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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Confusing on the CRS Property of CES Function

Say a CES function is that $$Y = A\left[\alpha K^{\rho}+ \beta L^{\rho}\right]^{\frac{1}{\rho}}$$. Clearly this function is constant return to scale whatever the values of $\alpha$ and $\beta$ take. ...
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Cobb Douglas Production: Identification issues for technical change

It's well know that under a Cobb Douglas production function, capital and labor augmenting technical progress cannot be individually identified. Accordingly, people usually assume Hicks or Harrod ...
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How do you convert or move from a linear cost function to a quadratic cost function?

I am reading a book on electricity cost modelling. I understand equation 2.7 below, which indicates that the total cost for an ith plant is a function of fixed cost(FC), fuel cost(FL), plant ...
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What does "the event of economic consequences" mean?

I read a paper talking about the Operating Cycle. On page 6th, they said: Sales of assets, no matter how disguised, are one-time events. In contrast, cycling capital through the cycle and generating ...
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Self-dual production functions that do not satisfy weak homothetic separability

I am looking for parametric production functions that do not satisfy weak homothetic separability (as first defined in Shephard, 1953), but that do allow for an analytical expression of the dual cost ...
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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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1 vote
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Production Set: Not satisfying Free Disposal Assumption

I saw the figure which satisfies the free disposal assumption in Mas-Colell, Whinston and Green (1995), but wondering if there is a figure that DOES NOT satisfy the free disposal assumption? Any leads ...
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Why does LRAC not connect the minima of SRAC curves? [duplicate]

Can anyone please provide an intuitive explanation and proper mathematical reason for non-intersection of SRAC and LRAC at the minimas of SRAC? I am seeing conflicting [1] [2] answers on the site ...
1 vote
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Finding long run total cost function

I am trying to find the long run total cost function, given the firm's production function $y=L^α K^β$ where $α,β>0$ and two inputs $L$ and $K$ where $L,K∈R_+^2$, with factor prices $w$ and $r$ ...
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Replicate Blundell and Bond (2000) results using R

I want to replicate Blundell and Bond (2000) Table III in R. I'm using the function pgmm from package plm, which (apparently) ...
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Relation between marginal cost and output elasticities

Does anyone know of any results that show the link between marginal cost and the output elasticities analytically? I am looking at production and cost theory books but can't find any results that ...
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1 vote
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I need to prove how an increase in output p increases profit-max. Can someone help to understand why IFT implies that z is a unique maximizing point? [closed]

MWG 5C6 asks: "Suppose a concave prod function f(z) with inputs $(z_1,...,z_L-1)$ and also that $\partial f(z))/\partial z_l \geqslant 0$ for all l and $z\geqslant0$ and that $D^2f(z)$ is ...
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How to get this Production Function in Growth Rates

I'm struggling to understand how Khan & Reinhart (1990) go from the next production function. $$y=A f(K,L,Z)$$ Where $y$ is the production of the economy, $A$ is a variable which contains the ...
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Under what condition is a cost function strictly concave in prices?

Define the unit cost function as $$c(w) = \min_{z\geq 0} w\cdot z$$ subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
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Social Planner problem: two period

The production function is $F(K_t,N_t)=AK_t^\alpha N_t^{1-\alpha}$ and depreciation $(\delta)$ is equal to 1. The given preferences are as follows: U(c_1,l_1,c_2,l_2)=\gamma log(c_1)+(1-\gamma)log(...
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References on Cobb-Douglas Function

I am wondering why everybody uses Cobb-Douglas production functions? Nowadays they are so standard that they are just written down without further discussion. Does anybody know more about this and can ...
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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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Quasi-Linear Production and Inefficiency

For quasi-linear production of $F(K,L)= \sqrt{K}+L$. I know for the optimal efficiency to exist $q \geq \frac{w}{2r}$ where w is the cost labour and r is the cost of capital. My question is what ...
1 vote
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How does aggregate production function shift by an increase in average and marginal productivity of labour?

Increasing productivity would mean increase in output for each given amount of labour employed, resulting in an upward shift of production function as shown below. However I'm unable to understand the ...
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