Questions tagged [cobb-douglas]

The Cobb-Douglas function is a commonly used functional form for a firm's production function or for consumers' utility, with a variety of convenient properties.

42 questions
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Stochastic frontier analysis in a unit out put production function. Taking logs is causing issues?

I wish to perform stochastic frontier analysis to calculate inefficiency of firms, but for a unit output isoquant ( imp) now y'=1, k'=k/y and l'=l/k. Now, these values lie between 0 and 1 (including 0)...
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Optimization with a Cobb-Douglas and demand function

I have a Cobb-Douglas-like function for a product consisting only of material a and material b (for example $a^{0.2}b^{0.8}$) and I know the unit prices of both a and b. I also have a demand function (...
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Derivation of demand function

Hello. I'm graduate student in Japan. This time, what I want to ask is how to solve the profit maximization problem using the image production function and derive the demand function. This ...
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Demand derived from Cobb-Douglas utility, interpretation, check

I derived demand, given a Cobb-Douglas utility function but I am not really sure if I did it correctly. I am especially struggling with the sum signs and the subscripts of $i$ & $j$. It would be ...
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How to Calculate the productivity multiplier?

Given a Cobb Douglas $Y_t = A (K_t^\alpha L_t^{1-\alpha})$ $K_{t+1} = sY_t + (1-\delta) K_t$ How do we get the multiplier on productivity to be equal to $\frac{1}{1-\alpha}$? I understand ...
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Linking top-down and bottom-up models for analyzing electricity price-based demand response: Expenditure constraint is violated?

I have a question about the contents of this paper*, which links a building energy model and a utility-maximization component. In it, the author tests several electricity prices using a Cobb-Douglas ...
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Maximizing a Cobb-Douglas Function

Suppose that a competitive firm receives a price of $P$ for its output, and pays prices of w, r and v for its labor $(L)$, capital $(K)$ and natural resources $(R)$ inputs, respectively. The firm ...
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Is Cobb-Douglas the only output function corresponding to a competitive economy?

Apologies if this is a rather simple question, I appreciate any guidance. $$Q(K,L) = AK^\alpha L^{\beta}$$ where A is a constant. Identify the conditions on $\alpha$ and $\beta$ for ...
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The factor elasticities from a Cobb-Douglas function in Romer's macroeconomy book

Good night, I'm reading the Romer's macroeconomy book in the page 42, "A complication" section title. The begin of third paragraph say: This is not a general property of production functions, ...
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Calculating growth rate of capital when not in steady state

Given a Cobb-Douglas production function, the annual population growth rate, savings rate, alpha, annual depreciation rate, and annual technological progress rate, how would one calculate the growth ...
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Indirect changes in Marshallian Demand

Suppose we have a Cobb-Douglas utility function: $$U(x,y)=x^\alpha y^\beta$$ and a budget constraint: $$p_{x}x+p_{y}y=I$$ where $\alpha+\beta=1$. It can be shown that the Marshallian demand for $x$ ...
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Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)?

My understanding of local non-satiation is that increasing your allocation of one good by a marginal amount increases utility. Suppose your utility takes the following form: $$U(x,y)=x^\alpha y^\beta$$...
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Given a standard Cobb-Douglas production function, how to estimate the output elasticity of labour and capital by country?

Given a standard Cobb-Douglas production function: $$Y_t=(A_t L_t)^{\alpha} K_t^{1-\alpha}$$ Moreover, the production function has constant returns to scale: $$\alpha + (1-\alpha)=1$$ How to estimate ...
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In the C.E.S. utility function do the parameters need to add up to unity to obtain the Cobb-Douglas utility function?

Consider the C.E.S. utility function $$U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}}$$ Is it true that we must have $a+b=1$ in order to obtain a Cobb-Douglas utility function as $c\rightarrow 0$?
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How does the limit of $U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}}$ as c approaches 0 yield the Cobb-Douglas utlity function? [duplicate]

\begin{equation*} U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} \end{equation*} I ask this mainly because after logging both sides of the Utility equation (the first step to proving the assertion, I ...
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Marginal Product of Capital in the Solow Model

In the classic form of the Solow Model: $$Y=K^\alpha (AL)^{1-\alpha }$$ Describe circumstances in which the marginal product of capital could rise over time, at least for a temporary period. I've ...
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When trying maximize the utility having a cobb-douglas utility function $u=x_1^ax_2^b$, with $a+b = 1$, I found the following formulas (Wikipedia: Marshallian Demand): $x_1 = \frac{am}{p_1}\\ x_2 = \... 1answer 87 views Derive a cost production function give prod f, only K In this question, only K is included and L is excluded how would I go about deriving it? Total cost= Fixed costs + Average costs. Since the variable input costs r per unit, the variable costs is r ... 0answers 504 views Marginal product versus marginal productivity in a Cobb-Douglas production function [closed] CFA Kaplan Schweser claim that Cobb-Douglas function exhibits constant marginal product of capital but diminishing marginal productivity of capital. I think this statement is not right. My view ... 2answers 9k views Cobb-Douglas and Logarithm Utility Functions Suppose I have a consumer with a utility function$U(x,y) = x^\alpha y ^{1-\alpha} $where$a \in (0,1)$. Suppose this consumer has wealth$w$and the prices for$x$and$y$are$p_x$and$p_y\$ ...
In most Microeconomics textbooks it is mentioned that the Constant Elasticity of Substitution (CES) production function, $$Q=\gamma[a K^{-\rho} +(1-a) L^{-\rho} ]^{-\frac{1}{\rho}}$$ (where the ...