Skip to main content
14 votes

How much do second-hand good purchases affect first-hand demand?

Coase (1972) has a classic treatments of this issue for monopolists selling durable goods. The general idea is that if Alice sells a textbook to Bob, Bob can resell it to Charlie when he is done with ...
BKay's user avatar
  • 16.3k
8 votes
Accepted

Two-Stage Utility Maximization Problem

Consider the Wikipedia definition (take from Hal Varian's book) of a quasi-linear utility function $$u(w,x_1,...,x_n) = w + h(x_1,...,x_n),$$ where $h$ is strictly concave. The example in this ...
Jesper Hybel's user avatar
  • 3,386
7 votes
Accepted

Econ Intuition for Jacobian inverse in demand system

For the 2x2 case being considered, write $$\mathbf{B}=\left[\begin{array}{cc} b_{1,1} & b_{1,2}\\ b_{2,1} & b_{2,2} \end{array}\right].\quad$$ It follows that the element (1,1) in $B^{-1}$ is ...
dlnB's user avatar
  • 595
7 votes
Accepted

Demand for minimum of $4$ different goods

You can solve it sequentially by noting the nesting structure of the utility function $U$. So first note that the utility function combines utility functions you are probably already familiar with $U=\...
Jesper Hybel's user avatar
  • 3,386
6 votes
Accepted

Finding demand functions for an unusual utility function

I assume you know how does $\min\{x,y\}$ look like? In order to draw utility function of interest, you need to consider cases: $u(x,y)=x+\min\{x,y\}=\begin{cases}2x, \;\; \mathrm{for} \;\; x \leq y \\ ...
bajun65537's user avatar
6 votes

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

The supply of masks can't keep up with soaring demand because mask producers have capacity constraints in the short run. See this recent article.
VARulle's user avatar
  • 6,900
6 votes
Accepted

Prove the equation

You don't need to use any fancy theorem, the trick is to disentangle the definitions. Everything follows directly from the definitions. $x^0=x^*(p^0,w)$ means that $p^0x^0\leq w$ and that $u(x)\leq u(...
Michael Greinecker's user avatar
6 votes
Accepted

Effect of price on utility

That was tricky. The idea is as follows: First, under standard assumptions, demand is continuous. If you change prices a little bit, demand will not change a lot. In particular, if your excess demand ...
Michael Greinecker's user avatar
6 votes
Accepted

Perfect substitutes and Lagrange

Your Lagrangian would be $$L = (ax+by)+\lambda (I−p_x x−p_y y) +\mu_x(x−0)+\mu_y(y-0),$$ where the final two terms represent the restriction that $x,y\geq0$. You then arrive at conditions $$\frac{\...
Bayesian's user avatar
  • 5,291
5 votes

Why isn't "long-run aggregate demand (or LRAD)" a thing?

The main reason why long run aggregate supply is vertical is that in the end the production capacity of every country is limited. In the end there is always some maximum number of number of stuff we ...
1muflon1's user avatar
  • 56.7k
5 votes

Prove that budget constraint is Lower Hemi Continuos (LHC)

I don't believe it is lower semicontinous. Let $w = (0,\dots,0)$, $p \in \mathbb{R}^n_+$ be any vector such that $p_1 = 0$ (the first coordinate being 0). The allocation $x=(1,0,\dots,0) \in B(p,w)$. ...
Walrasian Auctioneer's user avatar
5 votes
Accepted

what is monotonicity and strict monotonicity in preferences?

The word monotonic means "always moving in the same direction", in our case, always going up. Monotonic preferences mean that the customer always prefers more of a good. This comes in two ...
RegressForward's user avatar
5 votes
Accepted

Correct and complete characterisation of the Walrasian demand function

To solve $$\max_{x \geq 0} \ (x_1+1)^\alpha(x_2 + 1)^\beta$$ $$s.t. \ \ I \geq p_1x_1 + p_2x_2,$$ I would define $y_1 = x_1+1$ and $y_2 = x_2 + 1$ to get the problem $$\max_{y \geq 0} \ y_1^\alpha y_2^...
Jesper Hybel's user avatar
  • 3,386
5 votes

Upward sloping demand curves can’t exist!

Upward sloping demand curves are rare but they can exist for a class of a good that is called Giffen good. Upward sloping demand can exist because price of a good or service has two effects: ...
1muflon1's user avatar
  • 56.7k
5 votes
Accepted

Which number counts officially as the " slope of the demand curve" : $\frac {\mathit d P(Q)}{\mathit dQ}$ or$\frac {\mathit d Q(P)}{\mathit dP}$?

It is a gradient of $Q(P)$. $Q(P)$ is the demand function. $P(Q)$ is the inverse demand function. Even though confusingly when we plot demand we typically plot $P(Q)$, the demand function is actually $...
1muflon1's user avatar
  • 56.7k
5 votes
Accepted

What exactly is the demand for money?

When economists talk about "demand for money", they don't mean, "How much wealth do people want to have?" Because yes, presumably the answer to that would be "infinity", ...
Jay's user avatar
  • 320
4 votes

Finding demand functions for an unusual utility function

To provide some real world(ish) interpretation, you could consider the following: Wallace enjoys eating cheese on its own. He doesn't much care for crackers on their own, but he especially loves ...
H Rogers's user avatar
  • 638
4 votes
Accepted

Why is the graph of unitary elastic demand a hyperbola?

The price elasticity of demand is defined as: $$E_P=\frac{dQ}{dP} \frac{P}{Q}$$ Although generally elasticity depends on price there is a special type of functions (isoelastic functions) for which ...
1muflon1's user avatar
  • 56.7k
4 votes
Accepted

Price-consumption curve

It's true that given the utility function the $y$-good is a normal good, so the question is quite odd. Ignoring this, your calculations are correct, but you could simplify to $y(p_x,p_y,b)=\frac{b}{...
VARulle's user avatar
  • 6,900
4 votes
Accepted

Deriving a demand curve from a Cobb-Douglas utility

If you take the general class of CES utility functions, of which Cobb-Douglas is a special case, you do indeed get a demand function that depends on other prices. Specifically, the CES utility ...
Herr K.'s user avatar
  • 15.4k
4 votes

Prove that budget constraint is Lower Hemi Continuos (LHC)

One approach could be the following. For a $(p_n,w_n)$ in the sequence and $x \in B(p,w)$ define: $$ \alpha_n = 1 \text{ if } p_n x \le w_n$$ and $$ \alpha_n = \frac{w_n}{p_n x} \text{ if } p_n x > ...
tdm's user avatar
  • 12.2k
4 votes

elasticity from inverse demand

I will denote the demand function by $Q(p)$ and the inverse demand function by $P(q)$. Then $$ \forall q: Q(P(q)) = q $$ so for any $h > 0$ and $q$ we have $$ \begin{align*} p & := P(q) \\ p_h &...
Giskard's user avatar
  • 29.2k
4 votes
Accepted

Terminology, is elasticity used as "mean elasticity"?

I would not call it average elasticity rather its elasticity at an average price. For example take the first paper about elasticity of oil you cite (that is Cooper, J. C. (2003). Price elasticity of ...
1muflon1's user avatar
  • 56.7k
4 votes
Accepted

Walrasian demand with a twist of Leontief function

Why don't you just plug in some values for $x_1$ and $x_2$? Start with something like $x_1=1, x_2=1$ and find utility $u(1,1)=1+5*1$. Then increase $x_1$ or $x_2$ and let $x_1=2, x_2=1$ and find ...
Bayesian's user avatar
  • 5,291
4 votes
Accepted

CES utility function in an Edgeworth box

There seems to be some confusion in the expression for $x^*_i$ in the question that whether $i$ is for consumer of for the good. Assuming $i$ is for consumer: Let $x^*_i = (x_1^i,x_2^i)'$ be the ...
Dayne's user avatar
  • 1,735
4 votes
Accepted

Finding restrictions on parameters for a demand function

Demand is positive, so $A>0$. If $p_1$ goes to $\infty$, $x_1$ has to go to 0, since $p_1x_1$ is bounded by $M$. Thus $\alpha < 0$. If $p_2$ goes to 0, $x_1$ cannot go to $\infty$, since $p_1x_1$...
VARulle's user avatar
  • 6,900
4 votes
Accepted

Approaches in demand analysis

In general the demand for a certain good (say from a consumer) can be written as a function of the prices of all available goods and the total amount of money that the consumer has available. Take the ...
tdm's user avatar
  • 12.2k
4 votes
Accepted

Demand curve is same as Marginal Benefit curve?

Nuance matters: In the comments under 1muflon1's answer the quote given is The demand curve represents marginal benefit. The vertical distance at each quantity shows the mount consumers are willing ...
Giskard's user avatar
  • 29.2k
4 votes

Demand for minimum of $4$ different goods

To provide another answer with less equations: Consider first that the inner utility function $u_1 = \sqrt{x+y}$ and $u_2 = z + w$ are perfect substitutes implying that consumer only buy the cheapest ...
Jesper Hybel's user avatar
  • 3,386
4 votes
Accepted

Why it is unit elasticity

Assuming you mean unit elasticity of demand with respect to price the answer is yes. From the information you have, we can deduce that the demand function is as follows: $$Q^d(p)=10/p$$ (I always ...
user18214's user avatar
  • 805

Only top scored, non community-wiki answers of a minimum length are eligible