Questions tagged [economics]

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.

1602 questions
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Level curves of $Q(x_{1},x_{2})=\min\{2x_{1};x_{2}\}+\min\{x_1;2x_{2}\}$

I started thinking of different cases for example suppose $2x_{1}
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Formalizing (dollar) cost averaging

Let $P$ be a strictly positive real-valued function on $[0,1]$ (with however many niceties you want to impose on it). Is there anyway we can quantify that the following inequality is usually true,and that when it isn't true it usually isn't off by…
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Proof Doubt - Scale Elasticity Formula (Microeconomics)

My professor presented two concepts of elasticity in my last microeconomics class: Product Elasticity: $\mu_i=\frac{\partial f(x)}{\partial x_i}\frac{x_i}{f(x)}$ Scale Elasticity: $\mu(x)=\frac{d\ln(f(tx))}{d\ln t}\Bigr\rvert_{t = 1}$ Also, he asked…
Jackaba
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Economic Elasticity: where elasticity-equation come from?

I know the equation for economic elasticity is: $$\varepsilon = \frac{\%\,\Delta Y}{\%\,\Delta X}\frac{X}{Y} = \frac{\partial Y(X)}{\partial X}\frac{X}{Y} = \frac{\partial \log(Y)}{\partial \log(X)}$$ In fact, this is the generalization for any…
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What is the difference in the equations listed here

This is a question in economics where we create a model for GDP per capita. GDP per capita can be caculated in such formula where you take GDP/population. This formula (GDP/population) can be broken down in a way where you see what affects the GDP…
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How to compute elasticity of substitution using experience-education groups?

I'm reading "Competition in the Promised Land – Black Migrants in Northern Cities and Labor Markets", by Leah Boustan, and I'm trying to understand her computation of black and white elasticity of substitution in labor market She uses a Cobb-Douglas…
Lucas
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why do I invert the exponent (Economics)

This question refers to the Capital stock in macroeconomics, so K is the capital stock. Hi everyone. I have this problem where I don't actually understand why you invert the exponent. You still have to remove the exponent in the 4th step so why…
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Simple Algebra: How has this equation been rearranged?

Solving for ΔY So I'm doing economics and it's been a good 10 years since I've done any algebra. I'm having difficulty rearranging equations. In the picture it shows the equation moving from: ΔY = MPC x (ΔY-ΔT) to (1-MPC) x ΔY = -MPC x ΔT to the…
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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 stock of loans, B is the stock of bonds, K is the stock…
A H
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how to calculate effective annual rate if it's calculated once in 3 years?

Interest rate is $9\%$ a year, but it's calculated once every $3$ years. How to calculate the effective annual rate? The formula I know is: $$r = \left(1 + \dfrac in\right)^n - 1,$$ where $n$ is the period, which is $3$ years, and $i$ = $9\%$…
ERJAN
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Calculation of CPI

My class was canceled due to the coronavirus and I am supposed to solve the following problem: Assume that the consumer consumes only two goods, and his utility function is $u=x_{1}x_{2}$. Last year the prices of both goods were 10 and the consumer…
Peter
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Utility function with constant elasticity of substitution

I have a utility function with constant elasticity of substitution (CES) that takes the form: $$u(c)=\frac{c^{1-\sigma}-1}{1-\sigma}$$ where $\sigma >0$ is a parameter. Why is it that when $\sigma=1$, the function becomes $u(c)=\ln(c)$? I would have…
newbie
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First mover advantage stackelberg case.

So in the Stackelberg problem, there is usually a first mover advantage for the leading firm (where the first firm to enter has a competitive advantage). Is there ever a case where the leader firm produces less than a follower firm?
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How to calculate socially optimum provision of a public good?

Utility = $\ln (x_i) + 0.5 (g_1 + g_2)$ subject to $x_i + g_i = 15$. I have substitued the budget constraint into the utility function: Utility = $\ln (15 - g_i) + 0.5 (g_1 + g_2)$ I have tried differentiating the budget constraint but am unable to…
chloe
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Calculting interest on investment

Given an investment of 9550000 USD I want to know what the value of this investment is after one year if I have to pay 10% of interest per year. According to my understanding, that would be 90% of the investment which equals to 8595000…
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