# 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.

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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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### Regression on derived consumer preference

I have a data set with some demographics of consumers who bought a product that can be used to imply their preference (beta) using Cobb-Douglas (see comments of original question). I’d like to check ...
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### Consumer preference and price in the Cobb-Douglas function

I believe I’m using the most basic version of Cobb-Douglas: $U(x,y)=x^\beta * y ^{(1-\beta)}$. The question I have is: in this example would a consumer’s preference ($\beta$) change if the price of ...
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### Heckscher-Ohlin with different technologies

Consider two countries: Home and Foreign that produce two goods, cars and wheat. The production technologies are such that: $q_{c} = K_{c}^{0.5} L_{c}^{0.5}$ and $q_{w} = 0.5 K_{w}^{0.5}L_{w}^{0.5}$ ...
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Suppose we have utility: $$U(x,y)=x^{0.5}y^{0.5}$$ Then Marshallian Demand for good $x$ is: $$x(p_{x},p_{y},I)=\frac{0.5I}{p_{x}}$$ And Hicksian Demand for good $x$ is: $$x^{c}(p_{x},p_{y},U)=p_{... 1answer 117 views ### The factor elasticities from a Cobb-Douglas function in Romer's macroeconomy book Good night, I'm reading the Romer's macroeconomy book in the page 42, "A complication" section title. The begin of third paragraph say: This is not a general property of production functions, ... 2answers 1k views ### Calculating growth rate of capital when not in steady state Given a Cobb-Douglas production function, the annual population growth rate, savings rate, alpha, annual depreciation rate, and annual technological progress rate, how would one calculate the growth ... 2answers 263 views ### Indirect changes in Marshallian Demand Suppose we have a Cobb-Douglas utility function:$$U(x,y)=x^\alpha y^\beta$$and a budget constraint:$$p_{x}x+p_{y}y=I$$where \alpha+\beta=1. It can be shown that the Marshallian demand for x ... 2answers 1k views ### Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)? My understanding of local non-satiation is that increasing your allocation of one good by a marginal amount increases utility. Suppose your utility takes the following form:$$U(x,y)=x^\alpha y^\beta$$... 0answers 1k views ### Given a standard Cobb-Douglas production function, how to estimate the output elasticity of labour and capital by country? Given a standard Cobb-Douglas production function:$$Y_t=(A_t L_t)^{\alpha} K_t^{1-\alpha}$$Moreover, the production function has constant returns to scale:$$\alpha + (1-\alpha)=1$$How to estimate ... 1answer 674 views ### In the C.E.S. utility function do the parameters need to add up to unity to obtain the Cobb-Douglas utility function? Consider the C.E.S. utility function$$U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} $$Is it true that we must have a+b=1 in order to obtain a Cobb-Douglas utility function as c\rightarrow 0? 1answer 427 views ### How does the limit of U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} as c approaches 0 yield the Cobb-Douglas utlity function? [duplicate] \begin{equation*} U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} \end{equation*} I ask this mainly because after logging both sides of the Utility equation (the first step to proving the assertion, I ... 2answers 3k views ### Marginal Product of Capital in the Solow Model In the classic form of the Solow Model:$$ Y=K^\alpha (AL)^{1-\alpha } $$Describe circumstances in which the marginal product of capital could rise over time, at least for a temporary period. I've ... 2answers 945 views ### Constant Elasticity of Substitution: Special Cases Take an n-commodity constant elasticity of substitution utility function,$$U = \left[\sum^n_{i=1} \alpha_i x^\rho_i \right]^\frac{1}{\rho}$$How do we show the following: Show that as \rho \... 0answers 249 views ### Optimizing Cobb-Douglas like functions Economics isn't my home field, but I'm looking for references for a paper I'm working on and I'm hoping one of you can help. Are there many good references for optimizing a Cobb-Douglas like utility ... 1answer 64 views ### Optimizing Cobbs-Douglas given output I am trying to find L^* and K^* (Labour and Capital respectively) given the following: Q = K^{1/4} L^{3/4} where Q = 120, w=24, and r=128 (Not sure if you need w and r) I know that if I ... 0answers 303 views ### Given Cobb-Douglas production functions for 2 factories (same owner), how will the owner produce y? So my question is this: A company owns two factories, A and B, each with the following production functions: f_A(x_1,x_2)=x_1^{\alpha}x_2^{1-\alpha} f_B(x_1,x_2)=x_1^{\beta}x_2^{1-\beta} Now ... 2answers 640 views ### Fast way to write out the utility optimization problem for a Cobb-Douglas function? In my last problem set, I had to solve both the Utility Maximization Problem (UMP) and Expenditure Minimization Problem (EMP) for a Cobb Douglas utility function. Recall, Cobb Douglas is defined as$$...
Given $$U(x,y)= x^\alpha y^{1-\alpha}$$ $\alpha \in (0,1)$, are Cobb Douglas goods (here $x$ and $y$) complements, substitutes, or neither? Why? An explanation with mixed partial derivatives would ...