Questions tagged [mathematical-economics]

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

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Calculus in intermediate economics?

What are the best online resource on learning the Calculus used in college-level intermediate economics? Where can I find lots of problem sets and practice exams with solutions/explanations online for ...
1 vote
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Convergence of various forms of Prospect Theory?

I'm not a mathematician but it seems that my problem is a rather technical than an economic one, but i hope this is still the right audience. My problem is the following: I want to analyse the effects ...
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Why is the internal rate of return decreasing while the profit per unit of real gross value added is increasing?

I made a graph based on data from the Penn World Table showing that the internal rate of return has been decreasing over time in the US and the rest of the G7 (even more if you exclude Germany, whose ...
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Why is the consumption function concave?

I'm reading the topic concavity in risk aversion utility function of consumption function. I'm having trouble understanding why the consumption function is assumed to be concave. I tried looking but ...
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Dynamic Information Provision model setup - It generalizes Dirk Bergemann and Stephen Morris

The following model setup is from the paper Dynamic Information Provision: Rewarding the Past and Guiding the Future by Ian Ball. It generalizes both the ideas of strategic information transmission of ...
-3 votes
1 answer
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What does L mean in the money demand equation?

(M/P)^d=L(i,Y) M=Money supply P=Price d=Demand i=Nominal interest rate Y=?Output Does L mean liquidity? Or does it simply mean that the LHS depends on i and Y? Thank you!
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Errata to Analytical Methods in Economics by Akira Takayama

I found a mistake on page 312 and want to find out if there is an errata to this classic book somewhere. As for the typographic error, the third equation in the footnote on page 312 should read: $\...
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Derivate with respect to the ratio of variables [migrated]

I have following expression - $$ \sqrt{y\left(\frac{x}{z}\right)}ax + \sqrt{1-y\left(\frac{x}{z}\right)}bz $$ where a and b are constants. y is a variable which is a function of fraction $\dfrac{x}{z}$...
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Why isn't the money demand function called the real money balances demand function?

M=Money supply P=Price k= How much money people wish to hold for each dollar of income = exogenous. Y = output M/P= real money balances Money demand function: (M/P)^d = kY Why isn't the money demand ...
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Can following these marginal conditions have the net utility function converge to a maximum? [Edited]

I have the following net utility function which is made up of one positive utility (with a bliss point) and two negative utility (i.e., disutility) functions; $$Y(a_1,a_2)=y(a_1)+v(a_1,a_2)+w(a_2).$$ ...
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Question about the quantity theory of money

M = Money supply V = Velocity = Number of times the average bill changes hands in a time period. P = Price Y = Output T = Transactions Quantity equation M * V = P * Y, M * V = P * T Why do we have MV ...
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Is reserve deposit ratio + currency deposit ratio = 1?

Is reserve deposit ratio + currency deposit ratio = 1? Is cr=rr? Meaning (reserves/deposits=currency amount/deposits)? Thank you!
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Wealth Tax and General Equilibrium

Could we create a General Equilibrium model to study the effects of a Weatlh Tax; is such a model fit and adequate? It seems that Partial Equilibrium models are most inadequate to study the effects of ...
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1 answer
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Is debt eventually negative for nonnegative $y_t\to 0,c_t\not\to 0$?

Suppose $d_t=\sum_{k=0}^\infty \rho^k (y_{t+k}-c_{t+k})$ and $\rho\in (0,1),y_t\geq 0,c_t>0\quad \forall t\geq 0$. Does $y_t\to 0,c_t\not\to 0$ imply $d_t$ is eventually negative? My initial hunch ...
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CES nested in a Cobb-Douglas Function

I have the following CES nested in a Cobb-Douglas production function: $$y(i)=[l(i)^{\frac{\epsilon - 1}{\epsilon}} +\alpha(i)(\tilde{\gamma}x(i))^{\frac{\epsilon - 1}{\epsilon}}]^{\frac{\epsilon \...
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2 votes
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Modelling effect of renewable energy investment on GDP (via integrated assessment models)

I'm interested in modelling the effects of renewable energy investments and fossil fuel plant closures on the GDP using an energy-economy model of America's economy (eg. Nordhaus's RICE). Any ...
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How does I(r) replace 'Investment', to form this formula: I(r)=Y̅-C(Y̅–T̅)-G̅=S̅?

In the case of an equilibrium of loanable funds in the financial market: How does I(r) replace I, to form this next equation? I(r)=Y̅-C(Y̅–T̅)-G̅=S̅ This is an equation regarding the way by which I(r) ...
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Questions about the equation: S=(Y-T-C)+(T-G)=I, in a situation of Equilibrium, in the market of loanable funds

Equilibrium in the market of loanable funds We have: S=(Y-T-C)+(T-G)=I So, (Y-T-C)=S? If that's true, then (T-G)=0, in equilibrium. So the government doesn't have savings, since all taxes are spent ...
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Why is Y constant on the left side of the equation : Y̅=C(Y̅–T̅)+I(r)+G̅, of the Mundell Fleming model?

Since I(r) is not constant, how could Y be constant on the left side of the equation of the goods market equilibrium - IS curve function? Thank you! Ps: I don't know where I should write function, or ...
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Why are I and I(r) equal in the national income formula?

The national income formula is =Y-C-G =I =I(r) Why I=I(r)? Is it just the case in equilibrium? Thank you!
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Question regarding the Y̅=C(Y̅–T̅)+I(r)+G̅ function

How could we include I(r), a non-constant variable, while Y̅, on the other side of the equation, is constant? Thank you!
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2 votes
1 answer
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Why doesn't the consumption function include savings?

Why doesn't the consumption function C=C(Y-T) include transfer payments? If we assume that C=MPC(Y-T), and that the MPC assumes that one part of the increase of income goes to savings. But what about ...
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1 vote
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Consumer Welfare vertical differentiation [SOLVED]

Suppose consumers have the standard Tirole's utility $U_A = \theta q + \alpha X_A - P$ if they buy product A and $U_0 = 0$ if they don't buy this product (where $X_A$ is the actual demand of product A)...
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Solving separable system of differential equation in three variables

I have the following system of differential equations: $$ m \sqrt{y(x, z)} + \left( \frac{nz}{\sqrt{1-y(x, z)}} + \frac{mx}{\sqrt{y(x, z)}}\right)y_{1}(x,z) = 0 $$ $$ n \sqrt{1-y(x, z)} + \left( \frac{...
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1 answer
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Marginal Cost and lagrange multiplier

I'm studying basic micro, and I did not get how such a result is possible. According to what I studied, the marginal cost is simply the partial derivative of the cost function with respect to the ...
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Set of implementable allocations (Overlapping Generations Models)

My question is from overlapping generations $\Rightarrow$ I want to prove this part of the theorem $\textbf{First}$ proceed by showing that the allocations in a competitive equilibrium must satisfy(...
3 votes
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Unit cost function for CES

You do not need to make computations, you can just tell me how to make the following derivation: I'm studying a paper where the unique final good of the economy is produced according to the following ...
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4 votes
1 answer
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How do economists explain "If You Want to Win, Tell Your Team It’s Losing (a Little)." along with self-efficacy

How do economists explain: "If You Want to Win, Tell Your Team It’s Losing (a Little)." ? I read this article. And I learnt that— "The relationship between the score and the likelihood ...
1 vote
1 answer
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Please check those two production functions, they also seems to be quasiconvex?

Those two are generic production functions that we usually see, and I check the definition of quasiconvex and quasiconcave on wikipedia, and it seems those two graphs satisfy both definitions, and ...
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2 votes
1 answer
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Derivatives near optimal points

On page 52 of What Sustains Social Norms and How They Evolve?, Assumption 1 is as follows: Assumption 1: $d$ is continuously differentiable, $d'(x) \ge 0$ for all $x<0$ and $d'(x) \leq 0$ for all $...
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Hemi-continuity of demand and supply correspondence

Suppose a scenario in which the production set of each firm is compact and convex. How can we prove that each firm's profit function is continuous and supply correspondence can be proved to be upper ...
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Modeling adverse and extreme scenario

I am trying to find a simple way to forecast adverse and extreme scenario for GDP, inflation and other variables. I have the baseline projections. Could you propose some very simple models or ...
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11 votes
6 answers
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The Unreasonable Ineffectiveness of Mathematics in Economics

In 1960, the physicist Eugene Wigner wrote the article "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" explaining how unexpected it is that mathematical formalism can ...
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Is it possible to find missing indices using just a given indices data of some year? The question seem confusing. Try this!

I have been grappling with this question, and I think there is some missing parameter, I would deeply appreciate it if just anyone can wrap their heads around this. Thanks in advance. Index numbers ...
1 vote
1 answer
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Why should time-subscript notation be avoided in Bellman equations?

when I learned Bellman equations for macro, my lecturers were pretty loose about notation and switched between recursive and time-series notation. However, Prof Ben Moll says in his slides on Slide 15 ...
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1 vote
1 answer
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A derivative with respect to Euclidean distance?

I have a utility function $u(x,z)$ from $\mathbb{R}_+$ to $\mathbb{R_+}$, where $x,z \in \mathbb{R}_+$. I would like to turn the following statement into math: "the utility function $u$ is ...
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4 votes
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Solve Joint Distribution From An Equation

In Postel-Vinay & Robin 2002 they show an equation: $$\left\{\delta+\mu+\lambda_{1} \bar{F}(p)\right\} \ell(\varepsilon, p)=\left\{(\delta+\mu) h(\varepsilon)+\lambda_{1} \int_{p_{\min }}^{p} \ell(...
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1 vote
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Right-to-manage wage bargaining (simple algebraic steps)

I am following (and trying to understand) a paper where the wage of unskilled workers is determined as the outcome of wage bargaining between a single union and a single firm in a right-to-manage ...
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Nash equilibrium with mutually exclusive actions

consider a zero-sum game where action space for both players are the same. I want to compute the equilibrium under the constraint that players do not use the same action. For example, if player 1's ...
3 votes
1 answer
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Convexity of preferences (dissimilar definitions)

Varian's Intermediate Microeconomics describes convexity as $$\text{Given } x, y \in X: x \sim y \implies \forall t \in [0,1], tx + (1-t)y \succeq x,y$$ The other definition I read everywhere is: $$\...
3 votes
0 answers
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Solve Value Function Analytically

The context is the Schumpeterian growth model with incumbent innovation (see Aghion, Akcigit, Howitt 2014 Handbook of economic growth): the value function is $$ r V_{t}(n)-\dot{V}_{t}(n)=\max _{z_{i} \...
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3 votes
1 answer
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Average Discounted Payoffs in Continuous Time

While reading some theory papers that model a continuous time problem, I have noticed the way they represent the expression for average discounted payoff is of this form, where $r> 0 $ is the ...
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How do I calculate ROI if a cash flow is given?

In the image in the link below you see a cashflow. I wanted to calculate the ROI manually from this cashflow, but I don't seem to get it right. The program which also generates this cashflow gives me ...
2 votes
1 answer
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Do practicing economists actually use complex mathematics, or is it just a thinking tool?

I'm currently undertaking postgraduate theory units in microeconomics and macroeconomics for the first time and it seems like I am supposed to turn into an applied mathematician, not an economist. I ...
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Fundamental knowledge about invest, stock and economics for self learning [closed]

I am not expertised in the field of economics and stock so I do not know anything about invest. Would anyone please recommend any book/textbook for the initial leaner to get understanding of all these ...
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What would be some of the most basic and universal economic principles (independent of the school of economic thought)?

Comparing the principles of the neoclassical, Keynesian, neo-Keynesian, post-Keynesian and other schools, it is difficult to see a consensus on certain universal principles. There are ideas and ...
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Can someone please explain this housing prices equation?

Can someone please explain to me the following formula from this paper ? It's on the end of page 16 and the beginning of page 17. I don't know if it is asking too much, but I am looking at these ...
12 votes
1 answer
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Conventions for reading mathematically rigorous academic articles in economics

How would an informed reader typically go about reading a mathematically rigorous academic article in economics, with lots of notations, assumptions and postulations (e.g, a typical article published ...
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Risk aversion using multinomial choice model

Recently, I have stumbled upon this paper by R. Zhang. It introduces binary choice model to compute risk aversion equations for the natural selection process. My idea is to do something similar but ...
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1 answer
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Is this a function or vector space?

I want to make a function that states consumer $i's$ consumption $C_i$ in a shared bundle $X^n$ $\subset$ $\mathbb R^n$ depends on their preferences. That is, something like $C_i(\succeq_i)$. Since $\...
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