Questions tagged [mathematical-economics]

The application of mathematical methods to represent theories and analyze problems in economics.

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14 views

(Question) Immigration and Wage Equalization: Find wages after immigration wave? [closed]

Immigration and Wage Equalization: Suppose we have two cities: Miami and Atlanta. Individuals expect to live 10 years and face an interest rate of 0% per year. Workers in each city have a yearly ...
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Advanced Macroeconomics complete solution needed [closed]

I need complete solution to this problem please. it's really urgent.
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2answers
46 views

Clarification on amortization of constant payments

I have found this formula on wikipedia : $$P=C_k(1+i)^ {(n-k+1)}$$ which describe the constant payment that has to be paid every year ($C_k$ is the part of the initial loan that is extinguished with ...
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16 views

Taking the partial derivative of the demand function

Define the demand function which maximizes x -> U(x) as: $\sum_{i=1}^n$$p_i$$\zeta_i$(p, I) = I According to my textbook if I differentiate this with respect to $p_j$ I will obtain, $\zeta_j$(p, ...
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How to Calculate Weighted average cost of capital (WACC) and Minimum attractive rate of return (MARR)?

If given salvage value is 0 and Depreciation is 4 years straight line. How do I calculate WACC and MARR from the given data (In Image)? Assuming actual dollar data (Including inflation) Is any data ...
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17 views

Ramsey Model Market Clearing Condition

I have a problem understanding the market clearing condition for aggregated equilibrium in the Ramsey model. Market clearing implies that all resources are used up, hence: $Y_t=C_t+I_t$ , where $Y_t$ ...
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URGENT Lagrangian Multiplier for Microeconomics [closed]

How do I derive Lagrangian formula for L= U(C) + Ξ»(P1C1 + P2C2 - m) where U(C) = C1 + C2, and the constraint is P1C1 + P2C2 = m I get stucked because U'(C1) and U'(C2) are both 1 What a great way ...
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Completely lost on Economics Assignment [closed]

I am an economics student and one of the questions on my current assignment is: A new food is designed to add weight to mature beef cattle. The weight in pounds is given by W = 13xy(20 βˆ’ x βˆ’ 2y), ...
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Confusing Bertrand Problem [closed]

I am attempting to solve a Bertrand Equilibrium. I am given the information: $$p_1 = a-q_1-bq_2 \text{ and } p_2=a-q_2-bq_1$$ Profit = $(p_1-c)q_1$ for firm 1 and the same thing respectively ...
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14 views

Time-dependent market-clearing equilibrium price

I'm working my way through Chiang and Wainwright's Fundamental Methods of Mathematical Economics (4th ed) while holed up at home. On p. 532, in exercise 16.4 2. (b), the authors ask you to find the ...
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1answer
36 views

Continuity of preferences

Let $\succsim$ be a transitive and reflexive relation on a metric space $X$ with closed upper and lower contour sets. If $\succsim$ is not complete, does it hold that: for all converging sequences ...
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Relationship between strictly convex preference and convex preference

Let X be a convex subset of linear topological space and let binary relation >= be a complete preordering. prove: If preference relation is strictly convex and continuous, then it is convex. Since ...
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Is optimizing revenue and expense objectives simultaneously better than optimizing profit as composite objective?

In the profit maximization problem, I am curious if co-optimizing revenue and expense objectives simultaneously are better than optimizing profit (revenue - expense) as a single composite objective? I ...
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31 views

How to calculate the maximum willingness to pay? (Reservation price)

I have to solve the following exercise. I cant figure out what I have to do know. I hope i can get some help. Suppose you have the following utility: $U (x_1, x_2) = 4x_1 ^ .5+2x_2 ^ .5$ and you have ...
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1answer
34 views

How to determine price per unit and quantity sold of product from financial statement

Situation I hope I'm asking in the right place. I'm writing a paper on the application of quadratic functions in economics and intend to use the Total Revenue function as well as the Profit function ...
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1answer
56 views

An overview of 4 books for an undergrad course in Mathematical Economics

I plan to self-study, at an undergraduate level, Mathematical Economics. There's 3 main topics to cover Introduction to economy science Microeconomy Macroeconomy (each of these have lots of sub-...
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1answer
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Log-linearization of real exchange rate

I have a doubt on how to log linearize an expression for the real exchange rate. I have read in several papers that they express it using substitutions. I haven't been able to find out what ...
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2answers
60 views

Complementary slackness conditions (Kuhn-Tucker)

Consider the problem of maximising a smooth function subject to the inequality constraint that $g(x) \leq b$. The complementary slackness condition says that $$ \lambda[g(x) - b] = 0$$ It is often ...
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33 views

A question about homothetic function

What class of homothetic functions $y=f(x_1,x_2,...,x_n)$ is also homothetic in any $n-1$ factors, with the $n$-th factor held fixed at some level?
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1answer
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Log-linear version of the uncovered interest rate parity

I am trying to derive the log-linear version of the uncovered interest rate parity under complete asset markets. I know that the UIP condition is given by $$(1+i_t)=(1+i^*_t)\frac{S_{t+1}}{S_t}$$ I ...
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0answers
45 views

Transversality Condition

I am reading the first section of chapter 10 of the Obstfeld and Rogoff textbook Foundations of International Economics and I have a doubt in how the transversality condition is obtained. Even though ...
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1answer
30 views

What's the special notation?

I'm studying "ALGORITHMIC AND HIGH-FREQUENCY TRADING". Page 249 of it tries to find a formula for $h(t,q)$. First, it supposes $h(t,q) = \bar\kappa log \space\omega(q,t)$ then let $\omega(t)=[\omega(...
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1answer
59 views

How to find the maximum profit in a graph?

We know the maximum profit will occur at the quantity where the gap of total revenue over total cost is largest. But how can we find such gap?
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Mathematics of Marxian Economics

I have studied some Marxian economics, and realise that Marx's writings were not very mathematical. I recently came to know of Analytical Marxism and Neo-Marxian economics. I read the Wikipedia page ...
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4answers
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Macroeconomics for Mathematicians

I'm coming from a math background (so my mind is set up for Definitions-Observation-Lemma-Proof frameworks) and looking for recommendations of a Macroeconomics textbook mainly devoted to growth models ...
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1answer
44 views

Simple General Equilibrium Model of Public Goods: Intuition?

We assume a two person economy, denoted by person A and B. Good y is an ordinary private good, and each person begins with an allocation of this good given by $ y^{A*} $ & $ y^{B*} $ respectively. ...
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1answer
45 views

Minimizing consumption in a single market( Partial Equilibrium)

Let there be a good X where the optimal consumption is 0; i.e the social costs for any unit provided would always be greater than the utility surplus of the market. We know that prohibiting it( ...
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27 views

Calculating elasticity between log term and non-log term [duplicate]

Given the following, I am asked to calculate the elasticity of wages with respect to age: $$𝑙𝑛(𝑀_𝑖)=𝛽_1+𝛽_2π‘Žπ‘”π‘’_i+𝛽_3π‘Žπ‘”π‘’^2_𝑖+𝛽_4π‘Œ_𝑖+𝛽_5𝑇_𝑖+𝛽_6π‘€π‘Žπ‘Ÿ_𝑖+πœ–_𝑖$$ How does one ...
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1answer
36 views

Calculating elasticity between terms in a regression equation

Given the following regression: $ln(w_i)=\beta_1+\beta_2age+\beta_3age_i^2+\beta_4Y_i+\beta_5T_i+\beta_6Mar_i+\epsilon_i$ I am asked to calculate the elasticity of wages with respect to age. Is the ...
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1answer
51 views

Why can utility functions be continuous, and what does this imply for marginal utility?

I am studying microeconomics at the introductory undergraduate level and two related but distinct questions are puzzling me. First, my textbooks express utility functions as continuous functions by ...
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1answer
74 views

When to use a lagrange multiplier?

I have a question in regards to the use of Lagrange multipliers in macro models. I have seen that when writing a Lagrange there are two ways to write the Lagrange multiplier: 1) Indexed or 2) ...
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1answer
37 views

Notation? Inverse of demand function

I'm looking through The Investment Decisions of Firms by S.J. Nickell, and I've come across some notation that I don't quite understand. Any clarification would be very welcome. Nickell first assumes ...
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1answer
48 views

Supply and Demand plotted on a three dimensional Cartesian coordinate system

Is it possible ? if it's possible can someone give me a reference ? Thanks !
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2answers
25 views

Is there an index, parameter, ecuation, or anything to compare the tax pressure exercised by a country in relation to others countries?

In my country we are told often that the tax pressure over the companies and people is huge, making it unbearable and being a reason bankrupting the Economy, and one of the largests in the world. We ...
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34 views

Shortcuts for elasticity of substitution

How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
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1answer
33 views

Equations of “rational mechanics” and general equilibrium

Vilfredo Pareto, referring to the equations that determine equilibrium, wrote: These equations do not seem new to me, they are old friends. They are the equations of rational mechanics. This ...
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1answer
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Annual Fraud Recovery Over Time: Should I adjust for inflation?

I have a dataset of the total amount the U.S. Department of Justice obtained annually in settlements/judgments of government fraud cases from fiscal years 1988-2019. There's a lot of variation, but ...
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2answers
56 views

For the case of two goods, give an example of preferences that are represnted by a continuous utility function that allows for fat indifference curves

The question in the title sounds like a trick question, due to the monotonicity property that indifference curves have, such that for two goods x and y, strong monotonicity implies y > x. Possible ...
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1answer
30 views

How are low/middle/high classes defined mathematicaly?

I am only looking for mathematical references. I think this belongs to econometrics but am not sure nor where to look at it specifically. I suspect the definition is given with some kind of weighted ...
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Linearization of the dynamic system (I did it, but I have a mistake that I cannot catch. Help me please)

I have the following dynamic system in discrete time For p is price, d is demand and s is supply. $$p_{t+1}-p_t= a(d_t-s_t)$$ $$s_{t+1}-s_t=bp_ts_t-ws_t$$ $$d_t= k-gp_t$$ I have to linearize this ...
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Determine lot size with extra constraints and EOQ formula

Given a fixed price of 250,00 dollars for the warehouse and the price of the product is 5,00 dollars per product. The order cost is 500,00 dollars but if more than 1000 products are ordered then it ...
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2answers
27 views

How do you calculate the intrinsic value or fair value of real estate?

How do you calculate the intrinsic value or fair value of real estate? I mean how do you determine that the house/commercial estate is undervalued or overvalued?
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2answers
21 views

NPV but adding last year net value?

I have found the following NPV (Net Present Value) formula: CF = unlevered cashflow i = interest rate (WACC) $$NPV = -I_0 + \frac {CF_{2019}}{(1+i)} + \frac {CF_{2020}}{(1+i)^{2}} +\frac {CF_{2021}}...
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32 views

Behavioral Dictator Game

I am doing a self study on behavioral economics and I am trying to solve behavioral version of the dictator game with following utilities for person 1 and 2. $$ u_1( \sigma_1, \sigma_2 ) = \...
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1answer
50 views

A question on the accuracy of economic forecasts

I apologise if thi's question appears dumb or boring, but I am asking it as a lay person. The context is that I am always arguing with friends that they should trust the economists view that Bexit (...
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1answer
69 views

How do we define an efficient tax in microeconomics?

I am currently working through problems to study for an upcoming exam. I am not seeking a solution per se. I am looking at the intertemporal choice model. I am looking at two periods where consumption ...
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2answers
31 views

Definition of covered market

I do Industrial Organization course, and I've seen the phrase "market is covered" several times in my lecture slides, however, I'm struggling to find the formal definition of "covered market" and the ...
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1answer
27 views

Interpretation of dummy variable : Random Effects Model

I am running a RE regression and I have export similarity index between two countries as the dependent variable and have a dummy variable such as share a border(=1 if countries share border, 0 ...
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31 views

Why decreasing co-state variable (over time) is Compulsory?

I have a short question. In the continuous time infinite horizon optimal control maximization problem Like $$\max \int^{\infty}_0 u(c_t)e^{-pt}dt$$ I use current hamiltonian function and I obtain ...
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39 views

What is the economic interpretation of the solution of this optimal control problem?

I have the following optimal control problem $$\max_{c_t} \int^{\infty}_0 e^{-p_it}\ln(c_t(i))dt$$ subject to $$\dot{w_t}(i)=rw_t(i) -n_ic_t(i)$$ $$w_0(i)=w_0>0$$ I have some wealthy and ...

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