characteristic, the ...
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### Meaning of «intertemporal substitution effect dominates the income effect»

Assume a household intertemporal optimisation problem, where they only either consume or labour, and one of the equilibrium conditions states that labour will be a positive function of productivity, ...
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### Why is my elasticity of substitution wrong?

I am calculating elasticity of substitution for the following production function: $$F(K,L) = A(aK^{-\gamma}+bL^{-\gamma})^{-\mu/\gamma}$$ where $A, a, b, \mu, \gamma$ are constants. $A, a, b, > 0$,...
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### Price elasticity of demand of CES

Anyone would like to help me show the following ( or a book/paper reference would be a great help) " The price elasticity of demand is equal to $\sigma$ for the demand function of CES preference,...
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### How was CES utility function derived?

Is there any book/papers that I can refer to the proof (derivation) of the CES utility function? Or if anyone could help me with the derivation, I will be so much grateful to you.
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### How can you interpret one of the parameters of optimal consumption at the Merton portfolio problem?

Statement: Let the dynamics of wealth of the agent satisfy $$dX_{t} = \pi_tX_t\Big(\mu dt+\sigma dB_{t}\Big)- c_t X_t dt, \qquad \textrm{with}\quad X_0=x_0 \in \mathbb{R},$$ where $(\pi,c)$ is an ...
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### Capital in terms of labor

I have a question that asks to find $\frac{\partial K}{\partial L}$ from $Q=cL^aK^b$, when $Q$ and $c$ are constants. It lists 4 answer choices but I’m just not sure how to approach it. Implicit ...
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### Calculating price elasticity by asking a "this" or "that" question

Let's say 2 goods exist: A for 10 and B for 20 (B is more premium in this example) If I decrease the price of both goods by 10% and ask: "Do you prefer A for 9 or B for 18 " What sort of insights (...
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### Derivation of the elasticity of substitution of a general production function with labor-augmenting technological progress

I am following and trying to fully understand a famous and interesting work of Bentolila and Saint-paul (2003). They try to explain movements of the factor's share in terms of a relationship between ...
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### Negative elasticity of substitution in a CES production function

I have empirically estimated the elasticity of substitution parameter in the following model: $$Y_t=[(A_1L_tK_{t})^{\rho} +(A_2M_{t})^{\rho}]^\frac{1}{\rho}$$ here, $Y_t$ is output, $A_i$ is a ...
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### Elasticity of substitution

So, this is an economics question but the problem I have is a pure math problem I guess. So I have the following equation:f(x,y) this function have the elasticity of substitution(EOS): 1/(1-beta). a,...
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### How to simulate changes in quantity demanded when several prices change?

I am not sure if this is a straightforward question or not. Basically, I have a set of products along with their prices and quantities demanded. I also have own and cross price elasticities for each ...
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### If $X$ is a Giffen good then $Y$ must be a normal good

While going through some problems as part of self-study I encountered the following True/False question: Q. Steven only consumes two goods: $X$ and $Y$. If $X$ is a Giffen good for Steven, then $Y$ ...
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### Relationship between Elasticity of substitution of sectoral outputs and elasticity of substitution of inputs

There are two sectors Y1 and Y2. Composite output is given by CES form - Each sector employs Capital and Labor in combination through Cobb-Douglas Production Technology. The paper mentions that ...
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### Elasticity of substitution meaning

If I computed an elasticity of substitution of f.e. 0.9 between capital and labour, does this implicate that the factors are rather well substitutable or not? Since for 0 they are perfect complements ...
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### Raising the elasticity of substitution in an economy

Papers such as de la Grandville (1989) and Klump/de la Grandville (2000) have shown that a higher elasticity of substitution leads to higher economic growth. My question is, if there is a way to ...
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