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# Questions tagged [production-function]

A function whose value is the produced quantity associated with a given vector of factor inputs. The production function represents the technology available to the firm.

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304 views

### Is Artificial Intelligence a completely new (and underestimated) production factor?

Accenture research defines Artificial Intelligence as completely new production factor along labour and capital. Is such notion acceptable by economists? As far as I understand then every asset of AI ...
248 views

### Fisher Separation with negative interest rate

In class we discussed Fisher Separation which states that the investment decision is independent of the financing decision. The optimality conditions are that MRS = MRT = (1+i) (i = interest rate). ...
4k views

### How do you determine if the production function has decreasing returns to scale?

How do you determine this for the production function $f(k,l) = k^{1.4}l^{0.5}$ ? So far, I have found the marginal product of both labour and capital however, the marginal product of labour is ...
926 views

### the difference between cobb-Douglass and leontief production technology [closed]

whatis the differences between cobb-Douglass and leontief production technology
349 views

### Does the marginal product need to be diminishing to have a diminishing average product?

We have the rule 'If the marginal is less than the average, then the average declines'. So if our production function for an input x and output y is concave, does that mean that MP must be ...
300 views

### Some doubts about netput vectors

I have started studying producer theory on my own and there are some confusions. We know that a production plan is $y=(y_{1},y_{2},y_{3}....y_{L})$ where $y_{i}$ is an output if its greater than $0$...
88 views

### Is it possible to derive the marginal product of an input using a transformation function?

I'm using a transformation function $F(\cdot)$ to describe a production set $y = (x, z, L, K)$, where $x$ and $z$ are private goods denoted by positive numbers, $L$ is labour input, $K$ is capital ...
1k views

### conditional factor demand functions for capital and labor [closed]

I don't how to put maths in here so using an image:
304 views

514 views

### Estimating elasticity of substitution in nested CES functions

I have aggregate data on $L_t, K_t$ and $X_t$, and want to estimate elasticity of substitution parameters, $\gamma$ and $\sigma$ for these factors. Assuming the production function takes the following ...
562 views

### Contract curve for firms with linear utility functions

I am attempting to find a contract curve for a production economy with two linear utility functions. Normally, I would find the point where the Marginal Rate of Technical Substitution were equal for ...
11k views

### CES: Production function: Elasticity of substitution $\sigma = 1/(1 + \rho)$

I have to prove that $\sigma = 1/(1 + \rho)$ for the CES production function: \begin{align} q = (l^\rho + k^\rho)^\frac{1}{\rho} \end{align} I found out that I need to solve the following equation: \...
936 views

### Robinson Crusoe Production Economy [closed]

Robinson Crusoe’s preferences over coconut consumption, C, and leisure, R, are represented by the utility function U(C, R) = CR. There are 48 hours available for Robinson to allocate between labor and ...
256 views

### Examples of technical progress

I'm wondering if anyone can give me some intuition about technical progress. I can buy the idea that factors improve in quality over time. So 5 workers and/or 5 machines in 1990 can produce more than ...
2k views

### Transformation Function

In Mas-Colell microeconomics textbook I have found that profit maximization problem (as well as many further optimization tasks) could be represented with application of some transformation function (...
985 views

### CES production function estimation

Introduction There are different ways of estimating the parameters of a production function. For example, single-equation and system equation techniques are both possible. Another difference among ...
66 views

### Is a production function bilinear?

I believe the following is the multiplicative property of bilinearity: $$Y=F(K,AL)$$ $$c_1 F(K,AL) = F(c_1 K, AL)$$ $$c_2 F(K,AL) = F(K, c_2 AL)$$ But when we have multiplied through the ...
240 views

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### How does a positive capital shock cause an increase in land price?

I am trying to determine the exact theoretical mechanism for a positive capital shock to create an increase in land price. Assuming output is a function of land ($L$), labour ($N$) and capital ($K$) ...
428 views

### Aggregating CRS Production Functions

If thera are two firms and both of them have constant returns to scale production function. Will the aggregate/industry production function still be the sum of individual production functions. How ...
1k views

### Decreasing Costs, Increasing Returns to Scale, & C''(q)

Given a profit-maximizing firm with production function $f(x_1,x_2)$, I understand that we can formulate a firm's cost function $C(q)$ by using the contingent demand functions $x_1^c$ and $x_2^c$. We ...
1k views

### CES Production Function with $\rho>1$

In using CES production functions of the form $f(x_1,x_2)=(x_1^\rho+x_2^\rho)^{1/\rho}$, we always assume that $\rho\leq1$. Why do we make that assumption? I understand that if $\rho>1$, the ...
606 views

### Monotonic Transformation

How does positive monotonic transformation of production function effect the resulting profit function? For example if we had production function $f(x)$ and that gave profit function $\pi(p,w)$. Now ...
97 views

### Homothetic Production Technologies

Can someone suggest a good resource on homothetic technologies and what properties they imply about cost function, profit function, input demands, output supply etc? Also is it possible to have ...
651 views

### Homothetic production function and Profit Function

I know that homothetic production function implies that cost function is multiplicatively separable in input prices and output, and it can be written as C(w,y)=h(y)C(w,1). Can some one help me derive ...
900 views

### Examples of how economists come up with a production function for a firm?

I am a young man studying economics on his own. In every microeconomics text I find, they teach you what a production function is, but they never show examples (or practice problems) on how one comes ...
8k views

### Why does marginal cost (derivative of total cost) differ from variable cost at each level?

Why does the marginal cost equation (as the derivative of total cost equation) make predictions of variable costs that are very different from costs calculated using the Total Cost equation? Marginal ...
6k views

### Concave production function implies convex cost function

Let's assume we have an increasing production function $f:\mathbb{R^+} \to \mathbb{R^+}$ Now, assume this production function is concave and that the price of input z is fixed (this is a single-input ...
1k views

### Production function and isoquant slope

Given the company's production function $f(L,K)=L^{1/3}K^{3/4}$, find slope of the isoquant passing through $(L,K)=(20,40)$ is equal to $-4/5$ (K is on the vertical axis). I need to state whether ...
12k views

### What does it mean by 'intensive form'?

I encountered this phrase while reading up on growth models - that is to work with a function in intensive form. What does it mean when a function is in intensive form? Thanks!
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### Model for simple production chain economy

Given a simplistic economical model with a finite number of possible resources, and a set of machines that can be produced (with a cost) that that take some or none input, and give some output per ...
Cobb-Douglas is $Y = AK^{1-\alpha}L^{\alpha}$. What exactly is $L$ in Cobb-Douglas? Is $L$ the number of workers available in a single year? Working hours?