# 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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### Calculating cost-minimizing inputs with 3 inputs in production function [closed]

How can I determine the cost-minimizing input bundle with a standard Cobb-Douglas production function with three inputs. despite its simple process, the algebra becomes very hard as you go through the ...
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### Trying to understanding how an equation is arrived at in Sach's et al "Geography and Economic Development"

Within the paper's discussion of formal models, I'm struggling to understand how the authors arrive at a certain equation. First, a model of the growth rate of economy is presented, which I do ...
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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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### Cobb-Douglas Production Function - Finding units of labour to maximise production

Given production function $f(L,K)=16L^\frac{1}{4}K^\frac{3}{4}$, where each unit of labour costs £50 and each unit of capital costs £100 and you have a budget of £500,000. Find the number of units of ...
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### how to solve such UMP where utility function is quasi-linear with cobb-douglas function as the non-linear part [closed]

U =$X_1+X_2^aX_3^{1-a}$ $a ∈[0,1]$ $s.t. p·x≤w , x≥0$ I have tried FOC for x1 x2 x3 and λ, but I cannot get two pairs of equalities separately in order to express two unknowns as a function of ...
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### What is α in a Cobb-Douglas utility function?

Sorry if this is not the place to ask, I'm new here. I'm studying economy but I'm struggling to understand the Cobb-Douglas utility function. If we've one such that xt is consumption in period t, and ...
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### Deriving a demand curve from a Cobb-Douglas utility

Probably a daft question but I derived an equation for a demand curve from a general Cobb-Douglas utility function $$U(x,y)=\beta x^{\alpha}y^{1-\alpha}$$ given a budget constraint $$M=xP_x+yP_y$$ and ...
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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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### K in the Cobb Douglas function

I'm using the Cobb Douglas production function for a Mathematics investigation into how optimisation works in Economics. The assumption is that the firm require's only one type of capital, that is, a ...
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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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### Interpretation of Interesting Utility Function

Solving introductory microeconomics problems I have come across the following type of utility function:  f(K,L) = (\alpha K^{\frac{\sigma - 1}{\sigma}} + (1 - \alpha) L^{\frac{\sigma - 1}{\sigma}})^{...
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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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