Questions tagged [demand]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
6
votes
1answer
133 views

Econ Intuition for Jacobian inverse in demand system

Consider the following simple linear demand system (in vector notation) with n different products Demand: $\quad\mathbf{q=B\left(a-p\right)}$ Inverse demand: $\quad\mathbf{p=a-B^{-1}q}$ where $\...
5
votes
1answer
345 views

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 ...
5
votes
0answers
82 views

Afriat theorem for negative goods

GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative. I wonder if we can ...
4
votes
1answer
66 views

Correct and complete characterisation of the Walrasian demand function

I would like to propose to you the following problem and my proposed solution. In particular, I am unsure in how to correctly characterize the Walrasian demand. Can you please have a look at it and ...
4
votes
1answer
103 views

Perfect substitutes and Lagrange

How does one solve utility maximization of perfect substitutes using Lagrangian function? Consider the problem $$\max_{x,y} ax +by $$ subject to the constraint that $$px + qy \leq I$$ where $a,b,p,q,...
4
votes
1answer
245 views

Price-consumption curve

Suppose a consumer whose income is $b$ has a utility function given by $U(x,y) = 2xy+y^2$ with the price of $x$ being $p_x$ and the price of $y$ being $p_y$. Draw the price-consumption curve assuming ...
4
votes
1answer
71 views

Equilibrium with substitute goods

I am attempting to solve the following problem The demand functions for two substitute goods, the production cost of which equals $c_1$ and $c_2$, are $q_1 = a_1 + b_{11}p_1 + b_{12}p_2$ and $q_2 = ...
3
votes
2answers
123 views

Terminology, is elasticity used as “mean elasticity”?

Given a demand $q$ and a price $p$ sutch that $q=q(p)$, the elasticity of demand is given by, $\epsilon = \frac{p}{q}\frac{dq}{dp}$ which depends on the price. But, when reading papers about ...
3
votes
2answers
115 views

elasticity from inverse demand

I was wondering of my thinking here was right: Given $$ e=\frac{dQ}{dp}*\frac{p}{Q}, $$ where $ e $ is elasticity, $ dQ/dp $ is first derivative of demand function, $p$ is price and $Q$ is quantity. ...
3
votes
3answers
415 views

Price elasticity of demand always increases with price?

Is there a closed-form continuous demand function whose price elasticity of demand decreases with the price?
3
votes
1answer
522 views

Why is the graph of unitary elastic demand a hyperbola?

My teacher said that the graph of unitary elastic demand is a parabola: But i fail to understand how in a hyperbola the percentage change of price and quantity demanded remains same. Can someone ...
3
votes
1answer
1k views

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 ...
3
votes
1answer
68 views

Question about the relationship between Weak Axiom and Slutsky Matrix

We know that if a differentiable Walrasian demand function $x(p,w)$ satisfies Walras' law ($p^Tx=w$), homogeneity of degree zero ($x(\alpha p,\alpha w)=x(p,w)$), and the weak axiom of revealed ...
3
votes
1answer
172 views

Marshalian and Hickisian Demands and Slutsky Equation

everyone. I have the following question: A consumer has the following indirect utility function: $ V(p_1,p_2,b) = (p_2k-b)p_1^{-1} \left[ \frac{2p_2k - 2b}{p_2} \right]^{-2}, x_2 < k$ a) Find ...
3
votes
1answer
105 views

Find Price Elasticity of Demand for p = 0

Given a linear demand curve $q(p) = a - bp$, how would one find the price elasticity of demand at $p = 0$? The quantity that would be demanded is given: $Q_0 = a$ The formula for the price elasticity ...
2
votes
2answers
95 views

Prove that budget constraint is Lower Hemi Continuos (LHC)

I need to prove that the following constraint is LHC. $B=\{x \in R^n : px\leqslant pw)$ But Im not capable of finding and sequence $\{x_n\}$ such that $x_n \in B(p_n,w_n) \forall n$ and that $x_n\...
2
votes
1answer
55 views

Effect of price on utility

A consumer has an endowment vector $w$; at prices $p$ his demand for the first good exceeds his endowment; $x_1^+(p; pw)>w_1$ then a small increase of $p_1$ will lower his utility. I was discussing ...
2
votes
1answer
70 views

Finding restrictions on parameters for a demand function

I have a question that asks: Let $x_1$ be the quantity of a good 1, $p_1$ the price of good 1, $p_2$ the price of good 2, and $M$ is income. Let $๐‘ฅ_1(๐‘_1, ๐‘_2, ๐‘€; ๐ด) = ๐ด๐‘_1^๐›ผ๐‘_2^๐›ฝ๐‘€^๐›พ$ ...
2
votes
1answer
1k views

what is monotonicity and strict monotonicity in preferences?

I am really confused between monotonic preferences and strictly monotonic preferences, I saw some video and read certain answer where it is mentioned that the When preferences are monotone / weak ...
2
votes
1answer
65 views

Approaches in demand analysis

What is the difference between Engel Curve and the system approach of demand analysis?
2
votes
1answer
59 views

CES utility function in an Edgeworth box

Two consumers have the CES utility function $x_1^\beta +x_2^\beta$, for $0<\beta<1$, their initial endowments are $w^1=(1,0)$, $w^2=(0,1)$ Draw the Core of this economy in an Edgeworth box. Note ...
2
votes
2answers
65 views

How to explain negative correlation between quantity sold and expenditure on advertisement?

I have received the following dataset from our economics Professor. It has 15 observations and 4 variables - 'qsold' (quantity sold of product X), psn (price of X), ...
2
votes
1answer
50 views

Interpreting the q-intercept of the demand curve

Given a demand curve for a particular commodity, which I'll interpret as a function $p(q)$, the $p$-intercept can be interpreted as the choke price, i.e. the lowest price at which quantity demanded is ...
2
votes
1answer
59 views

When the global optimal is outside of the constraint set, what will be the demand?

$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex. $a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that ...
2
votes
1answer
46 views

Is saying that the demand is elastic or inelastic too oversimplified?

As we know that elasticity varies from infinity to zero as we move along a linear demand curve, then is it correct to label any demand curve elastic or inelastic as a whole?
2
votes
0answers
29 views

Market shares of Nested Logit demand model

Consider a Nested Logit demand model with two nests, $N_1, N_2$: $N_1$ contains the outside option only (labelled "0"), $N_2$ contains all the remaining alternatives (labelled "$j=1,...,...
2
votes
0answers
20 views

An Extension to CES Demand

I am reading a paper with an extended CES final good setting: The representative household consists of a continuum of members, indexed by $k$ $C_{t}=\int C_{k, t} d k$ $C_{k, t}=\left(\int_{j \in \...
1
vote
3answers
721 views

Why can't I find masks for the corona virus?

Not an economist by far, just a layman, and that's a layman question. How is this possible that it's difficult to find mask for the Corona Virus? I have been several times to 7/11, boots, Watson, and ...
1
vote
2answers
422 views

Finding demand functions for an unusual utility function

I have a utility function: $U = x + \min\{x,y\}$ I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements? Also, what preferences ...
1
vote
1answer
48 views

Prove the equation

Let $$ x^0=x^*(p^0,w)$$ then $$v(p,px^0)$$ is minimized at $$p=p^0$$ What theorem are we supposed to use in order to solve this, because I am a bit lost. Thanks in advance for all the suggestions/help....
1
vote
1answer
75 views

Walrasian demand with a twist of Leontief function

A consumer has the utility function $u(x_1; x_2) = \min(x_1; x_2) + 5 \max(x_1; x_2)$. Find its Walrasian demand $x^*(p; w)$. I've tried searching it up when we have two Leontief functions summed ...
1
vote
1answer
46 views

Examples of bounded, positive, inverse demand curves

The three most common examples of demand curves I am aware of are \begin{align} Q&= b - aP,\\ Q&= bP^a,\\ Q&= b e^{-aP}\\ \end{align} The first being our classic linear demand curve, the ...
1
vote
1answer
79 views

What additional axiom to GARP do we need to generate a differentiable or smooth utility function

After researching for a while, I find this: https://www.jstor.org/stable/1913607?seq=2#metadata_info_tab_contents They come up with an axiom called SSARP that generates a preference with smooth demand ...
1
vote
1answer
70 views

Marshall demand for simple CES utility

Assume that preferences are given by a utility function is given $$u(x_1,x_2) = (x_1^\rho + x_2^\rho)^{1/\rho}$$ what then are the Marshall demand given budget constraint $$p_1x_1 + p_2x_2 \leq I$$
1
vote
1answer
39 views

Budget Set- closed and boundedness

I am fairly new to economics, and we were introduced to budget sets, The professor mentioned that the budget set $B(p,w) = \{x \in R^{l}_{+}: px \leq w\}$ is non empty and closed - I could prove the ...
1
vote
1answer
133 views

confusion regarding elasticity of a demand curve

The following question is on a quiz at Marginal Revolution University: https://mru.org/practice-questions/calculating-elasticity-demand-practice-questions The elasticity of demand is 2.0. Is the ...
1
vote
2answers
44 views

Remove Linear Good From Quasi-linear Utility Function

Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$, $\beta > 0 $ What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) =...
1
vote
2answers
2k views

Difference between Engel curve and income expansion path

I was scrolling through many questions on this site about income offer path and it appeared to me that income offer path, income expansion path, engel curve all are different terms with same meaning, ...
1
vote
1answer
51 views

Homework Question - Price Floor / Elasticity of Demand

I'm currently taking undergrad microeconomics and came across the following question: The current price floor in the agricultural lettuce market makes it such that price of lettuce is 25% higher than ...
1
vote
1answer
56 views

Essential goods: How does one restrict the utility function?

I understand that solutions on boundary of the set under consideration when doing constrained optimization are often problematical. Usually it is said that we assume that goods are essential to insure ...
1
vote
1answer
71 views

Would Pilots and Air travel be considered complementary?

Now, my economics teacher and I have a disagreement. According to theory, as the price of air travel (airline tickets) increases, the demand for pilots will decrease as well because fewer people will ...
1
vote
1answer
104 views

Max Utility Function and Finding associated demand curve

I have a max utility function, therefore; U(x,y)= max(2x,y) and I am trying to find the demand function x = x(๐‘x , ๐‘y , ๐‘€), note this function cannot be differentiated. I am familiar that the ...
1
vote
1answer
198 views

How do I derive the aggregate demand function given two utilities functions?

Assume that we have two people with the same utility function of $U_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I_i$ is the income. Let $P_x$ denote price of good $x$ and $P_y$ denote price of good $y$. ...
1
vote
1answer
317 views

Reason behind the decomposition of price effect into substitution and income effects

I was studying the decomposition of price effect into substitution and income effects. I am finding it a bit complicated. This is what I have understood: (0) Let us assume that there are two ...
1
vote
3answers
55 views

Does investment directly influence demand?

I quote from the first page of India's Economic Survey 2019 (an official document) - Investment, especially private investment, is the โ€œkey driverโ€ that drives demand, creates capacity, ...
1
vote
0answers
29 views

Definition of strictly convex preference

Let $x,y\in X$. Does strictly convex preference (which implies that the utility is strictly quasiconcave) mean that: $x\succsim y$ implies $\alpha x+(1-\alpha)y\succ y$ for any $\alpha\in (0,1)$?
1
vote
0answers
21 views

functional form for a consumption shock

In a DSGE model, how can I add a disturbance/shock in the consumption of households? For example given my utility function $$ U(C,H) = \frac{C_t^{1-\theta}}{1-\theta} - \frac{B}{\eta} H_t^\eta,$$ ...
1
vote
1answer
91 views

GDP in equilibrium

I have to find the GDP in equilibrium for a IS LM model. It is given that $M^d (Y,r)=M_0+M_1Y-M_2r$ and $M^d=M/P$, $M_0,M_1,M_2>0$ and $M^d$ is money demand. my solution so far I have found that $...
1
vote
1answer
19 views

The optimal price for a demand curve with a steep slope

Given the demand function, $$D(p)=A-ap$$ I've found the optimal price, $$p=\frac{A+ac}{2a}$$ Where $c$ is cost and $A,a >0$. My question is how is the optimal price is dependent of $a$ (1) - what ...
1
vote
1answer
161 views

Generalizing demand for perfect substitutes utility function

I have the utility function: $U(x_1,...,x_n)=a_0+\sum_{i=1}^{n}a_ix_i\;\;\;\;\;\;\;\;\;a_j\in\mathbb{R}_+ \;\;\forall j=\{0,...,n\}$ (maybe $a_0$ could be zero) $\sum_{i=1}^{n}a_i\in (0,K)\;\;\;$ ...