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EC4004 Lecture 20
Consumption & Saving
Today
Recap
Consumption
Saving in 2 Periods
Saving in n Periods
Stuff to Know
Static BC
Multi Year Budget Constraint
Effects of changes in Investment
Recall
Household budget constraint
(Let π /P = 0)

 – C + (1/P)·∆B+ ∆K = ( w/ P)·L + i·( B/ P + K)
 – consumption+ real sa...
Consumption and Saving




                     5
Consumption and Saving
 Consumption Over Two Years
Year1
C1 + ( B1/ P + K1) − ( B0/ P + K0) = ( w/P)1 · L + i0 · ( B0/ P +...
So What?
Pensions.
Consumption and Saving
Consumption Over Two Years
Combine the budget constraints to describe a
household’s choice between ...
Chill.
Be Like Fonzi.
   I know.
Consumption and Saving




                     11
Consumption and Saving




                     12
Consumption and Saving



Present value
If the interest rate, i1, is greater than zero, €1
received or spent in year 1 is ...
Consumption and Saving


Euros received or spent in year2 must be
discounted to make them comparable to euros in
year1.


...
Consumption and Saving




The term 1+i1 is called a discount factor.




                                             15
Consumption and Saving
Choosing consumption: income effects
Household chooses the time path of consumption
—in this case, ...
Consumption & Income Effects
Consumption and Saving
Choosing consumption: income effects
– C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (w/P)1 · L
 + (w/P)2·L/...
Consumption and Saving
Choosing consumption: income effects
– V = ( 1 + i0)·(B0/P+K0) + (w/P)1·L + (w/P)2·L/
  (1+i1)
– p....
Consumption and Saving
Choosing consumption: income effects
– C1 + C2/(1+i1) = V − (B2/P+K2)/(1+i1)
– p.v. of consumption ...
Consumption and Saving
Choosing consumption: income effects

Since households like to consume at similar levels in the
two...
Consumption and Saving
Choosing consumption: the intertemporal-
substitution effect.
– C1 + C2/(1+i1) = V − (B2/P+K2)/(1+i...
A higher i1 provides a greater reward for deferring
consumption.

Therefore, the household responds to an increase
in i1 b...
Consumption and Saving
Choosing consumption: the intertemporal-
substitution effect.
– C1 + (B1/P + K1) − ( B0/P+K0) = (w/...
Consumption and Saving
Choosing consumption: the intertemporal-
substitution effect.
We know from the intertemporal-substi...
Choosing consumption: the
intertemporal-substitution effect.

Since year 1’s real income, (w/P)1 · L+ i0 · (B0/P +
K0) on ...
Consumption and Saving
The income effect from a change in the
interest rate
– C2 + ( B2/ P + K2) − ( B1/ P + K1) =
       ...
Consumption and Saving




                     29
Consumption and Saving
Consumption Over Many Years
Two-year budget constraint
    • C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (...
Consumption and Saving
Consumption Over Many Years
Multiyear budget constraint:
    • C1 + C2/(1 + i1) + C3/[(1 + i1)·(1 +...
Stuff to Know
Static BC
Multi Year Budget Constraint
Effects of changes in Investment
Next Time
Business Cycles
Recap on the Course
EC4004 Lecture 20
Consumption & Saving
EC4004 2008 Lecture20 Consumption & Saving
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EC4004 2008 Lecture20 Consumption & Saving

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EC4004 2008 Lecture20 Consumption & Saving

  1. 1. EC4004 Lecture 20 Consumption & Saving
  2. 2. Today Recap Consumption Saving in 2 Periods Saving in n Periods
  3. 3. Stuff to Know Static BC Multi Year Budget Constraint Effects of changes in Investment
  4. 4. Recall Household budget constraint (Let π /P = 0) – C + (1/P)·∆B+ ∆K = ( w/ P)·L + i·( B/ P + K) – consumption+ real saving = real income 4
  5. 5. Consumption and Saving 5
  6. 6. Consumption and Saving Consumption Over Two Years Year1 C1 + ( B1/ P + K1) − ( B0/ P + K0) = ( w/P)1 · L + i0 · ( B0/ P + K0) consumption in year1 + real saving in year1 = real income in year1 Year2 C2 + ( B2/ P + K2) − ( B1/ P + K1) = ( w/ P) 2 · L + i1 · ( B1/ P + K1) consumption in year 2 + real saving in year 2 = real income in year 2 6
  7. 7. So What?
  8. 8. Pensions.
  9. 9. Consumption and Saving Consumption Over Two Years Combine the budget constraints to describe a household’s choice between consuming this year, C1, and next year, C2. – B1/P + K1 = B0/P + K0 + i0·(B0/P + K0) + ( w/P)1·L− C1 – Real assets end year1 = real assets end year0 + real income year1 − consumption year1 9
  10. 10. Chill. Be Like Fonzi. I know.
  11. 11. Consumption and Saving 11
  12. 12. Consumption and Saving 12
  13. 13. Consumption and Saving Present value If the interest rate, i1, is greater than zero, €1 received or spent in year 1 is equivalent to more than €1 in year2. 13
  14. 14. Consumption and Saving Euros received or spent in year2 must be discounted to make them comparable to euros in year1. 14
  15. 15. Consumption and Saving The term 1+i1 is called a discount factor. 15
  16. 16. Consumption and Saving Choosing consumption: income effects Household chooses the time path of consumption —in this case, C1 and C2—to maximize utility, subject to the budget constraint. 16
  17. 17. Consumption & Income Effects
  18. 18. Consumption and Saving Choosing consumption: income effects – C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (w/P)1 · L + (w/P)2·L/(1+i1) − ( B2/P+K2)/(1+i1) – p.v. of consumption = value of initial assets + p.v. of wage incomes − p.v. of assets end year 2 18
  19. 19. Consumption and Saving Choosing consumption: income effects – V = ( 1 + i0)·(B0/P+K0) + (w/P)1·L + (w/P)2·L/ (1+i1) – p.v. of sources of funds = value of initial assets + p.v. of wage incomes 19
  20. 20. Consumption and Saving Choosing consumption: income effects – C1 + C2/(1+i1) = V − (B2/P+K2)/(1+i1) – p.v. of consumption = p.v. of sources of funds − p.v. of assets end year 2 20
  21. 21. Consumption and Saving Choosing consumption: income effects Since households like to consume at similar levels in the two years, we predict that C1 and C2 will rise by similar amounts. The responses of consumption to increases in initial assets or wage incomes are called income effects. 21
  22. 22. Consumption and Saving Choosing consumption: the intertemporal- substitution effect. – C1 + C2/(1+i1) = V − (B2/P+K2)/(1+i1) – p.v. of consumption = p.v. of sources of funds − p.v. of assets end year 2 22
  23. 23. A higher i1 provides a greater reward for deferring consumption. Therefore, the household responds to an increase in i1 by lowering C1 and raising C2. This response is called the intertemporal- substitution effect. 24
  24. 24. Consumption and Saving Choosing consumption: the intertemporal- substitution effect. – C1 + (B1/P + K1) − ( B0/P+K0) = (w/P)1·L + i0·(B0/P +K0) – Consumption in year1 + real saving in year1 = real income in year 1 25
  25. 25. Consumption and Saving Choosing consumption: the intertemporal- substitution effect. We know from the intertemporal-substitution effect that an increase in the interest rate, i1, motivates the household to postpone consumption, so that this year’s consumption, C1, falls on the left-hand side. 26
  26. 26. Choosing consumption: the intertemporal-substitution effect. Since year 1’s real income, (w/P)1 · L+ i0 · (B0/P + K0) on the right-hand side of equation (7.2), is given, the decline in C1 must be matched by a rise in year1’s s real saving, (B1/P + K1) − (B0/P + K0). The intertemporal-substitution effect motivates the household to save more when the interest rate rises. 27
  27. 27. Consumption and Saving The income effect from a change in the interest rate – C2 + ( B2/ P + K2) − ( B1/ P + K1) = ( w/ P) 2 · L + i1 · ( B1/ P + K1) The income effect from i1, [i1·(B1/P + K1)] – i1(B1/P) – i1K1 28
  28. 28. Consumption and Saving 29
  29. 29. Consumption and Saving Consumption Over Many Years Two-year budget constraint • C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (w/P)1 · L + (w/P)2·L/(1+i1) − ( B2/P+K2)/(1+i1) 30
  30. 30. Consumption and Saving Consumption Over Many Years Multiyear budget constraint: • C1 + C2/(1 + i1) + C3/[(1 + i1)·(1 + i2) ] + · · · = (1+ i0)·(B0/P+K0) + (w/P)1·L + (w/ P)2·L/(1+ i1) + (w/P)2·L/[(1+i1)·(1+i2) ] + · · · 31
  31. 31. Stuff to Know Static BC Multi Year Budget Constraint Effects of changes in Investment
  32. 32. Next Time Business Cycles Recap on the Course
  33. 33. EC4004 Lecture 20 Consumption & Saving

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