# 2.3 — Cost Minimization — Class Content

## Overview

Today we put our tools together (production functions/isoquants and isocost lines) to solve the firm’s cost minimization problem. Again, we do not solve this constrained optimization problem with calculus, but by looking graphically, and using an algebraic rule that should make intuitive sense.

Again, these tools and rules are almost *identical* to how we solved the consumer’s problem. Compare \(\frac{MP_l}{MP_k}=\frac{w}{r}\) to \(\frac{MU_x}{MU_y}=\frac{p_x}{p_y}\) or \(\frac{MP_l}{w}=\frac{MP_k}{r}\) to \(\frac{MU_x}{p_x} = \frac{MU_y}{p_y}\)!, with a major exception:

Consumers:

- choose goods to maximize utility subject to their budget constraint
- budget constraint (line) is what is fixed
- get on highest indifference curve tangent to budget constraint

Producers (Firms):

- choose inputs to minimize cost subject to producing the optimal amount (their constraint)
- isoquant curve is what is fixed (want to produce a specific amount!)
- get on
*lowest*isocost line tangent to isoquant curve

We finally wrap up with a discussion of *returns to scale*.

## Readings

- Ch. 6.4-6.7 in Goolsbee, Levitt, and Syverson, 2019

### Optional/Recommended Reading

- Increasing Returns — my newsletter with the theme of increasing returns

## Appendix

See the online appendix for today’s content:

## Assignments

### Problem Set 3 Due Friday October 14

Problem Set 1 (on classes 2.1=2.3) is due by 11:59 PM Friday October 14 on Blackboard Assignments.

## Slides

Below, you can find the slides in two formats. Clicking the image will bring you to the html version of the slides in a new tab. The lower button will allow you to download a PDF version of the slides.

I suggest printing the slides beforehand and using them to take additional notes in class (*not everything* is in the slides)!