The economics tag has no wiki summary.
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Econometrics Simultaneous equation Indirect Least Squares and Two Stage Least Squares
I still can't figure out this problem. PLEASE HELP!
(1) $F_t = a_1 + a_2.C_t + a_3.P_t + e_t$
(2) $P_t = b_1 + b_2.F_t + b_3.S_t + b_4.I_t + u_t$
4
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0answers
90 views
Open Problem in Fixed Point Theory [Prize]
This open problem appeared on the bulletins of Evans Hall at Berkeley this week.
I hope this doesn't violate StackExchange policy (the solution carries a $500 prize), but I thought why not re-post ...
1
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1answer
27 views
Random walk serial correlation
Given a model $$Y_t =b_0 + b_1 \cdot X_t + b_2 \cdot Z_t + e_t,$$ where the error term $e_t$ follows a random walk form of serial correlation $e_t = e_{t-1} + u_t$. Further assume $u_t$ has zero mean ...
3
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1answer
36 views
Stability under supremum of sets of social choice function with single peaked preferences
Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455.
The setting is as follows:
A non-empty finite set of ...
0
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1answer
23 views
Endowments & Utility Function to get Demand Function
We have two people, $A$ and $B$, A has $200$ units each of both good $X$ and $Y$ and $B$ has $100$ units each of both good $X$ and $Y$.
$A$ has tastes providing a utility function such that $u(X,Y) = ...
0
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1answer
43 views
How to build (and maximize) this equation
I'm trying to solve an economics problem but I cannot figure out how to build the equation system, or how to find the maximum in a piecewise function.
A simplified version of the function would be ...
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1answer
16 views
Find the transaction cost-adjusted expected return of the stock
Let $W^b_i$ denote the weight of stock i in the existing portfolio and $W^a_i$ denote the weight of stock i in the new portfolio to be created. Let $c_i$ denote the transaction cost of stock $i$.
If ...
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2answers
46 views
Geometric series to calculate price
I decided to add my extension to this question as a new question here.
I am trying to represent the following as a geometric series equation:
...
0
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1answer
30 views
Using limit argument with non-continuous social-choice functions
This question is related to another question of mine Invariance of strategy-proof social choice function when peaks are made close from solution, and it revolves around the use of limit arguments with ...
6
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1answer
58 views
Invariance of strategy-proof social choice function when peaks are made close from solution
A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428.
The setting is as follows:
A finite set ...
1
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2answers
59 views
Solving for steady state in macro model, probably just simple calc problem…
I am building a macroeconomic model and I am having trouble calculating the steady state.
GDP in the model is determined by
Y(L,B,K) = x*L+y*B+z*g*K
where (x,y,z) are known constants, L is the ...
0
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1answer
19 views
Finding the most profitable option
Right now, I have 1€. And I know exactly how to invest that euro to make profit, but I have 3 options:
Invest the euro, and win exactly 1€ (I'd have 2€ then)
Invest the euro, and earn some money ...
0
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1answer
47 views
Compound discount
I am trying to construct an equation for calculating a price, that takes into account compound interest of 10%.
1 item = $10
2 items = $19
3 items = $27.1
so ...
1
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1answer
36 views
Concept of efficiency in auctions
I have some confusions about the concept of "efficiency" in auction theory.
One interpretation is that an auction is efficient if it maximizes the social-welfare. But social-welfare is not well ...
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0answers
28 views
Wealth disribution explanation
There are many mathematical models that try to exlpain the character of wealth disribiton in different countries. What are there the most general and fundamental theories of wealth and income ...
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0answers
44 views
What kinds of sets are reasonable to place on the continuum?
Warning: I don't know anything about set theory so I wouldn't really know how to spot an existing answer if it were around.
Suppose I want to model some economic good or product. I would like to ...
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2answers
67 views
Does Arrow's Theorem apply when choosing a single best candidate?
According to Wiki, Arrow's Impossibility Theorem proves that we cannot create a social welfare function that obeys unanimity, non-dictatorship, and IIA.
However, in real elections, we want to choose ...
1
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1answer
73 views
Minimizing total cost function
In today's test (question c) I had to minimize equation $(3)$ and solve for N*.
I did it through deriving, setting to $0$ and solve for N (no doubts about that).
My question is, in this image it ...
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1answer
42 views
Calculating the bank multiplier.
The question is as follows:
In a simple close economy, banks are required to maintain a liquidity ratio of 8%. An additional £15 billion of currency is deposited in the banking system.
Calculate the ...
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0answers
37 views
Inventory control. Calculating annual cost
I wish I could help solve this problem if you think it is too much trouble. This is a task townhalls and Operations Research. I will be grateful if you give me any suggestions or detail. The problem ...
1
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1answer
42 views
Relation between quasilinear utility and quasilinear function
When we say Quasilinear utility, it is known that function is linear in numeraire. It is expected to be linear in one argument and hence it can be called *quasi*linear. Can any one tell me if there is ...
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0answers
40 views
Omitted Variable Bias?
The question is more involved on how to calculate the omitted variable bias. We were given data and are supposed to use SAS to run regression models. First, how do you know if results suggests there ...
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1answer
51 views
Quasilinear utility functions
Is the utility function below quasilinear?
$U(X,Y)=XY+10Y$
I know that an equation of the form $U(X,Y)=f(X)+Y$ is quasilinear but I'm not sure about functions of the form $U(X,Y)=f(X,Y)+Y$.
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199 views
Deriving demand functions given utility
A consumer purchases food $X$ and clothing $Y$. Her utility function is given by: $U(X,Y) = XY +10Y$, income is $\$100$ the price of food is $\$1$ and the price of clothing is $P_y$.
Derive the ...
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1answer
65 views
Deriving a demand curve intermediate microeconomics
The exercise says as follows: Zac consumes only pizza and Chianti in fixed proportions. 2slices of pizza per 1 glass of chianti. income is $100. Derive demand functions for pizza and Chianti.
How do ...
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1answer
36 views
Preference Relation and Utility Function - Problem with inductive proof
I have a problem with an inductive proof of the following result.
Theorem:
If $X$ is a finite set, a binary relation $\succ$ is a preference relation iff there exist a function $u:X\rightarrow R$ ...
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0answers
55 views
Differentiation help
I recently got some lecture slides, but needed a little help understanding the maths behind them.
(equations)
(Working and Answer)
Basically, I don't understand how to get from step (4) to (5). ...
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1answer
80 views
Find profit maximizing profit and quantity given willingness to supply curves and a merger
This is a homework problem, but I'm at my wit's end. I don't even know where to start on this, but I've tried a number of strategies.
Consider a regional market for wholesale electricity where ...
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0answers
33 views
Relation of stochastic process $\{x_t\}$ to the process of $\{\ln(x_t)\}$
I came by an assumption that states the following:
$$ \log(E_tD_t) = \alpha E_t \log(D_t) $$
where $ \log $ denotes natural logarithm and $ E_t $ denotes the expectation of a given value, being an ...
1
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2answers
118 views
Cournot-Nash Equilibrium in Duopoly
This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way of solving the following question:
There are 2 firms in an industry, ...
1
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1answer
32 views
Cointegration for Price levels Time Series
I don't understand why is the difference between price levels is a stationary process while the time series of price levels themselves is a non-stationary process.
For example:
...
1
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1answer
77 views
What is levy measure? Why is it needed, and what is $(1\wedge|x^2|)$?
A Borel measure $\nu$ on $\mathbb{R}$ is called a Lévy measure if
$\nu({0})=0$ and $\int_\mathbb{R}(1\wedge|x^2|) \, \nu(dx) < \infty .$ ...
1
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1answer
81 views
Proving that a function is monotone
Here is the setting: We have a middleman that buys a product from the producers, and sells the product to the customers. The middleman charges a price $R$ to the customers, and pays a price $p(R)$ to ...
4
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1answer
79 views
Gibbard–Satterthwaite Theorem versus Arrow Theorem
Arrow Theorem is a very classical result in social choice theory, stating very roughly that any reasonable voting procedure is either dictatorial or subject to tactical voting. More precisely, there ...
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0answers
42 views
Game theory question- information quality maximisation, opinions of the question
I am developing a game theory question to help in deconstructing situations where information quality is comprimised and requires valuation against a set of criteria. I would be interested to know any ...
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0answers
15 views
Is there a trade model which takes in account credulity?
I have to admit I'm not to familiar with mathematical economics but, as a student in mathematics, I was trying to play a bit with a toy trade model I'm try to build over a finite population.
My ...
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1answer
116 views
Cobb-Douglas utility function
A simple Cobb-Douglas utility function:
$$ U(X,Y)=\frac{X^{(1-\alpha)}Y^{\alpha}}{(1-\alpha)^{(1-\alpha)}\alpha^{\alpha}} $$
Here, I don't understand why we need the denominator: $ ...
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0answers
79 views
What is the (expected) outcome of this hybrid auction?
A certain hybrid auction can be accurately modelled as follows.
There are $n$ risk-neutral, rational participants $i=1,2,\ldots,n$, and a guy called Zerro: $i=0$.
Each, except Zerro, has a private ...
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0answers
28 views
Market Clearing Prices: find the set for the valuations
We express Gp=(X U Y, E) is the preffered graph where ij in E if j is preferred seller of X=buyers, Y=sellers
--> A vector of prices p is market clearing if Gp has a perfect matching( generally, ...
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0answers
20 views
Linear Regression for Econometrics
If I am given the line $y_{i}=1+.5x_{i}+u_{i}$ along with 10 observations of some variable X and 10 observations of error terms (pulled from a normal distribution with mean=0 and variance=10) and I am ...
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1answer
98 views
Normal distribution theoretical moments
how we can show that the following equality holds
$E[(x-\mu)/\sigma]=0$
$E[(x-\mu)^2/\sigma^2-1]=0$
$E[(x-\mu)^3/\sigma^3]=0$
$E[(x-\mu)^4/\sigma^4-3]=0$
3
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1answer
126 views
Finding mixed Nash equilibria in continuous games
I'm taking my first (graduate-level) game theory class. I understand how to find Nash equilibria in simple games, such as those given in finite tables, and can see (usually) how to find the mixed ...
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0answers
79 views
Can Fumio Hayashi's econometrics book cover first-year graduate course?
Of course instructor or professor will recommend the book, but generally, does Fumio Hayashi book cover almost all of first-year graduate econometrics course?
1
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1answer
154 views
Mean preserving spread vs higher variance
In the Wikipedia article for mean-preserving spread, the following is claimed without citation:
If B is a mean-preserving spread of A, then B has a higher variance than A; but the converse is not ...
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0answers
35 views
Suggestions for projects in mathematics of finance
I am looking for computational projects related to mathematics of finance suitable for a senior level independent study for a student who has seen the green light, (or the light of the green!). I had ...
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1answer
75 views
Elasticity of Substitution (CES)
This appears to be a nice forum. I just registered since I have a question...
I have a CES aggregator-function
$$
f(c,q) = (r c^{a} + b q^{a})^{1/a}.
$$
It is postulated that it can be rewritten as
...
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2answers
112 views
Slope of a nonlinear curve at a single point
This part of my microeconomics lesson plan has me baffled.
Consider for example the nonlinear continuous and differentiable function Y = f(X) = X 2 + 4. Suppose we want to know its slope at the ...
2
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2answers
57 views
Creating indices
Is there a "proper" formula for creating indices? I need to compute series of numbers into a KPI that can be tracked over time.
Example dataset is like this:
...
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2answers
103 views
Maximum feasible output of a company
Imagine, I have following model.
There is a company X, which produces one unit of final output from
0.2 units of input A and
0.8 units of input B.
Inputs A and B are bought from respective ...
1
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3answers
142 views
My brothers share from income.
My brother is driving a limo with his partner who told him that they will go 50-50 on income and also 50-50 on gas.
So if my brother earns \$1000 by spending \$200 on gas, what will be my brothers ...
