Videos from Fall 2020


August 24: There were two videos, a first and a second.  Topics include introduction to the class and, from page 2 of the "prerequisites" handout, how to write Greek letters by hand and how to pronounce them.


August 26: Topics from Section 1 of the "prerequisites"  handout, including convex combinations, convex sets, convex and concave functions (including their definition using the convex combination of two points on the surface of the function), strictly convex and strictly concave functions, quasiconvex and quasiconcave functions (including the definition of upper level sets (upper contour sets) and lower level sets (lower contour sets)), and quadratic forms (including positive definite, positive semidefinite, negative definite, and negative semidefinite).


August 31: Completion of the "prerequisites" handout.  First-order conditions and Lagrangians; second-order conditions and Hessians; comparative statics and Jacobians; and the Envelope Theorem.


September 2: Topics from Section 7.1: rationality (completeness and transitivity), continuity of preferences, existence of a utility function, difficulties with neoclassical assumptions on preferences.


September 9: Bordered Hessians and quasiconcavity, from the "prerequisites" handout.  Remaining topics from Section 7.1: preferences which are monotonic (weak or strong), convex or strictly convex, nonsatiated or locally nonsatiated, and the relationships between these.  Marginal rate of substitution.


September 14: Quasiconcave vs. concave utility functions; altruism, jealousy, and methodological individualism; Section 7.2 (budget constraints, indirect utility functions); Section 7.3, properties of the indirect utility function.


September 16: Shephard's Lemma (consumer theory version); continuation of Section 7.3: other properties of the indirect utility function; the expenditure function and some of its properties.


September 21: Questions from students (value functions, indirect utility, cardinality or ordinality of utility, and an extended discussion on the intuition behind the Envelope Theorem); remainder of Section 7.3, completing the properties of the expenditure function, including proof of its concavity with respect to prices.


September 23: Section 7.4 "Some Important Identities" (Roy's Identity; identities connecting expenditure functions and indirect utility functions; identities connecting the Hicksian and Marshallian demand functions).  Page 111 and 112, examples with Cobb-Douglas and CES utility functions.  Start of Section 8.1 (income expansion paths and Engel curves).


September 28: Section 8.1: luxuries and necessities.  Giffen goods; the Irish Potato Famine and Amartya Sen's theory of famines; Ray Battalio's rat lab experiment on Giffen goods.  Section 8.2 (the Slutsky Equation): income and substitution effects.  Section 8.3: using the dual approach to prove that the Slutsky Substitution Matrix is negative semidefinte and symmentric.


September 30: Section 8.4 is supersceded by material in Section 5 of the mathematical prerequisites handout.  Brief comments on Section 8.5 (integrability).  Section 8.6: deriving the utility function from the indirect utility function.  Remainder of Chapter 8: revealed preference and its relationship to the utility-maximizing approach.


October 5: Section 9.1: Endowments in the Budget Constraint.  The Slutsky Equation.  Perils with modeling "labor" and "leisure" as a choice, with "labor" always a bad thing and "leisure" always a good thing.  Section 9.2: The properties of homogeneous and homothetic functions and their application to utility functions.


October 7: More on homothetic functions and their relationship to consumer theory.  Brief comments on Section 9.3 ("Aggregating across Goods") and Section 9.4 ("Aggregating across Consumers").  Section 9.5 on inverse demand functions.


October 12: Section 9.6, the connection between discontinuous demand curves and nonconvex preferences); Section 1.1, introduction to description of production.  Section 1.2: Production Possibilities Set, Transformation Function, one-output framework, Production Function, Input Requirement Set, Isoquants.


October 14: Section 1.2, continued.  Problems with aggregation, particularly aggregation of "capital."  (Also, distinguishing physical capital from credit; the importance of credit but its absence from this course; credit is not produced from inputs (except for a small amount of labor and associated tools) but is a social relation.)  The neoclassical assumption that technology is known.  Frank Knight's distinction between "risk" and "uncertainty"; the correct ex ante "uncertainty" about an event can persist after the event has occurred.  The fallacy of modeling technological progress as obtaining more output from literally the same inputs.  Georgescu-Roegen's distinction between flows and funds, and critique of neoclassical production functions as not including methods.  Section 1.3, Activity Analysis.  Figure 1.1, Leontief technology.


October 21: Applying Section 1.3's Activity Analysis (as opposed to neoclassical smooth production technology): the history of the steel industry (an example from Capital and Time in Ecological Economics: Neo-Austrian Modelling by Malte Faber, John Proops, and Setfan Speck (1999), Edward Elgar; note that this "neo-Austrian" perspective is not the conservative "Austrian Economics" of von Mises and Hayek but instead builds on the concerns of authors like Eugen von Böhm-Bawerk).  Section 1.4 (monotonic technologies), Section 1.5 (convex technologies), Section 1.6 (regular technologies).  Section 1.7: smoothing isoquants to move from Activity Analysis to smooth technologies.  Pitfalls of smooth technologies: production possibilities not fully known (and irrational to attempt to fully know them); only one or a few techniques might be known or relevant.  Without smooth technology, calculus cannot be used, nor can the idea of the "margin" (so no "marginal cost," "marginal profit," "rate of technical substitution," "marginal rate of substitution"); the rest of neoclassical economics can be assumed (rational agents, profit maximization, etc.), but without calculus and marginal concepts, the distinction between neoclassical economics and non-neoclassical economics blurs.  Section 1.8 (the technical rate of substitution).


October 26: Section 1.9: elasticity of substitution); Section 1.10: returns to scale; elasticity of scale; Varian's argument that decreasing returns to scale does not exist, and its implication that competitve equilibrium prices are determined only by cost of production and not demand, just like the Classical economists said; Section 1.11: homogeneous and homothetic production functions;  Section 2.0: definition of profit; definition of price-taking ("competitive") firms; competitive equilibria as being supported by irrational expectations (firms think demand curves are horizontal but they are not, consumers think supply curves are horizontal but they are not); Section 2.1: profit maximization and the "profit function."


October 29:  Input markets & the real world: "efficiency wages"; raising wages, by increasing the "demand for labor" curve, may not cause an decrease in employment.  Cost functions.  Section 2.2: Input demand functions.  Supply (of output) functions.  Constant returns to scale implies zero profit if the markets are competitive, and since it also implies a horizontal output supply curve, the optimal output for each firm at the equilibrium price is nonunique (although the equilibrium output for the firms taken together is unique).  Joan Robinson and the inconsistency of price-taking agents adjusting prices to move closer to the competitive equilibrium price (hence the neoclassical model of perfect competition as a model of irrational expectations).  Section 2.3:  Input demands in a one-output framework are homogeneous of degree zero in "output price and input prices."  Comparative statics is "sensitivity analysis," but in microeconomics is often done in the context of assuming optimizing agents, which is an unusual assuption in other fields (and is to some extent also less used in macroeconomics than in microeconomics).  Section 2.4: Mostly posponed to Section 3.4, except for the proof that if a matrix is negative definite and symmetric then its inverse is also negative definite and symmetric.

 

November 2Sections 2.5 and 2.6 omitted.  Section 3.2 Hotelling's Lemma.   Section 3.1 properties of the profit function.  (Section 3.3, the Envelope Theorem, was already covered earlier.)  Section 3.4: proof that output supply curves are upward-sloping and that input demand curves are downward-sloping.

 

November 4: Section 4.1: cost minimization.  Firms have no budget constraints because revenues arrive at the same time as bills for inputs.  If that were not the case, firms might need credit, which is the real "capital" in "capitalism"; economists often call machines "capital" but they are "physical capital" and have no connection to "financial capital" which includes credit ("physical capital" also was around long before "capitalism").  Section 4.2: second-order conditions (already covered in the mathematical prerequisites handout).  Section 4.3: difficulties with cost minimization (corner solutions; existence is not usually a problem).  Section 4.4: cost minimization and comparative statics.  Section 4.5: omit.  Section 5.1: the cost function of a constant returns to scale production function.  Section 5.2: the equality of marginal cost and average variable cost in the limit as output goes to zero.  Section 5.3:  long-run total cost vs. short-run total cost; at the output level where LRTC=SRTC, LRAC=SRAC, and I prove using the Envelope Theorem that LRMC=SRMC.  

 

November 9Section 5.4: Shephard's Lemma and properties of the cost function.  Section 5.5: previously done.  Section 5.6: General comparative statics results for cost-minimizing input demand curves.  Also, Philip Mirowski's argument from More Heat than Light that basic neoclassical utility-maximization and cost-minimization theory resemble each other because both were designed to resemble the theory of electromagnetic fields, which was the epitome of scientific theories when the early neoclassicals were working.  (In other words, their design was not in the first instance inspired by considerations of economic behavior.)

 

November 11: Section 6.1: Cost functions with non-monotonic, non-convex, non-closed input requirement sets are identical to cost functions with monotonic, convex, closed input requirement sets.  Section 6.2: omit (but briefly discussed: sufficient conditions for an arbitrary function to be a cost function of an actual technology).  Section 6.3:  Obtaining the production function from the cost function.  Elasticity of scale.  Section 6.4:  Flat portions of isoquants generate horizontal portions of input demand curves; kink points on isoquants generate vertical portions of input demand curves; and nonconvex portions of isoquants (of input requirement sets) generate gaps in input demand curves.  Section 6.5: uses of duality.   

 

November 16Section 13.1: Competitive partial equilibria as being supported by non-rational beliefs; Joan Robinson's point from Section 2.2 repeated.  Section 13.2: Simple second-order conditions for profit maximization; potential nonexistence of a competitive equilibrium if those second-order conditions are not satisfied.  Section 13.3: Adding supply curves.  Section 13.4: Comparative statics of the market equilibrium.  Section 17.1: Notation for pure exchange economies.  The Edgeworth Box.  Section 17.3:   Gains from trade in the Edgeworth Box.

 

November 18: Section 17.3, continued: the Contract Curve.  Section 17.2: Equilibrium in a pure exchange economy.  Section 17.3, continued again: Market equilibrium in an Edgeworth Box.  Section 17.4  Walras' Law; free goods.

 

November 23Section 17.4, continued: When K-1 markets clear, so does the th.  Exact equality of demand and supply when goods are desirable.  Section 17.5: Prices: using a numéraire or using the "K-1"-dimensional simplex.  Equilibrium price and quantity as fixed points in partial equilibrium.  The Brouwer Fixed-Point Theorem.  The main proof of existence of a competitive equilibrium in a pure-exchange economy.

 

November 25Section 18.1:  Notation for general equilibrium with production.  Section 18.2:  Characteristics of general equilibrium under increasing, constant, and decreasing returns to scale.  Also, nonconvexities.  Section 18.3:  Labor income:  the neoclassical framing of "leisure" and "labor" (echoing the comments of Section 9.1).  The distribution of profit income.  Section 18.4:   Proof of Walras' Law.  Section 18.5:  Discussion of the assumptions behind Debreu's proof of existence of competitive equilibrium.  Section 18.8:  Robinson Crusoe economies with either constant- or decreasing-returns to scale.  Look at the class handout on this for more information.  Section 18.9:  The nonsubstitution theorem (sufficient conditions for a constant-returns-to-scale economy to have prices in general equilibrium to be completely determined by and equal to average cost (which equal marginal cost), so demand has no effect on prices).  Section 18.10:  The number and size of firms in general equilibrium under constant- or decreasing-returns to scale.  Section 10.1:  Money metric utility function; money metric indirect utility function.

 

November 30:  Rest of Section 10.1: equivalent variation and compensating variation; williness to accept, willingness (and ability) to pay.  Section 10.2: consumer surplus.  Section 10.3: quasilinear utility.  Section 10.4: under quasilinear utility, equivalent variation, compensating variation, and consumer surplus changes are all equal to each other.  Section 10.5: when utility is not quasilinear, the change in consumer surplus lies between equivalent and compensating variation.  Section 10.6: aggregation.  Section 13.6: competitive partial equilibrium when consumers have quasilinear utility.  Section 13.7: "competitive partial equilibrium when consumers have quasilinear utility" as the surplus-maximizing position when consumers have quasilinear utility.  Section 13.8: the "sum of utilities" welfare criterion. 

 

December 2Section 13.8:  Maximizing the "sum of utilities" was the objective of the Utilitarian school of thought).  Section 13.9:  The equivalence of weak and strong Pareto efficiency under divisibility; "Pareto efficiency" = "Pareto optimality" = "efficiency" = "optimality."  Section 17.6:  Finding the set of efficient points of an Edgeworth Box.  The First Theorem of Welfare Economics.  Section 17.7:  The Second Theorem of Welfare Economics (& critique).  Section 17.9: Social welfare functions.  Pareto efficient allocations maximize linear weighted social welfare functions with some choice of weights.  Section 21.1:  The core of an economy.  Equal treatment in the core.  The core shrinks to the competitive equilibrium.  Section 21.4:  A critique of Varian's presentation of dynamic approaches to a competitive equilibrium.   Section 18.6:  The First and Second Theorems of Welfare Economics for an economy with production.  Section 18.7:  Social welfare functions for economies with production.