Robinson Crusoe Model

Transcription

1 Robinson Crusoe Model Seyed Ali Madanizadeh Sharif U. of Tech. October 9, 2016 Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

2 Question Output per worker varies enormously across countries. Why? 35-fold di erence in output per worker between the United States and Niger. Capital : 1.5 Human Capital: 3.1 Remaining di erence: 7.7 (productivity residual) Why do some countries invest more than others in physical and human capital? Why are some countries so much more productive than others? Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

3 Why Income Di erences? Hall and Jones 1999 : Social Infrastructure Institutions Government policies They Determine the economic environment within which individuals accumulate skills, and rms accumulate capital and produce output. A social infrastructure favorable to high levels of output per worker provides an environment that supports productive Activities and encourages capital accumulation, skill acquisition, invention, and technology transfer. Such a social infrastructure gets the prices right In the language of North and Thomas (1973): Individuals capture the social returns to their actions as private returns Social Infrastructure ) (Inputs,Productivity) ) Output per Worker Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

4 Why Income Di erences? Productivity and Output per Worker Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

5 Why Income Di erences? Productivity Calculations: Ratios to U.S. Values Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

6 Why Income Di erences? Hsieh and Klenow 2010: Why TFP varies across countries? Misallocation of inputs across rms and industries H : Human Capital, K : Physical Capital Geography, Climate,Luck ) H,K,TFP ) Income + Institutions, Culture ) H,K,TFP ) Income + Policies, Rule of Law, Corruption ) H,K, TFP ) Income Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

7 Goal What are the factors a ecting Household Welfare? Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

8 Goal: what a ects output Output Production (GDP) Factors of production Labor Capital Input Materials TFP (Total Factor Productivity) Technology Allocation and Misallocation Macroeconomic Stability Macroeconomic policies Institutions Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

9 What a ect Output/Labor Force Decisions Robinson Crusoe Model of Macroeconomics Labor Leisure Decision Social Planner solution Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

10 Decentralized Economy Robinson Receives Wages and pro ts Firms produce and sells Markets clear Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

11 Decentralized Economy Income e ect Subsitution e ects How taxes a ect Labor supply Welfare Theorems How General Equilibrium works How results depend on productivity, leisure parameters Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

12 Intertemporal Labor supply decision a Two-period consumption-leisure-saving problem Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

13 References Hall and jones 1999: "Why Do Some Countries Produce So Much More Output per Worker than Others?" Hsieh and Klenow 2010: "Development Accounting" Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

14 Decentralized Economy Robinson Crusoe Household max U (C, H) s.t. pc wh + Π for U (C, H) = (1 α) log C + α log (T H) Robinson Crusoe s rm Equilibrium max Π = py wh s.t. Y F (H) = AH θ C = Y H d = H s Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

15 Robinson Crusoe Household U H U C = w p ) a C 1 α l = w p l = α T + Π w H s = (1 α) T α Π w Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

16 Robinson Crusoe Firm pθah θ 1 = w θap H d = w Y = A 1 1 θ 1 1 θ θ θp 1 θ w wh d = θpy Π = (1 θ) py = 1 θ wh d θ Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

17 Decentralized Economy Equilibrium H d = H s H = (1 α) T α 1 θ H ) θ H = (1 α) T 1 + α 1 θ θ θa w p = (1 α)t 1+α 1 θ θ C = Y = A 1 θ! 1 θ (1 α) T 1 + α 1 θ θ Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18

18 Decentralized Economy Income E ect Substitution E ect Seyed Ali Madanizadeh (Sharif U. of Tech.) Robinson Crusoe Model October 9, / 18