# Tag Info

Accepted

### Regression Optimization problem under constraints

The situation is given in the following picture The black line is the true conditional mean $E(y|x)$. If we truncate the data, all observations above the truncation $Y^A$ are not observed. For low ...
Accepted

### 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 ...
Accepted

### Budget hyperplane in n dimensions

Let matrix $A = \begin{bmatrix} p_1 & p_2 & \ldots & p_n \end{bmatrix}$. Let $\mathbf{x}^*$ be a fixed solution to $A \mathbf{x} = c$. Then for any vector $\mathbf{u}$ that belongs to the ...

### Calculating natural rate of unemployment

The model you fit is simply inadequate to estimate the natural rate of unemployment any results from it will be completely unreliable, so I am not surprised if they make no sense. Furthermore, natural ...
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### Why the definition of productive economy in Leontief Open Model is such?

This is a specific terminology employed in the literature on Leontief model. Productive here means that all sectors must be profitable (do not confuse it with notions of productivity used elsewhere in ...

### How do you convert or move from a linear cost function to a quadratic cost function?

Your eq (2.10) is not more general than (2.9), but corresponds to an alternative specification. A more general version would be: $$C_i(Q_i)=FC_i+a_{1,i}Q_i+a_{2,i}Q^2_i.$$ This specification allows ...
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### When gradient of utility function is a zero vector

This concerns the partial derivatives of the utility function with respect to goods, and not the partial derivative of the Lagrangian of the maximization problem. So a zero derivative, and moreover ...

1 vote

### How can difference equations with an infinite summation be represented in matrix form?

Maybe the differencing approach should work for you. Basically the idea is to reduce this series to a finite expression, using the lag operator. Let me explain with an example from Costa (2016, p.81) (...
1 vote

### Leontief input output model with column sum greater than 1

You are right when saying that mathematically in the cited theorem the condition of column sums being less than 1 is not an "if and only if" condition and thus exceptional circumstances are ...
1 vote
Accepted

### Leontief input output model with column sum greater than 1

In terms of if and only if statements according to Peterson & Olinick (1982); A substochastic matrix A is productive if and only if $I-A$ is nonsingular. In substochastic matrix the sum of ...
1 vote

### Calculating the elasticity of substitution between factors of production

First of all, I think that 'linear and homogeneous' is a typo of 'linearly homogeneous.' Indeed, it can be shown that if the production function $V$ is linearly homogeneous, Allen Elasticity of ...
1 vote

### Has this differential calculus inequality approach to optimizing the production possibility curve exist?

I don't really understand your optimization problem as it stands. Just as a few examples, when you write out \min \sum_m \sum_v \left( \frac{\partial \vec f_v (\vec Q_v)}{\partial \vec f_m (\vec ...
1 vote

### Budget hyperplane in n dimensions

I got some outside help for the ending of the proof I was attempting. I'll leave this question if by chance someone else finds it useful. So if we want to show \$p_1x_1 + \cdots + p_{n−1}x_{n−1} = 0 \...
1 vote

### How to deal with a singular Leontiev inverted matrix?

All right kids. You gave me the answer when Dismalscience wrote "this is still not a problem as long as the value of the good produced differs from the sum of the value of its inputs" ... actually, ...
1 vote

### How to deal with a singular Leontiev inverted matrix?

I didn't divided each column by the sum of the column. This would make no sence since the goal is to produce a technical coefficient matrix that links each input (row) needed by the industry (column) ...

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