# 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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### Are Cobb-Douglas preferences homothetic?

Our lecture defined a preference to be homothetic, if the following is true: $$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$ Cobb-Douglas preferences can be ...
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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 ...
Suppose a utility function $u=x_1^ax_2^b$ with $a+b=1$. The following formula finds the values for $x$: $x_1 = \frac{am}{p_1}\\ x_2 = \frac{bm}{p_2}$ But what if the utility function looks like $u=... 2answers 75 views ### Linking top-down and bottom-up models for analyzing electricity price-based demand response: Expenditure constraint is violated? I have a question about the contents of this paper*, which links a building energy model and a utility-maximization component. In it, the author tests several electricity prices using a Cobb-Douglas ... 1answer 282 views ### Maximizing a Cobb-Douglas Function Suppose that a competitive firm receives a price of$P$for its output, and pays prices of w, r and v for its labor$(L)$, capital$(K)$and natural resources$(R)$inputs, respectively. The firm ... 2answers 1k views ### Find Engel Curve with a Cobb-Douglas [closed] I have$U(x,y)=xy$,$p_1=4$and$p_2=1$. Income is unknown. Where do I start? 1answer 120 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 86 views ### 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 ... 1answer 147 views ### 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}})^{... 0answers 28 views ### 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 ... 1answer 169 views ### 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 ... 1answer 172 views ### 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} ... 0answers 104 views ### MRS in Walrasian equilibrium price expression? I have the utility function U^A=\alpha ln(x^A)+\beta ln(y^A) for consumer A and U^B=\gamma ln(x^B)+\phi ln(y^B) for consumer B. They are endowed with \omega^h_x and \omega^h_y of x and ... 1answer 2k views ### Profit maximization with Cobb-Douglas function I'm trying to maximize a firm's profit given the production function F(L,K)=L^\alpha K^\beta (where L is labor and K is capital) and that \alpha + \beta \neq 1. So, I know that this ... 1answer 707 views ### Marginal product of capital net of depreciation I am trying to understand how marginal product of capital net of depreciation is the following: Given that the production function is quite standard I understand the first term of the marginal ... 1answer 232 views ### Notation of a Cobb-Douglas function printed in 1989 I am trying to understand a paper written back in 1989 about long run population growth. It seems like the PDF is a scanned image of the paper. The notation for the function is on page 11 of the pdf (... 1answer 61 views ### Growth Accounting with variable factor shares Under the assumption of competitive markets, the usual growth accounting equation using Cobb-Douglass function is as follows: \Delta Y/Y = \Delta A/A+w_l\Delta L/L+w_k\Delta K/K Y is output K... 2answers 12k 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 ... 2answers 1k 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}$$How do we show the following: Show that as \rho \... 0answers 561 views ### Marginal product versus marginal productivity in a Cobb-Douglas production function [closed] CFA Kaplan Schweser claim that Cobb-Douglas function exhibits constant marginal product of capital but diminishing marginal productivity of capital. I think this statement is not right. My view ... 0answers 147 views ### Unitary model with cobb-douglas function We have these following from the first order conditions: {U_{LA} \over U_C} = w_A \to MRS_{C,LA}=w_A {U_{LB} \over U_C} = w_B \to MRS_{C, LB}=w_B {U_{LA} \over U_{LB}} = {w_A \over w_B} \to ... 2answers 1k views ### Calculating growth rate of capital when not in steady state Given a Cobb-Douglas production function, the annual population growth rate, savings rate, alpha, annual depreciation rate, and annual technological progress rate, how would one calculate the growth ... 2answers 275 views ### Indirect changes in Marshallian Demand Suppose we have a Cobb-Douglas utility function:$$U(x,y)=x^\alpha y^\beta$$and a budget constraint:$$p_{x}x+p_{y}y=I$$where \alpha+\beta=1. It can be shown that the Marshallian demand for x ... 1answer 3k views ### Using the Slutsky equation Suppose we have utility:$$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_{... 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 469 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 ... 1answer 695 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$c\rightarrow 0$? 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 ... 0answers 257 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 ... 2answers 32k views ### Marshallian Demand for Cobb-Douglas 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):$x_1 = \frac{am}{p_1}\\ x_2 = \...
I am trying to find L$^*$ 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 ...