# Questions tagged [demand]

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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 ...
31 views

### 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: ...
1 vote
35 views

### 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 ...
1 vote
88 views

### 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?
1 vote
58 views

### 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 ...
12 views

### 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-...
22 views

### 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 ...
1 vote
80 views

### 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 ...
1 vote
67 views

### 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 ...
63 views

### 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 ...
32 views

### 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 ...
1 vote
75 views

### 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 ...
72 views

### 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 &...
171 views

### 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 ...
52 views

### 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 ...
1 vote
43 views

### 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 ...
53 views

### 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 ...
1 vote
90 views

### 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 ...
1 vote
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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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### 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 ...
1 vote
341 views

### 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 ...
1 vote
54 views

### how and why Roy's equation works?

i know that the roy's identity is: $x_{i}^{m}(p,w)=-{\frac {\frac {\partial v}{\partial p_{i}}}{\frac {\partial v}{\partial w}}}$ but i can't understand why it works. why the fraction ...
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1 vote
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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 ...
32 views

### 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 ...
366 views

### 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 ...
72 views

### 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 ...
89 views

### 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 ...
2k views

### 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 ...
186 views

### 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 ...
1 vote
53 views

### 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 ...
1 vote
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 $y = p x_1 + x_2.$
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 ...