2.2 — Production Technology — Class Content

Meeting Dates

Wednesday, March 1, 2023 and Monday, March 6, 2023

Overview

Today we continue with setting up the second stage of the firm’s problem, the cost-minimization problem, where firms choose inputs $(l,k)$ that minimize total cost $(wl+rk)$ in order to produce the optimal amount of output $q^{\ast }$. For now, we are merely assuming the amount of output that is optimal, later we will explicitly solve for it as our first stage (profit maximization problem).

In doing so, we need to split up production activity into the short-run, where firms cannot change all inputs (we traditionally assume capital is fixed $\overline{k}$ and firms can only change labor $l)$, and the long run, where firms can change all inputs. We discuss short run production and associated input-based metrics: marginal product and average product.

In the long-run, firms can choose many combinations of inputs $(l,k)$ that yield a desired output. We introduce two tools that will remind you a lot like the tools from consumer theory: (1) an isoquant curve¹ that, similar to an indifference curve, contains all the combinations of inputs that yield the same output, and (2) an isocost line² that, similar to a budget constraint, contains all the combinations of inputs that are the same total cost. We discuss some properties about each of these things and do some examples in anticipation of putting these tools together in the next class to solve the problem.

For some students, it takes this second time around with the tools of consumer theory for them to finally “click,” and that’s okay!

Readings

• Ch. 6.2-6.4 in Goolsbee, Levitt, and Syverson, 2019

Appendix

See the online appendix for today’s content:

• Derivation of MRTS Equation (as ratio of marginal products)
• Solving the Firm’s Problem in One Step
• The Firm’s Supply and Demand Functions
• The Geometry of Short-Run Production
• The Relationship Between Marginal and Average

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.

Tip

You can type h to see a special list of viewing options, and type o for an outline view of all the slides.

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

Download as PDF

Footnotes

1. Call it an output curve to remember it better.

2. Call it just a cost line to remember it better.