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-3

I Don‘t know any theory as I dont have an economic background, but there are infinite possibilities. One would be: C(V)=C_m V/(a+V) where V is the volume and a is a constant of half saturation. I.e. if V=a, the costs are half of the maximum costs C_m.


5

Partial answer: for simplicity let $P_c =1$. The budget constraint: $c= wn + \Pi$ Simplify (plug in $\Pi$): $c= F(n)- fc$ Goods clearing: $c = F(n)$ The household's budget constraint is inconsistent w/ goods market clearing. The firm pays a fixed cost that doesn't go to anyone. In a "true GE model" all payments have to go to someone in the economy. ...


8

Since the exponents add to one the production function has constant returns to scale, which means that, given factor prices, total cost is linear, which means that it's derivative (= marginal cost) is contant. If you change the exponent 1-alpha to beta where alpha+beta < 1, there will be decreasing returns to scale (but still homotheticity) and you will ...


0

Hint: Think how many units of $x_1$ and $x_2$ are needed to produce $q=1$ in order to minimize the cost. What about producing $q=2$? Can you generalize it? In order to minimize the total cost, you want to use as few units of either input as possible. Imagine you wanted to produce $q$ units. You would need at least $x_1=q$ and $x_2=q$ (otherwise you wouldn't ...


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A common technique we use in Python through Pandas is the introduction of means, medians and modes (depending on the structure of data) in the stead of these missing values. Another great technique is introducing fitted values by a regression model, thus, predicting the missing values. In this case you'd want a command to drop your NaNs, estimate a model, ...


1

The first order conditions equate marginal revenue per factor to the price of that factor: \begin{align} p\cdot\alpha\frac{y}{x_1} &= w_1\\ p\cdot\beta\frac{y}{x_2} &= w_2, \end{align} Where I used the property of power function $(x^n)'_n = n \frac{x^n}{x}$. Divide the second FOC by the first to get the relation between the relative prices and the ...


4

To understand what is the issue here, try dutifully to examine all possible sub-cases in the production function. The production function is $$Q_0 = \min\{K_0, L_0^{1/2}\}$$. Consider cases A. $K_0 < L_0^{1/2}$ Here $Q_0 = K_0$. Consider $Q_{\lambda }\equiv \min\{\lambda K_0, \lambda^{1/2}L_0^{1/2}\},\;\;\; \lambda>1.$ Subcase A1. If $\lambda K_0\leq \...


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