Questions tagged [self-study]
Questions about self-studying economics, including curriculum design, study strategies, resources, etc.
0
votes
0answers
32 views
Help needed to understand proof of outcome consequentialism
In decision under uncertainty, there's this lemma, for which I don't understand the proof (actually, it seems overcomplicated to me).
Is it really necessary to introduce the new binary relation with ...
0
votes
0answers
53 views
Image of binary relation
From the book:
"a binary relation $R$ associated to each element $x$ of $X$ some elements $y$ of $X$. We denote by $R(x) = \{y \in X : x R y\}$ the image of $x$ through $R$"
but then is an example:
...
0
votes
1answer
47 views
Prove that $u$ is a utility function for $\succsim$
If X is finite, define this function $u : X \rightarrow \mathbb{R}$ by $u(x) = |\{z\in X:z \prec x \}|$. Prove that $u$ is a utility function for $\succsim$.
Is it sufficient to prove that the ...
0
votes
2answers
70 views
Doubt about equivalence relation
In class I was taking notes about equivalence relations defined as:
Given a generic relation $R$ on $X$, $xIy$ if both $xRy$ and $yRx$
Now, I don't really understand the following proposition:
...
2
votes
1answer
40 views
If $\succsim$ is transitive but irreflexive, then it is asymmetric, proof
If $\succsim$ is transitive but irreflexive, then it is asymmetric.
this is my proof:
Suppose $\succsim$ is not asymmetric, which means that for any $x,y \in X$ $x\succsim y \rightarrow y \succsim ...
3
votes
1answer
60 views
separable utility function and cross price effect
Suppose that consumer's utility function for three goods is separable, that is,
$U(x_1, x_2, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ ...(i)
where $f_i$ is increasing and strictly concave, i=1,2,3. ...
1
vote
0answers
17 views
Prove that in presence of many goods, the law of DMRS implies that at least one good must be a net substitute for any other good
I've been reading a book where the author claims that "if there are two goods they are always net substitutes. Along an indifference curve an increase in price of good 2 leads to less of good 2 and ...
1
vote
1answer
30 views
Income gap in Ramsey model
Ramsey model with income tax
Question:
For this question you are required to setup a Ransey-Cass-Koopmans model economy with a Cobb-Douglas constant returns to scale production technology, with ...
0
votes
2answers
42 views
when a=0, would economy accumulate more physical capital? Why?
Utility function is
$U(c_t,l_t)=(1-a)ln(c_t)+aln(l_t)$
$l_t$ is leasure time
$c_t$ is consumption
Production function is $y_t=k_t^e(1-l_t)^{1-e}$
$k_{t+1}=i_t+(1-\delta )k_t$
where k is ...
0
votes
0answers
34 views
Risk-neutral principal question
An employer is hiring a worker to work on his behalf. The worker produces an output whose value is a random variable. The employer writes a contract that pays the worker w(x) if the output is worth x. ...
1
vote
0answers
59 views
Signaling questions (separating equilibrium)
Consider two firms
Inverse functions: $p(q)=max\{a-q,0\} $
$q$ is total production and a is positive constant.
This value of a takes two values ah=2 (high demand) and aL=1 (low demand). Their ...
0
votes
0answers
19 views
Book suggestion related to the subjects of two questions in the yellow box
I have two types of questions as:
policy optimality requires that government precommitment to future actions.
And the second one:
the intertemporal approach to the current account ...
1
vote
0answers
54 views
Maximization under two different states of the world [closed]
What I did is the following one but I am not sure at all:
Any help will be appreciated. Thank you.
-1
votes
1answer
162 views
Profit maximization and allocative efficiency result
I completely stuck to the last part of this exercise. I cannot understand how can I determine an allocative efficiency result.
Any help will be appreciated. Thank you.
2
votes
1answer
139 views
Stackelberg setup
I am completely confused because I cannot find the leader's best response. I do not know if it is exactly the same as it was a Cournot game. What I did is:
Any help will be appreciated a lot. Thank ...
4
votes
1answer
187 views
Bertrand game - Nash equilibrium
The quantity is limited to 300 but the monopoly quantity is equal to 400 and gives a monopoly price of 600. But if we plug the quantity of 300 into the demand function we get a price of 700.But I am ...
2
votes
1answer
102 views
Subgame perfect equilibrium and expected profit
I am so confused because I cannot set up the monopolist's profit maximization problem.What I did is the following one:
Any help will be appreciated. Thank you.
1
vote
1answer
219 views
Pure exchange economy with free and non-free disposal
Question is as follows:
My answers are
(I)
Let k is constant utility level
Then
$$k=\sqrt{x_A^1x_A^2}$$
$$k^2/x_A^1=x_A^2$$
The first derivative is negative. So the indifference curve is ...
0
votes
2answers
164 views
Question on profit maximization with government taxation
(I) A monopolist has a cost function $c(q)=q$. It faces the following demand function $ q(p)=100/p$ for $p\le 20$ and $q(p)=0$ for $p\ge 20$. What are the profit maximizing price and output.
(ii) a ...
0
votes
1answer
148 views
Question on consumption theory
Question:
What my did is
I proceed this question until that point. But, I will be happy if help me to solve this question.
Thank you.
-1
votes
1answer
195 views
Finding the optimal tax
I have a problem regarding the last two questions of this exercises because I can not understand how to set up my model in order to find the optimal tax the optimal quantity to be as there was not a ...
0
votes
2answers
59 views
a question on the endogenous growth model
I have such a question on the endogenous growth mode”:
In the macroeconomics literature there are various ways in which the growth process in the Ransey-Cass- Koopmans model has been endogenized. ...
3
votes
2answers
229 views
Subgame Perfect Nash equilibrium: two stage game
Charitable organizations are ranked according to the proportion of their total budget that is spend on programs(what directly goes to the recipients of their services) relative to money spent on ...
3
votes
1answer
426 views
Cournot Competition game with 3 Firms
Three firms are in Cournot competition. The inverse demand curve is denoted p(q) where p is the price if a total of q units are produced. Assumptions are: p(0)>0 and p'(q)<0 and p''(q) $\le 0$ ...
0
votes
1answer
55 views
Capital accumulation
I have following dynamic optimization problem
$$V(k_0)=\max \sum_{t=0}^{\infty} b^t((1-a)ln c_t+a ln(l_t))$$
Subject to $l_t+e_t=h$ and $y=Ak_t^pe_t^{1-p}$ and $k_{t+1}=i_t+(1-x)k_t$
...
1
vote
1answer
114 views
Maximization with disposable income
Consider a welfare system u dear which a single cash transfer(guaranteed income ) is given to every citizen. Then for each dollar the person earns the payment is reduced to by a where 00 you get a ...
3
votes
0answers
119 views
Market clearing condition with Walras law
I have a diamond overlapping model
The question is as follows
Let us consider an infinitely lived production economy populated at time t by $N_t$ identical and perfectly competitive adult ...
1
vote
1answer
21 views
Where can I look up a companies Herfindahl index?
Where can I find Herfindahl indexes on companies (current or past)? Are there any published lists put out by a research institution?
0
votes
0answers
14 views
An error in *The Taming of Chance*?
Ian Hacking's The Taming of Chance is interesting if a bit heavy reading for my usual taste (I'm about 2 weeks and 24 pages through it).
It's about the slow decay of determinism and rise of ...
0
votes
1answer
59 views
The verification of my solution
Farmer Smith's cattle wander into Farmer Jones' land once a month and cause $\$3,000$ of damage. If Smith reduced the size of his herd by half it would reduce the damage by half but it would also ...
1
vote
2answers
192 views
Finding subgame perfect equilibrium
The main part of the question is as follows
(if you cannot read this, I can immediately write it)
My question is how to find the subgame perfect Nash equilibrium for the both cases $\bar{g_2}\ge \...
0
votes
0answers
27 views
Help with a computational method in solving expected payoffs for really large Bayesian game
Im looking for some advice on I can solve my game below computationally because by hand it would take forever.
$(1)$
$(2)$
$(3)$
$(4)$
$(1)$ is combination of type $[a,c]$
$(2)$ is combination ...
-1
votes
1answer
122 views
Question on oligopoly.
Consider an oligopoly between two identical firms producing a homogenous good with constant marginal cost where firms face linear market demand. $B_i(q_j)$ denotes firm i’s best response given the ...
1
vote
1answer
116 views
Kuhn-Tucker and optimization (continue)
This is a question related to the question: Kuhn-Tucker optimization problem and game theory .The question is: Some cultures emphasize more social interaction more than others. Is there a role for ...
1
vote
1answer
161 views
Revenue maximization
We have two firms with identical cost structure compete in a market
Demand function = $p=a-bq$
And $q=q_1+q_2$
They are identical in every way. However, firm 1 maximizes profit and firm 2 ...
2
votes
1answer
100 views
Cournot equilibrium question
There are two firs in the market. They produce perfect substitutes at cost $c(y_i)=y_i/3$ for i=1,2. The demand function is $p=1-(y_1+y_2)$
Consider the Cournot competition where firms ...
-2
votes
1answer
64 views
Auction question
I’m studying on auction. But I couldn’t understand some questions about this topic. And I cannot solve such type questions. For example,
I know that a set of symmetric and risk neutral bidders ...
1
vote
0answers
80 views
Kuhn Tucker optimization problem and game theory [duplicate]
Consider a game with two players, where each player i= 1 ,2 has preferences $u_i$= $s_i^a$$c_i^{1-a}$, where c_i is the consumption and $s_i$ is social interaction. $s_i$ is given by :
$s_i$ = $t_i$ + ...
1
vote
1answer
61 views
Profit maximization question
Two firms are in a market together. They produce a product.
Total revenue from sales is $y=K+L$
K is the amount of capital
L is the amount of labor
These two firms each specialized in supplying ...
-1
votes
1answer
285 views
Inferior and normal good and the change in price of those goods
In general, We know that if a good is normal, then as your income increases, then demand of that good increases as well as price is fixed. Similarly, if a good is inferior, then as your income ...
-4
votes
1answer
154 views
Question about budget constraint and utility maximization [closed]
I have also following budget set
$$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$
where y is income.
Assume that there are two stories. The agent can shop in both of them. The first store ...
2
votes
2answers
191 views
Show that First order conditions are necessary and sufficient for utility maximization
I have a budget set
$$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$
where $y>0$ is income.
Assuming the preferences are strictly monotonic and convex, I want to show that first order ...
0
votes
2answers
68 views
Philosophy books for decision theory and economics idea
I have learned economics so far, the most astonishing economics' thing is its though which is talkable and visually in the real world or the abstract world that is worth researching and talking. What ...
3
votes
1answer
316 views
Optimization problem with Kuhn-Tucker conditions
Consider a game with two players where each player $i=1,2$ has preferences $u_i=s_i^a c_i^{1−a}$, where $c_i$ is consumption and $s_i$ is social interaction. $s_i$ is given by $s_i=t_i+t_{ij}\times t_{...
1
vote
1answer
73 views
Kuhn Tucker optimization problem
Assume that the player I select $x_i \ge 0$ at constant cost level $c>0$
The payoff function for player i is
$$v(x_i,t)-cx_i$$
where $t$ is technology parameter.
The function v(.)is twice ...
0
votes
1answer
131 views
Mixed Nash equilibrium
I have game table posted below:
$$\begin{matrix} &\#2 \\ \#1 &
\begin{array}{c|c|c|c}
&D &E &F \\ \hline
A &4,4 &6,6 &2,6 \\ \hline
B &6,4 &2,2 &0,4 \\ \...
2
votes
1answer
86 views
How to write budget constraint if the agent sell the goods that buy
Della’s utility is $U(G,R)$
G is the consumption of gasoline per week
R is the the consumption of other goods
Just help me to write down budget constraint.
I think that
$$R*1+(G-20)*10+20*1=...
2
votes
2answers
670 views
Utility maximization question setting up.
Consider a consumer whose preferences can be represented by the following utility function: $$u(x_1,x_2)=\dfrac{x_2}{(1+x_1)^2}.$$
Assume the agent's income is $y=5$. The price of one unit ...
2
votes
0answers
37 views
Firm Dynamic Optimization Problem
A firm has received an order at time $0$ for $M$ units of product to be delivered by time $T$. It seeks a production schedule for filling this order at minimum cost. Let $x(t)$ denote inventory ...
3
votes
1answer
42 views
The relationship between gross profit and tax
I tried to do following question but I am not sure about my solution. Please tell me your opinions
Since gross profit is strictly concave, I can say that $R’’(y)-C’’(y) <0$
Now I maximize the ...
