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 ...
- 16.2k
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 ...
- 3,276
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 ...
- 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=\...
- 3,276
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 \\ ...
- 911
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.
- 6,355
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(...
- 11.4k
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 ...
- 11.4k
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 ...
- 53k
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 $x=(1,0,\dots,0) \in B(p,w)$.
...
- 1,849
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 ...
- 3,467
5
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
$$\frac{\...
- 5,260
5
votes
Accepted
Correct and complete characterisation of the Walrasian demand function
To solve
$$\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^...
- 3,276
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:
...
- 53k
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 $...
- 53k
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", ...
- 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 ...
- 605
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 ...
- 53k
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}{...
- 6,355
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 ...
- 15.3k
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
$$ \alpha_n = \frac{w_n}{p_n x} \text{ if } p_n x > ...
- 9,802
4
votes
elasticity from inverse demand
I will denote the demand function by $Q(p)$ and the inverse demand function by $P(q)$. Then
$$
\forall q: Q(P(q)) = q
$$
so for any $h > 0$ and $q$ we have
$$
\begin{align*}
p & := P(q) \\
p_h &...
- 28.4k
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 ...
- 53k
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 ...
- 5,260
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 ...
- 1,705
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 $p_1x_1$...
- 6,355
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 ...
- 9,802
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 ...
- 28.4k
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 ...
- 3,276
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 ...
- 805
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