Mathematical Economics

Mathematical Economics Notes.pdf

Semester: Spring 2022

Lecturer(s): Pim Heijnen, Daniel Vullings

Grade: Erasmus course, University of Groningen (Netherlands)

Book: Microeconomic Analysis, 3rd edition, Norton Varian, H.R.

General Comment: This was my favorite Erasmus course since I connected it directly to our Microeconomics for Business course in my mind. Pricing methods, companies' production numbers, utility functions... I love working with them.

Keywords (for me): Cobb-Douglas utility function, Pareto efficient, mixed equilibrium, Roy's identity, Shephard's lemma, Marshallian demand function

Story of the course in my eyes:

We went through 3 stages in the Mathematical Economics course. First, we thought about the company, the manufacturer. Here, the firm accepted the price already in the market and tried to minimize its cost to maximize its profit (Producer Theory). In this case, we tried to reduce the cost and production functions by placing a constraint. Then we came to the consumer side of the story (Consumer Theory), where the consumers attempted to maximize the utility and would get from the product according to their budgets. Then we put the two of them together and showed how they work in a closed economy. For example, two people have (4,1) and (2,3), respectively. The first person has 4 x and 1 y products; the second person has 2 x and 3 y products. Think of them as loners on the island. Both have separate utility functions in the form of U(x,y). Product x or y for someone with a utility function like "x+y" doesn't matter (person 1). Still, for the other one with a utility function like "3x+y" (person 2), product x brings much more benefit. However, person 1 has an extra x; even if it's y, it doesn't matter to him. Moreover, when we write the demand function of these people from their utility functions (Marshallian Deman Function), we can also see that person 2 demands x. So what do we do? We increase the price of x because the demand for x is high on the island.

Lastly, we focus on oligopolistic markets (Cournot, Bertrand Duopoly Model, Stackelberg Model) and Public and Private provision (maximize consumers' utility from two different views).

  • Quantity competition: Cournot

  • Price competition: Heterogeneous Bertrand

  • Quantity leadership: Stackelberg