Life cycle

Question 1

Consumption-retirement puzzle

Answer 1

• Retirment is associated with consumption drops

Question 2

Possible explanations for the humped-shaped profile

Answer 2

• Uncertainty about future income when young is high: Jensen inequality might explain this if BR<1
• Survival probabilities: might work if BR>1
• Non-separable leisure: if consumption and leisure are substitutes, this might help to explain the drop of consumption at retirement

Question 3

Becker model

Answer 3

• Time and expenditures are inputs in the production of non-tradable consumption services
• Two constraints
  
  • Time constraint
  • Budget constraint
• Usual assumptions over the production function
  
  • F_xl(x,l)>0

Question 4

Household problem

Answer 4

Question 5

Implications FOC

Answer 5

• Ratio of factors is independent of the level of consumption and independent of the wealth of the household
  
  • With CES function, x/l tracks the ratio of w/p
  • x/l will be hump shaped over the life cycle
  • changes in consumption services and the change in the ratio of factor x/l move in opposite directions
  • Allocation into the production of domestic consumption services will be U-shaped over the life cycle

Question 6

Elasticity of substitution between expenditure and time def

Answer 6

Question 7

Life cycle profile of consumption expenditure

Answer 7

It depends on the relationship of the elasticity of intertemporal substitution and elasticity of substitution between time and consumption services

Question 8

Habit formation problem

Answer 8

Habit formation break the link between IES and RA

• Remember that breaking this link is important for the equity premium puzzle