Questions tagged [demand]
The demand tag has no usage guidance.
152
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Give bundles $x,y\in \mathbb R^n$, there must exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?
For a problem in revealed preference. Give bundles $x,y\in \mathbb R^n$, must there exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?
Intuitively, this mean that we have two bundles, and ...
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How to prove Paasche index is less or equal to CPI if preferences are homothetic?
Given that
$$CPI=\frac{e(p^1,u^0)}{e(p^0,u^0)}$$
and the Paasche index
$$PPI=\frac{p^1\cdot x^1}{p^0\cdot x^1}$$
How do I show that $PPI\leq CPI$ if preferences are homothetic?
Here's what I've done:
...
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How to calculate direct utility from indirect utility in this exercise?
A consumer has an indirect utility function given by
$$v(p_1, p_2, R)=\frac{R}{p_{1}+p_2}$$
Where $p_1$ and $p_2$ denote the prices of the two goods consumed by the individual and $R$ the income.
How ...
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How to derive the demands from this rather bizarre utility?
I have a rather bizarre utility function, which is neither differentiable nor quasi-concave
$$u(x_1,x_2)=\max\{\min\{x_1,2x_2\},\min\{2x_1,x_2\}\}$$
How to derive the demand function?
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Does WARP still imply Compensated Law of Demand even if one of the goods is indivisible?
Consider 2 goods, $x_1$ and $x_2$. Let's assume $x_1$ is indivisible (we can only consume integer units of $x_1$). And suppose the consumer satisfies budget balance and homogeneity of degree 0, and ...
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Conversion rate models for multi-touch digital advertising over time
Is there any literature on the conversion rate of multi-touch advertising over time, showing that how decreasing the time between touches increases conversion rate?
For example, a chart showing:
Y-...
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Proof for calculating market elasticity of demand
I have heard that the market elasticity of demand for a good is the weighted sum of the individual price elasticities of demand for that good but cannot find any information about it online. Could ...
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Question About Non-Discriminating Monopolist - Mathematics for Economists by Simon and Blume Chapter 17 Exercise 7
I am working on Mathematics for Economists by Simon and Blume Exercise 17.7. I know there is an Answers Pamphlet. However, the solution to this question does not make any sense to me. It seems that ...
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Is it possible to get back the consumer’s utility function from their demand functions?
I am curious about if it’s possible to reverse the utility maximization process, i.e. given the consumer’s Marshallian demand functions, find their utility function.
I was thinking of trying to find ...
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Is there a simple language explanation for Hick's Reciprocity/Symmetry Theorem?
It is a well known fact in consumer theory that for a Hicksian demand curve the cross-price effect of good i with respect to the price of good j equals the cross-price effect of good j with respect to ...
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Why would lowering quantity supplied cause to quantity demanded to increase?
I am reading an article about price-takers vs. price-makers, and it says the following:
A Price Maker can alter the output of its product at any time to suit its needs for profit maximization. For ...
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Finding the profit from a demand equation
The demand equation for a company's product is $3p + x = 400$, where $x(t)$ units can be sold at a price of $p$ each. If the demand increases at a rate of 3 units per year when the demand reaches 50 ...
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CES in Slutsky matrix (weird results)
We have a Slutsky matrix:
\begin{bmatrix}
\partial x_{1}^H/\partial P_1 & \partial x_{1}^H/\partial P_2 & \dots & \partial x_{1}^H/\partial P_n \\
\partial x_{2}^H/\partial P_1 &...
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The formula for expansion path
Is there a way how to precisely compute the expansion path?
I know a consumer's utility function $U(\boldsymbol{x})$, I know the budget constraint $\sum P_i x_i \leq M$, I am able to compute the ...
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Linear Engel Curve
How to prove that if the Engel curves (expenditures as a function of wealth) are linear in wealth, then the indirect utility function has the form $v_{i}(p,a_{i})=\alpha_{i}(p)+\beta(p)a_{i}$ for an ...
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Are other 'variables' in demand functions always fixed?
My question is whether our demand functions e.g. Hicksian (compensated) demand, are ever functions of 3 or more variables, or if the other price variables and utility are always fixed, and hence just ...
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Integrating over the Y Axis: (∆CS)
The traditional formulae for consumer surplus is: $\text{CS} = \int_{0}^{x_0} [x(p_x,\overline{p_y}, \overline{m})]dx - x_0P_{x_0}$.
This is the area under the Marshallian demand curve, that is only ...
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Calculating the substitution effect with the derivative
Substitution Effect (SE) for a price increase of $P_x$ to $P_x'$ can be written as:
$h(P_x', P_y, U) - h(P_x, P_y, U) = ∆h$, where $h$ is Hicksian demand. Correct?
The Slutsky equations decomposes a ...
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Are grains a Giffen good? Also does circumstances make a good - Giffen good?
I was going through microeconomics course and I came across the Giffen good. Now I have a scenario with me. A family only buys grains and chocolate from the shop and the price of grain is increasing. ...
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Is there a situation when a shift in supply and demand leads to a shortage?
For my intro health economics class, my professor asked us to explain how certain scenarios impact the supply and demand of health care (using only supply/demand analysis). He raised an example of a ...
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Finding demand function in Walrasian equilibrium
Maybe the title doesn't reflect what I mean perfectly but basically, I wanna derive demand functions from those two utility functions:
where $x_{11}$ is the consumption of good 1 by agent 1 and $x_{...
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Expenditure function only dependent on prices
I'm struggling with a problem where I want to derive the Hicksian demand from a given expenditure function $e(p,u)$. I would do that by using Shephard's Lemma, so that the first partial derivative of $...
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What exactly is the demand for money?
If the demand for money is the total amount of money that people want, then wouldn’t it just be infinite, considering people want as much money as they can get? I also don’t get why when people’s ...
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Why is the demand function homogenous of degree $0$ in all prices and income?
Why is the demand function homogenous of degree $0$ in all prices and income?
If I know that the expenditure function is homogenous of degree $1$ in prices and income, how do I show, using the lemma ...
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how and why Roy's equation works?
i know that the roy's identity is: ${\displaystyle x_{i}^{m}(p,w)=-{\frac {\frac {\partial v}{\partial p_{i}}}{\frac {\partial v}{\partial w}}}}$
but i can't understand why it works.
why the fraction ...
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Complements/substitutes estimation from data (Slutsky matrix)
Estimation of complements/substitutes by Slutsky matrix from observable data
Hello everyone,
I was curious about the following problem: I can observe price $P_i$ of $n$ goods and the amount of goods $...
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138
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Question regarding perfectly elastic demand
I know that perfectly elastic demand looks like a horizontal line on a graph, but this implies that somehow the quantity demanded is multiple values simultaneously at a single price point. How is this ...
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Does the compensated law of demand hold for giffen good?
Considering 2 goods good 1 and good 2 where good 1 is given. Can you show me with a help of a diagram when the price of good 1 aka the giffen good increases?
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Contractionary monetary policy to tame inflation. Paradox?
One of the consequences caused by high inflation is lower economic growth.
The central bank, by contractionary monetary policy, increases interest rates in order to decrease aggregate demand and lower ...
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What are the most plausible scenarios for Eurozone economics without Nord Stream 1 gas?
As you may have heard, the Nord Stream 1 and 2 gas pipelines are no longer available.
It is possible to foresee the most probable economic outcomes of that events to the Eurozone area? My main focus ...
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Homogeneity of compensated demand for Leontief (perfect complements) function
In my assignment I have a Leontief (perfect complements) function u(x,y)=min(x,2y). Keeping utility fixed, we minimize the expenditure. Since we have a Leontief function, at a fixed level of utility u(...
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Price Elasticity for a group of products
I am given a list with items and corresponding prices and units sold. Those items can be clustered into product groups. For most of the items, between 2 and 3 different prices can be observed. This ...
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Uncompensated and compensated demand functions
I came across this lecture note online and some of the points below confuse me. I have added the part that confuses me as an image and here is the lecture note for further reference, if needed.
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I need help interpreting a diversion curve diagram (transport economics)
In my handbook of transport economics (Blauwens, De Baere, Van de Voorde, 2020), while discussing infrastructure assignment and the diversion curve method, the following diagram is shown (minus "...
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If the income increases by $\$d$, will it mean the utility at the optimal point increases by $\lambda d$?
I read that if the income increases by $\\\$d$, then the utility at the optimal point will increase by $\lambda d$. How do I get a sense of this, both mathematically and intuitively?
Can we write that ...
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How Can I Model Demand Elasticity?
Can demand elasticity be determined by examining the distribution of marginal utility across a potential customer base?
For example, if the distribution of marginal utility among potential customers ...
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Does continuous preference imply upper-hemi continuous demand correspondence?
Let alternative $x,y,z\in R^N$.
$\succsim$ is convex, rational, monotonic, and continuous.
Let $B=[y,z]$ be a budget segment.
Let demand correspondence be $D[y,z]=\{x\in B||x\succsim B\}$
$D[y,z]$ is ...
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An attempt at using a graphing calculator to visualize the price elasticity of demand for a point moving on the demand curve
I assume a demand function ( of price) : $Q(x)= 10-2x$ , and therefore, a price function (of demand ): $P(x)= -\frac 12 x +5$.
The demand curve ( $y =-\frac 12 x +5$) represents the price function, ...
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Checking negativity condition in demand system model
Let's assume you want to estimate a demand system model, e.g. the AIDS, based on observational data. Then you usually test first whether the homogeneity and symmetry condition hold in order to check ...
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Which number counts officially as the " slope of the demand curve" : $\frac {\mathit d P(Q)}{\mathit dQ}$ or$\frac {\mathit d Q(P)}{\mathit dP}$?
This is a very elementary question from a complete novice, and aiming first at preventing a possible misunderstanding. Thanks in advance.
Suppose we have a linear demand curve with Y intercept $(0,...
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Budget line for mean variance utility
Consider the mean-variance utility used in CAPM. The budget line when allocating a risk-free and a risky asset is the line connecting the $r_f$ and the risky asset.
Suppose that I have fixed amount ...
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Law of demand with time component
As I understand it the law of demand works at one particular instant. I.e. it make a claim that the higher the price of an item at time t, the lower the quantity that will be purchased. Is there an ...
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A utility function (neither perfect substitues nor perfect complements) which stems from a CES f. and leads to gross complements or gross substitutes
So the most prominent preferences are perfect substitutes, perfect complements and cobb-douglas preferences. Perfect complements and perfect substitutes are extreme cases and I was asked whether there ...
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Relative prices in demand system estimation
Context/ Setup:
Microeconometrics offers many tools to study features of the demand for different goods/ groups of goods, such as the well known Almost Ideal Demand System (AIDs). The AIDs model ...
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Complement in production and the slope of factor demand curves
Considering a firm taking prices for granted and maximizing profits
$$pf(x_1,...,x_K) - \sum_{i=1}^K q_i x_i,$$
where $f$ is strictly concave. Furthermore, let the factor demand curves be the ...
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How much do second-hand good purchases affect first-hand demand?
For the purpose of this question, I'm only interested in relatively cheap goods (clothing, appliances, furniture, phones), not extremely substantial purchases like cars or houses.
Proceeding from ...
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Two-Stage Utility Maximization Problem
Actually I don't know how to solve such utility maximization problem, only know using FOC and budget constraint to solve for demand. I will appreciate it if someone tell me the procedure facing such ...
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Is it possible to get a demand function as function of income and utility from this log linear indirect utility?
I have this indirect utility function:
$$v=-c\frac{p^{(-β+1)}}{(-\beta+1)}+\frac{y^{(-\gamma+1)}}{(-\gamma+1)}$$
with constraint Y = c + pq
I have posted before about getting the utility function from ...
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What is the typical utility function of the standard loglinear demand function?
What is the typical utility function of this demand function?
$$x_1 = \ln(x_2) - \beta \ln(p_1) + \gamma \ln(y).$$
With budget constraint $y = p x_1 + x_2.$
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How to derive utility function from indirect utility and Marshallian demand?
c is composite good with normalised price, q is good with price p. y is income.
I have this indirect utility function:
$$v=-c\frac{p^{(-β+1)}}{(-\beta+1)}+\frac{y^{(-\gamma+1)}}{(-\gamma+1)}$$
And ...
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