I don't know how to obtain the equations from the last slide using the equations from the first two slides. Can anybody
Posted: Thu May 05, 2022 7:28 pm
I don't know how to obtain the equations from the last slide using the equations from the first two slides. Can anybody help me?
thank you!
Equilibrium ▸ Households maximise utility subject to their budget constraints. FOC's result in a (nominal) Euler equation: u' (C₁) = (1 + i) / / / P2 Bu' (C₂) ► Firms choose investment to maximise profits subject to their technology. The FOC is: A2 = P/ (1+i₁). P2 ► Output market clears at every period C₁ + K₂ = Y₁₁ C₂ = Y₂. ▸ Money market clears at every period P₁C₁ = M₁.
Equilibrium under Flexible Prices ▸ Prices adjust to guarantee output at its potential level: Y₁ = A,K₁. ► Substituting this in the general equilibrium conditions above + ▸ using market clearing conditions to substitute out Cp and C₂ in the Euler equation ► and using profit maximixation condition to substitute out (1 + i)P₁/P2 in the Euler equation gives A₂ = u' (A₁K₁ - K₂) Bu' (A₂K₂) ▸ which implicitly defines K₂ as a function of parameters and K₁ which is given. Once we know K₂ we can solve for C₁ and C₂ and Y₂ ► Assume CRRA utility with elasticity of substitution o u(C₁) = 47 1 110
Equilibrium under Flexible Prices ► With CRRA utility, solution of real quantitites is (31₂) A2 Cla = (A₁K₁) σ 1+ BA₂ A2 A2 C₂ = (A₁K₁) 1 + A₂) A2 BA, 1 1₁ = K₂ = 1 BA₂ Y₁ = A₁K₁ Y₂ = σ 1+ A2 1 + (2+2) A₂ A2 BA₂ (A₁K₁) A2 (A₁K₁)
thank you!
- I Don T Know How To Obtain The Equations From The Last Slide Using The Equations From The First Two Slides Can Anybody 1 (38.77 KiB) Viewed 40 times
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- I Don T Know How To Obtain The Equations From The Last Slide Using The Equations From The First Two Slides Can Anybody 3 (40.78 KiB) Viewed 40 times
Equilibrium under Flexible Prices ▸ Prices adjust to guarantee output at its potential level: Y₁ = A,K₁. ► Substituting this in the general equilibrium conditions above + ▸ using market clearing conditions to substitute out Cp and C₂ in the Euler equation ► and using profit maximixation condition to substitute out (1 + i)P₁/P2 in the Euler equation gives A₂ = u' (A₁K₁ - K₂) Bu' (A₂K₂) ▸ which implicitly defines K₂ as a function of parameters and K₁ which is given. Once we know K₂ we can solve for C₁ and C₂ and Y₂ ► Assume CRRA utility with elasticity of substitution o u(C₁) = 47 1 110
Equilibrium under Flexible Prices ► With CRRA utility, solution of real quantitites is (31₂) A2 Cla = (A₁K₁) σ 1+ BA₂ A2 A2 C₂ = (A₁K₁) 1 + A₂) A2 BA, 1 1₁ = K₂ = 1 BA₂ Y₁ = A₁K₁ Y₂ = σ 1+ A2 1 + (2+2) A₂ A2 BA₂ (A₁K₁) A2 (A₁K₁)