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Hot answers tagged elasticity-of-substituion

7 votes
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Econ Intuition for Jacobian inverse in demand system

For the 2x2 case being considered, write $$\mathbf{B}=\left[\begin{array}{cc} b_{1,1} & b_{1,2}\\ b_{2,1} & b_{2,2} \end{array}\right].\quad$$ It follows that the element (1,1) in $B^{-1}$ is ...
• 595
7 votes

How was CES utility function derived?

To understand the CES utility functions, which I guess is your question, a good starting point is the Wikipedia page on constant elasticity of substitution. In particular, The CES aggregator is also ...
• 6,672
6 votes

How was CES utility function derived?

The C.E.S functional has been introduced in Economics in the context of production theory, by Arrow, K. J., Chenery, H. B., Minhas, B. S., & Solow, R. M. (1961). Capital-labor substitution and ...
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5 votes
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If $X$ is a Giffen good then $Y$ must be a normal good

Reason: Both goods cannot be inferior. Let's say originally you consume $x$ and $y$. So your budget constraint looks like $$p_x x + p_y y = I.$$ If both X and Y are inferior, when income goes down ...
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5 votes
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Contradictory FOC and maximizing solution

As alluded to by Bertrand in his +1 comments this is because FOCs do not tell you where maximum or minimum occurs. This is common misconception among some students but it simply does not hold. FOCs ...
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4 votes

• 8,487
2 votes

Empirical measurements of consumption and production elasticity of substitution?

The elasticity of substitution of production factors derived from empirical data depends on the data. In the case of simple production, you can estimate the production function (fit your data to the ...
• 151
2 votes
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Derivation of the elasticity of substitution of a general production function with labor-augmenting technological progress

You have that in equilibrium each factor is paid its marginal product, so $$\tag1\frac{w_i}{p_i}=B_if'(l_i)$$ and $$\tag2\frac{r_i}{p_i}=f(l_i)-K_if'(l_i)\frac{B_iL_i}{K_i^2}=f(l_i)-l_if'(l_i)$$ so ...
• 4,168
2 votes

How to find the elasticity of substitution for the general CES-function?

four things : The desired result is actually which is the answer you are getting if you multiply the negative into the denominator( you can cross-check on https://en.wikipedia.org/wiki/...
• 136
2 votes
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Meaning of «intertemporal substitution effect dominates the income effect»

I suppose the right approach is to start with the statement: "Real wage is also a positive function of productivity". Let's start with the income effect: If both goods, free time and ...
• 520
2 votes

Example of a (not quasi-linear) production function whose inputs are not perfect substitutes but are not asymptotic at the axes

You could, for example take the function $f: \mathbb{R}^2_+ \times[0,1] \to \mathbb{R}$. $$f(L,K, \rho) = L + K + (1-\rho) L K.$$ For $\rho = 1$, we have $f(L, K, 0) = L + K$ which is a production ...
• 8,652
1 vote

Elasticity of Substitution of CRS Production Function

1muflon1's answer is entirely correct. Let me give another alternative derivation, which might be a little bit easier to remember, although probably not more intuitive. Let $k = K/L$ be the capital to ...
• 8,652
1 vote

How to compute elasticity of substituion in general?

The formula you already have there is a general formula for elasticity of substitution, but I can see that it might be difficult to apply to your problem here given that $MU_{x_2}=1$. There is also ...
• 45.1k
1 vote

• 7,880
1 vote

Obj function yielding independent goods demand functions

So if we take a simple example with 2 goods and consider the consumer's problem: $L=u(x,y)+\lambda(I-p_xx-p_yy)$ This yields the ratio of FOC: $u_1/u_2=p_x/p_y$ Now plugging these guys into the ...
• 756
1 vote

Estimating elasticity of substitution in nested CES functions

Neglecting technology parameters and assuming constant returns to scale, the parameters $\sigma$ and $\gamma$ are jointly estimable via dynamic (least squares) programming. See this paper.

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