📘 mathematical economics

1. Let's start with a common problem in mathematical economics: finding the equilibrium price in a market where demand and supply are given by linear functions. 2. Suppose the dema

1. **Problem statement:** We have the economic model equations: $$Y = C + I_0 + G_0$$

1. **Problem 1.1.1: Calculate equilibrium price and quantity using matrices.** Given demand: $Q_d = 20 - 2P$

1. (a) Prove that the empty set $\varnothing$ is a subset of every set $A$. 1. By definition, $\varnothing$ contains no elements.