Our book contains over 80 major examples as well as numerous in-text examples.

Chapter 1

  1. Example 1: The Ramsey Problem
  2. Example 2: Endogenous Uncertain Lifetimes
  3. Example 3: The Rawls Maximin Utility Function
  4. Example 4: Majumdar's Example
  5. Example 5: The Cake-Eating Problem
  6. Example 6: A convex model of endogenous growth
  7. Example 7: Human capital and endogenous growth

Chapter 2

  1. Example 1: Equivalent metrics
  2. Example 2: lp spaces
  3. Example 3: The product topology on sm
  4. Example 4: Non-compact order interval
  5. Example 5: [0,1] is connected
  6. Example 6: Normed spaces
  7. Example 7: Convergence in sm
  8. Example 8: The dual of l1 is l∞
  9. Example 9: The dual of c0 is l1
  10. Example 10: The dual of sm is c00
  11. Example 11: α-norm on l∞(β)
  12. Example 12: Banach limits
  13. Example 13: L∞ duality trickery

Chapter 3

  1. Example 1: Continuity and TAS preferences
  2. Example 2: The maximin criterion
  3. Example 3: The overtaking criterion and the golden rule
  4. Example 4: Cake-eating and utility values
  5. Example 5: Long-run average criteria and Banach limits
  6. Example 6: Admissibility
  7. Example 7: The TAS extension problem
  8. Example 8: Banach limit utility and myopia
  9. Example 9: The KDW aggregator
  10. Example 10: “Partial sums”
  11. Example 11: Overtaking and recursive utility

Chapter 4

  1. Example 1: Existence of an optimal maximin program
  2. Example 2: Upcounting
  3. Example 3: Nonclassical models
  4. Example 4: Weak maximality and the cake-eating problem
  5. Example 5: Long-run average optimal paths
  6. Example 6: The von Neumann model With fixed labor supply
  7. Example 7: The neoclassical multisector model
  8. Example 8: The Ramsey model
  9. Example 9: Nonconvex Ramsey model
  10. Example 10: A convex endogenous growth model
  11. Example 11: A human capital model
  12. Example 12: Von Neumann models
  13. Example 13: EH utility with constant returns to scale
  14. Example 14: KDW utility with constant returns to scale
  15. Example 15: An asset pricing example
  16. Example 16: Extended utilitarianism and arbitrages
  17. Example 17: Stationary differentiable one-sector model
  18. Example 18: Reduced-form models
  19. Example 19: Neoclassical two-sector model

Chapter 5

  1. Example 1: Is f(0) = 0 important?
  2. Example 2: Positive marginal products and regularity
  3. Example 3: Uzawa-Epstein-Hynes utility
  4. Example 4: KDW utility
  5. Example 5: Decreasing rate of impatience
  6. Example 6: Linear technology
  7. Example 7: Homogeneous TAS felicity
  8. Example 8: Dolmas model
  9. Example 9: Convex endogenous growth
  10. Example 10: δ-normality in the one-sector TAS model
  11. Example 11: Golden rules in two-sector neoclassical models
  12. Example 12: Symmetric cross terms
  13. Example 13: Sutherland's optimal cycles
  14. Example 14: Weitzman's interior cycles
  15. Example 15: Two-sector neoclassical model
  16. Example 16: The tent map

Chapter 7

  1. Example 1: The One-Sector Model
  2. Example 2: The Two-Sector Model
  3. Example 3: Two-Sector Models and Joint Production
  4. Example 4: Malinvaud Technologies
  5. Example 5: Nonclassical Technology
  6. Example 6: Capital Accumulation and Wealth Effects
  7. Example 7: Capital Income Tax Reform and Capital Deepening
  8. Example 8: TAS Utility
  9. Example 9: Epstein-Hynes Utility
  10. Example 10: The UEH Aggregator

Chapter 8

  1. Example 1: Nonexistence of individually rational Pareto optima in l∞
  2. Example 2: Nonexistence of individually rational Pareto optima in R2
  3. Example 3: Nonexistence of dual equilibrium prices
  4. Example 4: One-sector models with diminishing returns
  5. Example 5: Multisector models with diminishing returns
  6. Example 6: An economy of firms
  7. Example 7: The sum of closed convex cones need not be closed
  8. Example 8: Equilibrium with recursive utility