Microeconomics

Budget A definition for Budget Economist want simple models to start to model things. One of the things we will model here is how do you describe what you can afford about some goods. Budget Set $$ \text{Budget Constraint inequality}:p^{T}x \leq m $$ We define Budget Set to be $P_{p, m} = \left\{ x \in \mathbb{R}^{d} : p^{T}x \leq m\right\}$ Composite Goods $$ p_{1}x_{1} + x_{2} \leq m $$ Where $x_{2} = \sum_{i = 2}^{n} p_{i}x_{i}$. In this case, $x_{2}$ is called composite good, which is a sort of abstraction to simplify some calculus. ...

Here we analyze how demand changes when prices and income changes. Types of Goods Here we will define two main types of Goods: Normal Goods: The demand increases linearly with the income. Inferior or Ordinary Goods: The demand decreases when the income is higher, one example is low quality food. Necessary Good: The demand is increases sublinearly (e.g. constantly) with respect to the income. Luxury Good: The demand increases more than linearly with the income. Giffen Good: The decrease in price leads to a decrease in demand. Curves of Demand Income offer curve It is quite intuitive to visualize: just expand the income while keeping utility and priced fixed, you will see the optimal point translating along the curve. ...

Let’s consider first a simple model for apartments in a college. Here we are interested to predict the prices of the rooms, and how we can allocate them to students. For simplicity, we will assume that they are all equal except for the location, which could be inner or outer. Types of variables Economist will say that parameters for a model, i.e. variables that are fixed for some type of analysis exogenous variables, while the variables of interest of a model endogenous variables. In this setting, it could be the location for a certain room. ...