# 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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### Negative elasticity of substitution in a CES production function

I have empirically estimated the elasticity of substitution parameter in the following model: $$Y_t=[(A_1L_tK_{t})^{\rho} +(A_2M_{t})^{\rho}]^\frac{1}{\rho}$$ here, $Y_t$ is output, $A_i$ is a ...
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### Optimization problem of a Cobb-Douglas function with 3 inputs

A perfectly competitive firm uses 3 inputs to manufacture a certain product according to the following Cobb-Douglas production function: $$Q = A L_1^{\alpha_1} L_2^{\alpha_2} L_3^{\alpha_3}$$ ...
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### Capital in terms of labor

I have a question that asks to find $\frac{\partial K}{\partial L}$ from $Q=cL^aK^b$, when $Q$ and $c$ are constants. It lists 4 answer choices but I’m just not sure how to approach it. Implicit ...
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### The shift of Marginal Cost Curve

In standard microeconomics textbooks they usually assume that the cost curve consists of just two variables which are Capital and Labor ( I'm talking about this equation: TC = rK + wL) So when we ...
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### Percentage of workforce change, with two PPFs

A hypothetical economy produces two goods, X and Y. The performance (yield) for every worker is steady, and every worker for Y can produce 10 units of product. If $L_x+L_Y=200$ (meaning that the ...
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### When do we have diminishing marginal returns to labor?

When we have a production function exhibiting constant returns to scale, with only labor and technology, why don't we have any diminishing marginal returns to labor?
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### Production for multiplant firm?

A multi-plant firm will never produce at a plant with an increasing marginal cost when they own another plant with a decreasing marginal cost. Is this true? My reasoning behind this is that firms ...
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### Decreasing and increasing returns to scale question

Hi, I have deduced that this function exhibit increasing returns to scale but I am not sure how to verify part d. My answer doesn't show that there is decreasing returns to scale but I can't be sure d ...
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### Question about an economy with 3 components household, firm and government with functions given

I've spent considerable amount of time on this question, in vain. It is from one of the competitive exams for admission to a grad econ program. Help would be tremendously appreciated. Thanks. An ...
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### Economic interpretation of a CES production function

I am following a paper where a production function of this type is used. $$Y=\left [\beta K^{- \rho}+\alpha \eta \left (\frac{K}{L} \right )^{-c(1+\rho)}L^{- \rho} \right ]^{-1/\rho}$$ It is a ...
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### Capital - augmenting and energy-augmenting technical progress

I've read a number of papers on factor - augmenting technical progress and directed technical change. Authors do not note about the implications of factor - augmentation in sufficient details. Assume ...
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### Anything written on the process behind “multiplicative” production function?

Intuitively, one might make a naive first guess that the production function of the economy, or of a firm, should be a "leontief" production function: "for example, you need both a factory and a ...