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Introduction to Numerical Equilibrium Models in Economics

Explore the OLG model, steady state solutions, and optimal consumption decisions using numerical equilibrium models. Learn about assumptions, production functions, factor prices, and general equilibrium concepts. Simulate and analyze convergence to steady state in economics.

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Introduction to Numerical Equilibrium Models in Economics

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  1. Arbeiten mit Numerischen Gleichgewichtsmodellen Ein Einführungsmodell

  2. Assumptions of the model • OLG model • Steady state solution • 2 generations , live for 2 periods • Fixed labor supply in period 1 • No labor supply in period 2 (retired) • Period 1: wage income • Period 2: interest earnings

  3. The optimal consumption decision • Budget constraint: • Utility function: • Max U s.t. B.C. using lagrange

  4. Aggregation • No population growth • The size of both cohords are equal

  5. Factor prices • Production function • Profit function • First order conditions

  6. General equilibrium • All markets (labor, goods, assets) must clear • But no restrictions on labor market: • Capital market is simply: • GE when equilibrium on goods market: • Simulation:

  7. Iteration procedure Initial guess of K r and w c1, a2 and c2 new value of K Aggregation: C and K Y(K,L) Check: |Y-C| < 0.000001 no yes General equilibrium

  8. Convergence to steady state • Why do we even reach a solution? • Because

  9. Potential and expansions • Adjust parameters, interaction effects, optimal tax • Smopec • Public sector • More generations • More periods • Transition period • Etc….

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