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Questions tagged [self-study]

Questions about self-studying economics, including curriculum design, study strategies, resources, etc.

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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 ...
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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: ...
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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 ...
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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
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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
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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. ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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.
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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.
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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
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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
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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.
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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 ...
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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 ...
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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.
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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 ...
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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. ...
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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
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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) $\le 0$ ...
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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 $k_{t+1}=i_t+(1-x)k_t$ ...
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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 ...
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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 ...
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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?
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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 ...
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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
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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 \...
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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 ...
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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 ...
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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 ...
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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
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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 ...
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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 ...
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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 : $s_i$ = $t_i$ + ...
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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 ...
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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 ...
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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
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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 ...
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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
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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_{...
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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 ...
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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
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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=...
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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
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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
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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 ...