Worksheet 4 - Module 2 - Lecture-by-Lecture to-do-list

Econ 1540 Module 2 - complete by end of week 8 – In module 2, we extend optimization to functions of two and more variables. If you get stuck, it might be helpful to revisit chapter 8 (from 1530). Optimization is essential to the study of economics (along with the concepts of equilibrium and opportunity cost). As economists we care both about the optimal choice (result of the optimization) and how the optimal choice and the optimal (realized) value change as external parameters change (comparative statics). Optimization in multi-variate functions is both more interesting and more complicated that optimization with one variable. We first tackle a simple case: Characterizing optima for unconstrained optimization problems in two variables. Second, we get some practice with comparative statics and learn about the magic of the Envelope theorem. We then add constraints and introduce the Lagrange method, before expanding to more than two variables and revising the Envelope theorem in this more general setting. As in 1530, quadratic objective functions play an important special role both in this module and in economics in general. Unconstrained Optimization with functions of two and more variables (lecture 6A) Terminology  Glance over chapters 13.1. – 13.4 , jot down all cursive words. (Unconstrained opt.)  Make a list of the terminology.  Practice and learn the terminology. Learn  Read through chapters 13.1. - 13.4, (even if not everything is clear). (Unconstrained opt.) Make sure to take note of theorem 13.3.1 on p. 505. What are the key concepts? What’s the most puzzling? Practice Work through (with pencil and paper) the examples worked out in the text on  p. 496-498  p. 500-506  p. 509-512 (Unconstrained opt.) Pay particular attention to example 13.3.2. Can you cover the solution and answer the question without looking at the solution? Ask questions during office hours if there’s anything in those examples that’s not clear. Solve the following practice questions Unconstrained optimization  p. 499, #1  p. 499, #2  p. 503, #2  p. 508, #2  p. 508, #5  p. 515, #2

Check your answers against the solutions in the back of the book. Ask questions during office hours if there’s anything about the questions/ answers that’s not clear. Constrained Optimization with functions of two and more variables (lecture 6B, 7) Terminology  Glance over chapters 14.1. – 14.4, and jot down all cursive words. (Constrained opt., 2 variables) Note the distinction between solutions and solution candidates .  Glance over chapter 14.6, jot down all cursive words. (Constrained opt., many variables)  Make a list of the terminology.  Practice and learn the terminology. Learn  Read through chapters 14.1. – 14.4 (even if not everything is clear). (Constrained opt., 2 variables) Note the box on p. 535. It’s key! Carefully read the bottom of p. 548.  Read through chapter 14.6. (even if not everything is clear). (Constrained opt., many variables) What are the key concepts? What’s the most puzzling? Practice Work through (with pencil and paper) the examples worked out in the text on  p. 534-538  p. 541  p. 548 (Constrained opt., 2 variables) Pay particular attention to example 14.1.3. Can you cover the solution and answer the question without looking at the solution?  p. 553-556 (Constrained opt., many variables) Pay particular attention to example 14.6.2. and 14.6.4 Can you cover the solution and answer the question without looking at the solution? Ask questions during office hours if there’s anything in those examples that’s not clear. Solve the following practice questions Constrained optimization, two variables  p. 539, #1  p. 539, #2  p. 539, #5  p. 540, #9  p. 542, #4  p. 544, #1  p. 549, #1 Constrained optimization, many variables  p. 557, #1  p. 557, #3 Challenge 1: Master the Lagrange Method