For questions regarding the mathematical analysis of economic models and problems. This includes questions about the formulation or solution of models from microeconomics or macroeconomics.

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-1
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0answers
12 views

Bertrand differentiated goods Substitutes or Compliments? [on hold]

Suppose we have two goods with the following demand: D1(p1, p2)= 200-4p1+2p2 D2(p1, p1)= 300-6p2+2p1 Are these goods compliments or substitutes?
0
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0answers
14 views

Gross Substitutes under continuous perturbations

Let $v_i(S)_{i \in [n], S \subseteq G}$ be a collection of Gross Substitute valuations. I am wondering if I can add a small perturbation to each valuation and still get Gross Substitute valuations. ...
0
votes
1answer
25 views

Envelope Theorem and Static Optimization

The Statement of the Problem: For fixed $r \gt 0$ and $m$, find the maximum value of $1-rx^2-y^2$ on the constraint set $x+y=m$. Find the value function $f^*(r,m)$ and compute $\frac{\partial ...
0
votes
3answers
38 views

How much is 6% a year in months?

I am currently in high school where we are learning about present value. I struggle with task like these: Say you get 6% interest each year, how much interest would that be each month?
1
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0answers
10 views

Identifying a subclass of the class of monotonic transformations

Let $u$ be a continuous function from $R$ to $R$. Then $v$ is called a positive monotonic transformation of $u$ if $u(x) < u(y)$ if and only if $v(x)<v(y)$ and similarly for greater than and ...
1
vote
1answer
59 views

Can I embed $\mathbb R^{\mathbb N}$ with a partial order into $^\ast\mathbb{R}$ with the linear order?

Define a relation $\prec$ on $\mathbb R^{\mathbb N}$ as, For all $f, g \in \mathbb R^{\mathbb N} $, $f \prec g$, if for all $n \in \mathbb N$, $f(n) \leq g(n)$, and there exists a $m \in \mathbb ...
0
votes
0answers
9 views

Supply Curve and Consumer's Surplus Help

The following information is given: p=S(x)= 80e^(0.05x) ¯x=15 What I am struggling to figure out is how to obtain the value of ¯p I set S(x)=15 and got that ¯p was -33.47952, but am unsure if this ...
1
vote
1answer
6 views

Profit Function where total revenue is re-spent on production?

I'm trying to find a function that finds the net profit gain over multiple iterations. For example, if I produce a unit for 5 dollars , and can sell it for 8 dollars, I would have a net gain of 3 ...
-5
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0answers
16 views

How do I solve? [closed]

A firm faces the following inverse demand equation for the commodity it produces: P = 100 – Q where P represents the price/unit of the commodity ...
0
votes
0answers
27 views

Perfect equilibrium - consumer, producer surplus

Inverse function of market demand for certain good is equal to $P=100-0.25Q$, inverse supply function is $P=20+0.55Q$. Calculate equilibrium price and quantity. Furthermore calculate consumer and ...
0
votes
2answers
28 views

Using Lagrange for finding Marshallian Demand

I want to find the marshallian demand function for the user function $u(x_1,x_2) = x_1^ax_2^{1-a}$ where $a \in (0,1)$. This is what I have so far: $$L = x_1^ax_2^{1-a} - \lambda(p_1x_1 + p_2x_2 - ...
0
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0answers
9 views

Calculating the conversion factor for a bond

It is june 25 2005. The futures price for the June 2005 CBOT bond futures contract is 118-23. Calculate the conversion factor for a bond maturing on Jan. 1, 2021, paying a coupon of 10% : since the ...
0
votes
1answer
248 views

Does one necessarily need an MS in Math before taking a PhD in Math? [closed]

I finished bachelor's in mathematical finance and am nearly finished with master's in mathematical finance (I am already done with thesis), and I plan to pursue a PhD not in mathematical finance but ...
1
vote
0answers
24 views

Quasiconcavity of $g(x)=xf(K-x)$

The function $f(x)$ is strictly increasing, finite, positive and twice continuously differentiable on the compact interval $[0,K]$, and $f(0)=0$. I'm trying to either find a counterexample to, or a ...
-4
votes
0answers
26 views

Asymmetric information about company's worth, maximizing profit

ABC Ltd is worth $v$ to its owners who will sell if they get an offer at least $v$. XYZ Ltd doesn't know $v$ but knows that $v$ can be $2m$, $3m$, $4m$, or $6m$ and considers these $4$ outcomes are ...
3
votes
1answer
35 views

Core vs. Strong Core in Housing Allocation Games

I am presently reviewing the course notes for my Game Theory course, and I'm struggling with the concepts of the core vs. the strong core. In the notes, we have three players, with preferences ...
2
votes
1answer
44 views

Mathematical question about currencies

I've tried to get an answer for this question elsewhere but with no luck, so I would appreciate a mathematical analysis of it. Assume $0\%$ commission. Consider three currencies, let's say the Zong, ...
2
votes
0answers
27 views

Average Cost of Obtaining in game Item

I know this will sound like a trivial maths problem, but recently I've been playing a game in which you can pay 5 in game gems to get a Rare (R), Super Rare (SR), and Ultra Rare (UR) characters ...
1
vote
0answers
9 views

Endogenous covariate in first-difference panel data model

I have a linear panel data set (murder.dta, standard STATA dataset). First I estimate a first difference model. An assumption from this model is that the first differences of the covariates and the ...
-1
votes
0answers
16 views

How to find the equilibrium quantity?

what is the equilibrium quantity if the supply curve is given by Q=P-20 Also, How do I derive the demand curve from this supply curve where the quantity is 900 and the price is 300 on the curve
1
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0answers
38 views

Personal Experiences with Probability Simulation

Simulations methods are increasingly used in theoretical and (especially) applied probability. Personally, I have used simulation for purposes that range from recreational Q&A to applications of ...
0
votes
0answers
27 views

When the company will stop production?

Given total costs function $C(q)=100+10q-6q^2+3q^3$. For which price the company will stop production given that all of the fixed costs are sunk? Do not know how to approach those type of questions, ...
0
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0answers
11 views

Assistance with exponential inflation equations

We are trying to model an exponentially inflationary currency exchange, let's say converting dollars into clams, based on a compounding rate. Our cost equation looks like this: c = b(b*r)^e Where: c ...
0
votes
0answers
55 views

Finding the equilibrium quantity of goods produced

Consider a market with 3 types of goods, $a$, $b$ and $m$. There are two types of consumers: 100 consumers of type X and 100 consumers of type Y. All consumers of the same type are identical to each ...
3
votes
1answer
74 views

Given domain and range of a monotone function, what is the maximum slope?

I'm looking for a reference in answer to one of the following questions: Is there a general result out there that will give the maximum possible slope of a monotone function, given its domain and ...
0
votes
0answers
26 views

How to calculate the max home purchase price based on a maximum Debt to Income ratio?

I'm trying to calculate the maximum home purchase price a home buyer can afford given their annual salary, monthly debt, and a maximum debt to income ratio of 44%. I am not super familiar with ...
1
vote
1answer
34 views

Stochastic dominance characterization

Consider two probability measures on $\Bbb R$ given by $\mu$ and $\nu$. We write $\mu\leq \nu$ if there exists a joint distribution $P$ with the latter marginals such that $P(x\leq y) = 1$. In ...
0
votes
0answers
49 views

How to calculate $p_i$ in Blau's Index of Heterogeneity

I came across this: "Therefore, board gender diversity and board racial diversity are calculated using Blau's index of heterogeneity $(1 - \sum p_{i}^2)$, where $p_i$ is the proportion of group ...
1
vote
0answers
25 views

From utility function (3 products) to demand function (2 products)

I am struggling with this exercise and would appreciate some help. Consider two goods and a representative consumer whose utility is given by: $U(q_{0}, q_{1}, q_{2})= ...
1
vote
0answers
63 views

Utility maximization of n goods

I have a question that involves finding the optimal demand of n goods for a consumer. However, I haven't anything like this before and I'm not sure how to proceed. The consumer has a utility ...
-2
votes
1answer
27 views

micro economics [closed]

If production function is linear and given by: $Y=3K +L$ Find the marginal rate of technical substitution. If price of capital equals the price of labour what is the best combination of capital ...
0
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0answers
34 views

how to solve a simplex with n variables

I don't know how to resolve a simplex with n variables I have this primal problem \begin{cases} \text{min}& z=-x_1 - x_2 -... - x_n\\ &a_1x_1 + a_2x_2 +... + a_nx_n \le 1\\ &x_1... ...
-1
votes
1answer
18 views

I need som help with price ratios.

Okay, so I'm doing some econ. homework and I'm supposed to draw a graph where the relative price of $P$ is $4 T/P$. Thing is that my brain stops working anytime I try to think about ratios. I know ...
0
votes
0answers
9 views

Engel Curve in Economics

I have a utility function in the form $U = B^{.67}Z^{.33}$ I am supposed to find an Engel curve assuming that the price of goods B and Z are $P_b$ and $P_z$ respectively with income level $Y$. I can ...
0
votes
0answers
14 views

Density - Excess Bunching - Bunching Estimator

Saez defines excess bunching at the kink as the area under the density in the dominated region: $$ B = \int^{z^*+d z}_{z^*} h(z)dz \approx h(z^*)dz^* $$ where income $z$ is distributed according to a ...
0
votes
1answer
21 views

About uniqueness of interest yield

I am not sure this belong to this site, in case I will post it elsewhere. Let $P$ be the price of a bond, let $C_k$ the promised cash flow in year $k$. Then we define the interest yield $y$ as the ...
0
votes
2answers
45 views

dynamical systems applied to economics

I'm ending my undergraduate economics course and I'd like to extend my MA research program to dynamical economic systems. Knowing that my mathematical basis is calculus of 1 and 2 variables, linear ...
1
vote
0answers
27 views

Convolution of which distribution will give a uniform distribution?

Suppose there are two IID random variables x1 and x2. What should be the distribution of these random variables so that the distribution of x1-x2 is a uniform distribution?
0
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0answers
20 views

Proving the expenditure function $e(p,u)$ is strictly increasing in $u$ when $u$ is not assumed to be an increasing function.

Hello I am wondering how best to prove that the expenditure function $e(p,u)$ is strictly increasing in $u$ assuming that $u$ itself is not an increasing function (which is the opposite of what $u$ is ...
0
votes
0answers
28 views

Submodular function of 2 variables with specific properites

For an application in economics, I am looking for an example function with the following properties: Function of 2 variables on the unit interval, i.e., $f : [0,1]\times[0,1] \rightarrow ...
3
votes
1answer
93 views

Reference Request - Introductory book on Mathematical Modelling in Economics and Business

I have to take a compulsory course named Mathematical Modelling in Economics and Business this semester and have absolutely no background on the subject. I also noticed there is no post on this site ...
0
votes
0answers
34 views

Optimal choice of job based on multiple ranks

First of all I should state that I am a non-mathematics student but am pretty mathematically-inclined. I have a problem that I can't find a solution to on Google. Here is the hypothetical: I have ...
1
vote
1answer
16 views

Find the OLS estimator $β_1$ when a new variable is added to the regression

Suppose $y_t$ = $β$$x_t$ + $u_t$ , where t = 1, 2, ..., n. We know, in this case, the OLS estimator is $\hatβ$ = ∑$x_t$$y_t$ / ∑$x_t^2$ . Now suppose one more observation $x_{n+1}$ is added. At the ...
0
votes
1answer
51 views

Optimization of utility function with Lagrange multiplier

Let u: ${\mathbf R^n_+ \rightarrow \mathbf R}$ be a utility function of n goods which you buy in quantities $x_1,…,x_n$ to the prices $p_1,…,p_n$ under the budget K. So maximize $u(x_1,…,x_n)$ subject ...
0
votes
1answer
23 views

State the likelihood function and the appropriate objective function which must be maximized for maximum likelihood estimation

Consider a simple exponential employment duration model where $t_j$ is length of the employment and $x_j$ is a suitable economic explanatory variable. The distribution of $t_j$ is assumed to be ...
0
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0answers
17 views

Solving the production scheduling problem using optimal control

I want to solve the production scheduling problem with quadratic production costs and no inventory costs using optimal control without discounting. My work: The quadratic production cost is $c_{1} ...
0
votes
1answer
32 views

Simple PPF question

Econoland and Free Enterprise are two economies each producing two goods: airplanes (A) and grains (G). Currently the two economies do not trade with one another. The table below provides ...
0
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0answers
9 views

Quasilinear Utility

We know if the utility function is quasilinear(QL) w.r.t say good 1, then the demand for other goods is independent of income (no income effect for goods 2...N). But is the reverse implication also ...
3
votes
0answers
354 views

Can I get a PhD in Stochastic Analysis given this limited background?

General advice on PhD apps welcome Given my limited background in stochastic analysis and other information (below), can I apply for a PhD with stochastic analysis for my dissertation topic? 1/4 I ...
0
votes
0answers
36 views

Implicit differentiation: Differentiating function with respect to integral

I am stuck on a simple problem and would highly appreciate your opinion. I have a optimization problem over $x$ with the objective function $$F=aG(x,y)+ (1-G(x,y))(1-x)$$ So the first order condition ...