# Intermediate/Advanced Micro

**Select individual Videos below, or choose one of the following playlists:**

**Math Review for Intermediate Playlist**

**Supply, Demand, and Elasticity Playlist**

**Preferences and Utility Theory Playlist**

**Production Theory Playlist**

**Game Theory Playlist**

**Advanced Topics in Micro Theory Playlist**

**Advanced Micro & Uncertainty: Risk Aversion & Moral Hazard Models**

**Individual Videos: Find advanced Material Toward the bottom!**

**Intermediate Micro: Math Review**Intermediate Micro Math: Exponents Review A quick review of all of the exponents rules, including fractional exponents and negative exponents, and how to simplify them.Equations with strange exponents Solving equations like x

^{0.4}= 10 on your calculator.Level Curves (Indifference, IsoQuants...) How to graph a level curve, or parametric curve. If Q=x*y=4, how do we graph this curve. Useful for isoquants and indifference curves in Intermediate Micro.Level Curves Visualization More of the above with better visualization, with a at z=4. *FILE LevelCurvesintro.wxm* Basic Derivatives & Micro: NEWHere we review derivatives of polynomials, and the interpretation as a slope, or marginal.Partial Derivatives & Micro (NEW)A look at partial derivatives, and a little bit about how we can use & interpret them in Econ. Basic Derivatives & Micro (OLD) Here we review derivatives of polynomials, and the interpretation as a slope, or marginal.More on Partial Derivatives (Old) I review the idea of a one-variable derivative again, then discuss partial derivatives in more depth.Quick Calculus for Economics 1: Derivatives and Integration Introduction and integration to find variable costs, total benefit, consumer surplus, and producer surplus.Quick Calculus for Economics 2: Integration to find variable costs, total benefit, consumer surplus, producer surplus, and deadweight loss with a production quota.

**Intermediate Micro: Basic/Review Material**Equilibrium and Comparative Statics: Basics Example of calculating equilibrium of Supply and Demand using algebra and graphing, and using "comparative statics": examining what changes when an exogenous variable changes the equilibrium.Add Linear Demands How to add two linear demand functions together to get a total demand function.Adding Nonlinear Demands Here we add two Cobb-Douglas Demands and plot them using Maxima *File maxima add cd demands.wxmDemand, Marginal Revenue, and Profit Another example of looking at demand, along with marginal revenue. How separating markets can increase profits.Supply Shocks & Equilibrium: ANWR Example Here I discuss a problem similar to one in Jeffrey Perloff's Text: How could we model how drilling in ANWR could help keep prices down when a supply shock happens.Elasticity and Tax Incidence A brief review of tax incidence, and of how price elasticity of demand and supply can predict the incidence of a per unit tax.Demand and Elasticity 1 Given two points on a demand curve, find the equation and calculate elasticities.From Elasticities to Linear Supply and Demand Here I show how to take price elasticities of supply and demand to derive plausible linear functions to represent them.Demand elasticity back of envelope Using the price elasticity of demand, price and quantity, we approximate the demand function for Jack Daniels whiskey in Virginia

**Intermediate Micro: Intermediate Surplus and deadweight loss analysis**Cost Functions, Marginal Cost, and Perfect Competition Here is a basic look at cost functions, and using calculus to figure out how many units a perfectly competitive firm should produce, and its relationship to Producer Surplus.Ceiling Worst Case Scenario With a price ceiling, what you normally calculate in Introductory Micro is the "Best Case Scenario". Let me show you the Worst Case Scenario, or "Least efficient Outcome".

Maximum Tax Revenue: Take your skills to the next level In this video we derive the tax-revenue maximizing per-unit tax. First with a graph, then with example equations, then derive the analytical solution. Extremely fun way to see mathematical economics in action! Handout

**Intermediate Micro: Preferences, utility functions, and Indifference Curves**Utility 1 A look at a total and marginal Utility Function with only one variable. Using calculus, we look at what a marginal function means.Utility 2a Visualizing a 3d utility surface, thinking about marginal utility. In this video we only do visualization so that you can better understand the calculus that comes next. *File Utility.wxm*Utility2B: Marginal Utility and MRS Using calculus to find marginal utility and marginal rate of substitution for a utility function, looking at indifference curves. Utility2C: MRS for Cobb Douglas I show a trick for finding the Marginal Rate of Substitution function if you have a cobb Douglas utility function. Works for MRTS (marginal rate of technical substitution) as well.Indifference Cures: Different Types We look at intuition, graphs, functions of several types of preferences people could have: Cobb Douglas, Quasilinear, perfect complements/substitutes, bads, and goods we could take or leave.A few points about Indifference Curves Some of the finer points: Why they can't slope upwards (with two GOODS), cross, be thick, there are infinitely many, and a review of MRS.Utility3: Maximizing Utility with Budget Constraint How to solve a constrained optimization problem with a utility function and budget constraint; maximizing utility. Just set the slope of the budget line = slope of indifference curve! Quasilinear Utility Maximization Instead of the usual Cobb-Douglas, here I illustrate maximizing utility with a quasi-linear utility function.Equal MU per $, or Bang for Buck rule Graphs, calculus, numbers, and discussion to explore details of the =equal marginal utility per dollar maximization condition.Utility Maximization and Demand Here we demonstrate how to show where demand curves come from, by doing several utility maximization problems.U Max and Demand New Version! Also includes Price Consumption and Income Consumption Curves Download HandoutThe Dual Problem Here we look at the DUAL problem to utility maximization. Instead of getting the highest utility with a given budget, here we find the cheapest way to attain a certain level of utility.Income and Substitution Effects If you already know how to maximize utility, this video shows you how to find income and substitution effects using the Slutsky Equation (Hicks' Decomposition). Income/Subs Effects, Price Decrease Here we look at a Cobb-Douglas utility function with a price decrease.Overview: Inc/Subs/ Compensating/ Equiv. Variation. This is an overview of graphing and interpretation of income and substitution effects, and compensating and equivalent variation. A focus on graphing and interpretation, rather than on calculation. *File* INCSUBS INTERPRETWhy Subsidies Suck! Using Consumer Theory to show why subsidies are inefficient. *File* Subsidies Suck.pdfYet Another Example Utility Maximization, Price Change, Income and Substitution Effects, and Compensating Variation file: income.subs.another.example.pdf

**Intermediate Micro: Cost Minimization and Production Functions**MRTS and Elasticity of Substitution Production functions, non-economic regions, interpreting marginal rate of technical substitution, perfect substitutes and perfect complements (Leontief production functions), and the elasticity of substitution measure.IsoQuants and Returns to Scale Here we look at the definition of returns to scale, isoquants, and Cobb-Douglas Production Functions. As usual, I give you the shortcuts along with the intuition and math. I briefly describe the difference between RTS and marginal returns.Production Theory: Cost Min 1 *File* IM Production Theory Example Returns to scale, input demand functions, marginal rate of technical substitution, isocosts, isoquants, etc. SR vs. LR cost minimization. Production Theory: Cost Min 2 Continuation of above, Returns to scale, input demand functions, marginal rate of technical substitution, isocosts, isoquants,etc.A interesting discussion of a boring problem Given L, K, and the exponents, solve for the constant. Why would we want to do this? Here are some things to think about.

**Consumer Theory: More Advanced Topics**Cobb Douglas Exponents: Do they have to Sum to 1? The answer is No, but you CAN represent any CD Utility function with exponents summing to 1: Here's how!Lagrange Multiplier Method Here is a different, more powerful method many use to solve constrained optimization problems. I show how it is really the same thing, with one twist.Handout: Advanced Consumer Theory on One Page Here I give an overview of a handout explaining the relationships between Marshallian Demand, Hicksian, Indirect, Expenditure functions, Money Metric Utility, Roy's Identity, Shephard's Lemma, and a couple of other tricks. *File* consumer theory.pdfAdvanced Topic: Roy's Identity, Indirect Utility, Hicksian Demand, Expenditure Functions Here I use the Lagrange Multiplier method to derive some advanced ideas in Micro-- using a simpler method than presented in most textbooks. I use Maple to do the math for us, but explain what we are doing as we go, and why. *File* marshall hicks.mw marshall hicks.pdfConsumer Theory Expression Simplification Response to a Viewer Question about how to simplify the expression for the Expenditure Function in my Consumer Theory handout. The answer is: Find the Common Denominator!Advanced consumer theory by hand 1: Marshallian and Indirect By request: Deriving Marshallian and Indirect utility functions for a Cobb-Douglas utility function, and then using Roy's Identity.Marshallian, Indirect, and Roy's: One more time Here is another example of taking a Cobb-Douglas Utility Function, deriving the Marshallian demands, deriving Indirect Utility Functions, and then applying Roy's Identity to get the Marshallian Demands back.Advanced Consumer Theory by Hand 2: The Hicksian Demand By request: Looking at another part of my Consumer Theory Handout, a viewer asks to see how to set up and solve for Hicksian (Compensated) Demand Functions.Slutsky Equation Derivation: Preparing you for the journey In this video we pull out the "BIG GUNS": If you want to see how you can derive the Slutsky Equation, you need to review some high-powered math: Lagrangians, total differentials, and Cramer's Rule. Here we set the stage for the next video.Slutsky Equation Derivation: Going through the steps After you have armed yourself with the mathematical tools in the previous video, you are ready to take on the derivation of the Slutsky Equation. Here we go!Slutsky vs. Hicks: Income/ Substituion Effects ++ Slutsky vs. Hicks for Income and Substitution Effects. Also discuss Compensation and Equivalent Variation, and the connection to Laspeyres and Paasche price indices. HandoutCES Functions: Const. Elasticity of Substitution An introduction to elasticity of substitution, and everything you could ever want to know about CES functions. CES Utility: Analytical Solution Marshallian In this video I take a generalized CES Utility function and derive the analytical solutions for the Marshallian Demand Functions. CES Utility Max Part 2: Indirect Utility Here we take the Marshallian Demands derived previously, and derive the Indirect Utility Function, completing the earlier video about Analytical CES Utility AnalysisCES 3: Show that Indirect is Homogenous We show that Indirect Utility Function for CES is Homogenous Degree 0 in prices and Income.Analytical Consumer Theory: Cobb Douglas and Perfect Complements No numbers! How to derive demand functions with analytical solutions. I show some common tricks for simplifying complicated expressions. Analytical Consumer Theory: Cobb Douglas with Subsistence Level:Pt 1 Here we assume that if you don't get at least "d" amount of x, you'll get no utility! How does this affect the demand and indirect utility functions?Subsistence Part 2: Compensation for Tax Here we derive the compensating variation for a tax on the Consumer with a necessary Subsistence level for X above.Elasticity for Marshallian Demand Functions Here we get analytic solutions for the Marshallian Demands for Cobb Douglas and Perfect Complement Utility Functions (Own Price, Income, and Cross Price) Link to CD Elasticity Handout Link to "The Mother of all Elasticity Handouts"

**Utility Maximization: Other Interesting Cases**Two Period (Inter-temporal) We go through the basic idea of intertemporal utility maximization with two periods. We solve a basic problem with a Cobb-Douglas Utility function and an interest rate.Intertemporal: Additional Problems Here we see how taxes and a forced saving program affect utility and decisions.Risk Aversion and Expected Utility An overview of Risk aversion, visualizing gambles, insurance, and Arrow-Pratt measures of risk aversion.Principal Agent Problems: Moral Hazard Part 1 We look at a model with the potential for Moral Hazard (Hidden Actions that might hurt the Principal), but first assume that you can observe the effort of the agent. We solve for the optimal contract in the next video. Principal Agent Problems: Moral Hazard Part 2 In this video we solve for the optimal contract when effort is unobservable, and take a quick look at a state-space diagram.