A Hamiltonian & Lagrangian General Form You may remember high school physics class and being introduced to Newtonian mechanics (F=ma, anyone?). If you stuck with physics, you would learn about two alternative, but complementary, approaches—Lagrangian and Hamiltonian classical mechanics. So, how do we get from physics to economics? What’s all this about Hamiltonian and Lagrangian mechanics, […]

What is a Pontryagin System? | Pontryagin Maximum Principle, Optimal Control Theory, & Dynamic Optimization Pontryagin — Optimal Control Framework A Pontryagin system is a system of equations in optimal control theory used for finding optimal controls in dynamical systems. In this article, I’ll break down the concept, background (maximum principle), and use cases—no prior experience needed!

What is the Bellman Equation in Economics? | An Introduction to Bellman Methods, Reinforcement Learning, and Dynamic Programming Bellman Value Iteration In this article, I introduce the core concepts driving the Bellman equation and its use in dynamic programming and reinforcement learning (don’t worry if you’re not familiar with those terms!). Here’s a quick rundown

A Monte Carlo Simulation — we’ll explain this in the article! Monte Carlo simulations seem to be on the recommended skills sheet of every big investment bank and consulting group. Yet, at least in my experience, it’s also near-entirely ignored by the degree curriculums supposed to prepare you for those jobs. So, I’ll introduce some of the conceptual basics

Finding AC, MC, and Natural Monopoly from a Nonlinear Cost Function In this problem, we’ll analyze a cost function to explore how it affects a firm’s average and marginal costs. We’ll derive these costs, interpret and graph their relationship, and assess whether this cost structure reflects a natural monopoly. If you’re looking for a full cost minimization

Solving a Cost Minimization Problem Using Isoquants and Isocosts with a Cobb-Douglas Production Function Continuing my recent streak of micro 101/201 walkthroughs, here we’ll walk through a classic cost minimization problem using a Cobb-Douglas production function with capital and labour. We’ll see how firms can minimize costs for a given level of output, and graph this

Solving Equilibrium Price, Quantity, and Welfare in a Monopolistic and Competitive Market (Econ Follow-Along) Solving Equilibrium Price and Quantity and Welfare in a Monopolistic and Competitive Market Understanding and calculating how firms choose output and price, as well as how these choices affect net welfare, is a cornerstone of micro, and something you’ll come across

Signaling Model in Labor Economics (Education & High/Low Productive Workers) As an economics student, or if learning for fun, you’ll often run into signaling problems. I’ll break down a straightforward labor-economics signaling model with education and two types of workers. We’ll work out: What wage firms will set without directly observing ability. The threshhold share of

Hey all! Whether you’re studying or here for fun, I’ll walk you through a Perfect Substitutes Utility Maximization problem. You can see similar articles here. We’ll focus on core concepts throughout and the intitution behind the steps. Leave a comment if you get confused! Say we have a consumer who likes Coke C just as much

In this article we’ll explore a few different rules about the differences of sums and differences of differences as applied in economics. Continue reading on Medium »