Work in progress. The tools are still being developed and checked. Feedback of any kind is very welcome: errors, unclear explanations, ideas for new tools.
Lecture 1 Production theory: substitution and scale properties
Production Explorer
A production function in 3D, seen along an isoquant, along a ray and along an axis.
Input Requirement Sets
Drag two input bundles and check free disposal, convexity and constant returns to scale.
Building the MRTS
Why the slope of the isoquant is MRTS₂₁ = φ₁/φ₂, the ratio of the marginal products.
Homogeneous and Homothetic
Isoquants at equal output steps: what their shape and spacing say about returns to scale.
Two Elasticities: e(z) and σ(z)
The elasticity of scale along the ray, the elasticity of substitution along the isoquant, in one picture.
Frisch's Chocolate Data
A real production function: Frisch’s 1935 measurements at the Freia chocolate factory.
Lecture 2 Firm optimisation: one step and two step approach
Cost Minimisation
Push the isocost line down until it just touches the isoquant.
Cost Curves and Supply
From marginal and average cost to the supply curve, and why increasing returns and price taking do not mix.
One Step vs Two Steps
Maximising profit directly, or minimising cost first: both give the same input bundle.
*Two Technologies and a Kink
A firm that needs two technologies: a kinked isoquant and a range of prices at which the input mix does not move.
*Concavity and Returns to Scale
A quasi-concave production function without increasing returns that is not concave.
Lecture 3 Properties of the firm’s optimal behaviour
Lecture 4 Comparative statics: “what if” questions
What If? Comparative Statics
How output and input demand respond to prices, and why ordinary demand is flatter than conditional demand.
Marshall's Law of Derived Demand
The elasticity of labour demand as a weighted average of substitution and product demand.
Translog Cost Shares
Cost shares that are linear in log prices, and what Arnberg and Bjørner (2007) found.
Substitution or Composition?
Two firms that cannot substitute, whose aggregate data still look like substitution.
Lecture 5 The firm and the market
From Firms to Market Supply
Adding the firms’ supply curves: with fixed costs, market supply jumps and may miss demand.
Firms That Affect Each Other
When one firm’s output moves the other’s costs, market supply is no longer the sum of marginal costs.
Free Entry and Industry Size
Profits attract entrants until the next one would make a loss.
Monopoly and Product Differentiation
MR = MC: less output at a higher price, and how substitutes remove the profit in the long run.
Lecture 5 Consumer preferences
Budget Sets
Income, endowment and a two-part tariff: the shapes a budget set can take.
Better, Worse, Indifferent
Better and worse sets for five preference relations, and the axioms each one satisfies.
Utility Is Ordinal
An increasing transformation f(U) leaves the indifference curves and the ranking unchanged.
Lecture 6 Demand theory
UMP and EMP: Two Sides of One Tangency
Maximise utility on a budget, or minimise spending for a utility level: the same bundle.
Substitution and Income Effects
A price change split into a substitution and an income effect, including a Giffen good.
Income Expansion Paths and Engel Curves
Necessities, luxuries and inferior goods: how demand moves with income.
Lecture 7 Welfare measurement
Lecture 8 Decentralisation in a simple economy
Lecture 9 General equilibrium
The Edgeworth Box
Offer curves, equilibria, the core and the welfare theorems in a two-person exchange economy.
Excess Demand and Equilibrium
Three goods, two firms, two consumers: the prices at which excess demand is zero in every market.
*The Core Shrinks
As the economy is replicated, the core shrinks towards the competitive equilibrium.