0. Lecture 13 Neoclassical Model
Chapter 7 had a single focus: the in-depth development of the Solow model. In contrast, Chapter 8 is a survey of many growth topics. First, the Solow model is extended to incorporate labor-augmenting technological progress at an exogenous rate. Then, policy implications are discussed. There’s a nice case study on the productivity slowdown (pp ) and another on the “new economy” (pp ). These are followed by a discussion of growth empirics, including balanced growth, convergence, and growth from factor accumulation vs. increases in efficiency. Finally, the chapter presents two very simple endogenous growth models.
The models presented in this chapter are presented very concisely. If you want your students to master these models, you will need to have them do exercises and policy analysis with the models. The chapter includes some excellent Problems and Applications for this, which you can assign as homework or use in class to break up your lecture.
If you are pressed for time and are considering skipping this chapter, I encourage you to consider at least covering sections 8-1 and Section 8-1 completes the presentation of the Solow model begun in Chap. 7. One class period should be enough time to cover it, allowing for one or two in-class exercises if you wish. Section 8-2 discusses policy implications; it is not difficult or time-consuming, yet students find it very interesting - it helps give additional real-world relevance to the material in Chap 7 and in Section 8-1.

1. Economic Models Real economy is too complicated to understand
Built your own, simple economy
Ingredients
People
Goods and technologies
Institutions

2. Microfoundations
Use models that explicitly incorporate household and firm decision problems
Allows to capture how decisions adjust when economic environment of policies change

3. Using Models Tools to predict outcomes:
Optimization
Market Clearing
Check whether model matches data:
Yes: Likely that model world captures key features of the real world
No: Build new model

4. A Simple Market Economy
One consumer, one firm
Consumer and firm trade in markets
Markets for consumption C and labor N

5. Market Prices Prices: Price of consumption normalized to one
Price for N is real wage w

6. The Household’s Problem in the Market Economy
Utility function U(C,l)
C: Consumption (coconuts)
l: Leisure
Budget constraint
Consumption expenditure equals income from capital and labor
p is given, capital income
N is given by time constraint: N=h-l

7. The Consumer’s Preferences
Utility function U(C,l)
Assumptions:
More is better than less: ,
Diversity is good: Falling MRS
Consumption and leisure are normal goods

8. Indifference Curves

9. Properties of Indifference Curves
Downward sloping: Follows from positive marginal utilities
Convex: Follows from falling marginal rate of substitution

10. Indifference Curves

11. Marginal Rate of Substitution
MRS: the minimum # of Coconuts consumer is willing to give up for another unit of leisure
Equal to minus slope of indifference curve
Mathematically:

12. The Budget Constraint

13. The Optimization Problem
Maximize utility subject to the budget constraint by choosing l and C
s.t.

14. Graphical Representation
Draw indifference curves as before
Draw budget constraint as a function of leisure
Optimal choice is point in the budget set that lies on the highest indifference curve

15. Graphical Optimization

16. Outcome Slope of indifference curve equals slope of budget constraint
Slope of budget constraint: wage w
Result:
wage = MRS
This is a very general result: the MRS between any two goods is given by the relative price!

17. Mathematical Optimization
Substitute constraints into U(C,l)
First-order condition with respect to l:
Result (once again): wage = MRS

18. Example wage equals 10 coconuts per hour Time: 24 hours
Profit and tax: p=30 and T=30

19. Example
Maximization problem:
Solution: ,

20. Predicting the Reaction to Changes in the Economy
Separate income and substitution effects
Pure income effect: consume more of every (normal) good
Pure substitution effect: consume more of the good that gets cheaper
In practice, often both effects are present

21. A Pure Income Effect

22. An Increase in the Wage

23. The Firm’s Problem in the Market Economy
Production function
Number of coconuts produced with capital and labor input
Assumptions:
: both inputs required
: positive marginal products
: decreasing marginal products

24. Graph of

25. The Marginal Product of Labor

26. Effect of an Increase in Productivity

27. Effect of an Increase in Productivity

28. The Firm The firm maximizes profits subject to the production function
Profit π: output minus cost

29. Graphical Profit Maximization

30. Optimization Result
Slope of production function equals slope of cost curve
This is a very general result: the MP of any factor of production is given by its price!

31. Mathematical Profit Optimization
The maximization problem:
First-order condition:
Wage equals marginal product of labor

32. Equilibrium Requirements for equilibrium:
Consumer maximizes utility
Firm maximizes profits
Demand equals supply in every market
Combining firm and household optimization, we get

33. What is the Simple Model Good for?
The ultimate task of any economic model is to shed light on the real world
The only thing the model could be good for is explaining labor-leisure choice
Does the model explain U.S. data?

34. Average Workweek in U.S.

35. Average Workweek in U.S.

36. How is the Model Evaluated?
Model abstracts from many potential factors
Want to know whether model is sufficient to explain decline in time worked
Need to specify model more precisely

37. Making the Model More Precise
No capital for simplicity
Variables:
C: consumption
l: leisure
N: labor
w: wage
z: total factor productivity
g: growth rate of z
Productivity grows over time
Want to determine N as a function of z

38. Choosing Functional Forms
Production function:
Utility function:
Budget and time constraints:

39. Profit Maximization
First order condition:

40. Utility Maximization The maximization problem: First-order condition:
Labor constant, independent of wage!

41. What does It Mean? Model appears to be a complete failure!
Reason: with log utility, income and substitution effects on labor supply cancel (i.e., they have equal size and opposite sign)
Is this realistic in the cross-section?

42. Using the Model for Cross-Country Comparision
European countries (France, Germany, Sweden etc.) have higher taxes and higher transfers
Is like a negative substitution effect: income tax lowers the perceived wage
Model predicts less work and more leisure in Europe
这一张和下一张ppt感觉有点奇怪，我没看懂它们想说什么

43. What Else Could Explain the Facts?
There are alternative explanations:
Labor-force participation
Taxation
Relative productivity of “leisure” sector
Try new models in case of failure

44. Intertemporal Choice Most of macroeconomics is about changes over time
So far, have jus considered the decision of work versus leisure
Need to add choice of today versus tomorrow

45. Examples Some intertemporal choices: Borrowing and saving by consumers
Investment by firms
Human capital investment by students
Family decisions

46. Important Factors for Intertemporal Choice:
Preferences over time (patience)
Expected return on investment
Expected future economic conditions

47. Modeling Intertemporal Choice
For simplicity:
Look at one consumer in isolation
Two periods only
Variables:
: consumption today and tomorrow
: discount factor (measures patience)
: income today and tomorrow
: saving
: interest rate (return on saving)

48. The Setup Utility function: Budget constraints:
Want to know how and depend on
(intertemporal preferences)
(economic conditions)
(return on investment)

49. Mathematical Solution
Substitute constraints into utility function:
Setting derivative wrt. s to zero:

50. Outcome MRS = Interest rate Same as before – Simple Model:
Choice between leisure and labor
MRS(l,C) = Relative price (l, C)
Intertemporal model:
Choice between today and tomorrow
MRS = Relative price

51. The Present-Value Budget Constraint
Present value of x dollars tomorrow:
Amount needed to be saved today to have x dollars tomorrow
Solving period-2 constraint for s:

52. The Present-Value Budget Constraint
Plugging the result into the period-1 constraint:
PV(total consumption)=PV(total income)

53. Graphical Analysis Lifetime wealth: we = PV(total income)
Rewriting the budget constraint:
Can now represent choice in standard diagram

54. The Diagram

55. Outcome MRS = Relative price
Pure income effect (increase in either or ) will increase both and
Implies that s increases when rises
Implies that s falls when rises
Only present value of income matters, distribution irrelevant for consumption

56. Example: Log Utility
FOC for and

57. Computing Consumption
Example I:
Example II:

58. Conclusions
Model predicts strong consumption smoothing: timing of income does not matter
Result relies on perfect capital market
Even so, evidence for consumption smoothing is strong

59. Consumption Smoothing in Practice
Life-cycle consumption: borrow early in life, then save for retirement

60. Informal Capital Markets
Default risk prevents some people from borrowing
Society often finds ways around that problem:
Transfers from parents and relatives
Gift giving and neighborhood help
Social insurance

61. A Neoclassical Growth Model
Overlapping generations:
Each consumer lives for two periods
Each year, one old and one young consumer are alive
The young work one unit of time
The old are retired and supply capital

62. Generational Structure

63. The Decision Problem of a Consumer Born at Time t
Utility function:
Budget constraints:
Notice that:
There is no income in the old period
Savings are capital in the old period

64. Solving the Consumer’s Problem
Choose to solve:
First-order condition:
Solution:

65. The Profit-Maximization Problem of the Firm
Firm maximizes production minus cost:
First-order conditions are:

66. Closing the Model Market clearing for capital and labor:
Assume constant productivity (for now):

67. Working out the Predictions of the Model
Using market-clearing conditions in equations for w and r:
Using wage equation in saving equation of household:

68. Using the Law of Motion for Capital
Have derived a law of motion for capital (capital tomorrow depending on capital today)
Starting at any initial capital, can determine how capital will develop in the future
Can compute production and growth rates over time

69. Example
Parameter choices:
The law of motion is:

70. Graph of the Law of Motion

71. Convergence

72. Capital Over Time

73. Result
Model predicts convergence across countries with different initial capital
Intuition:
Returns to capital are decreasing
Wage increases less than proportionally with capital
Savings increase less than proportionally with capital

74. Long-run Predictions Capital convergence to steady state
Solving for capital in steady state:

75. What Happens if there is Productivity Growth?
Steady-state level of capital depends on productivity z
Steady state shifts upwards if productivity increases
Assume constant productivity growth g:

76. The Law of Motion after a Change in Productivity

77. Implications
In the long run, capital k grows at the same rate as productivity:
What happens to output and the return to capital?

78. Implication for Growth
Output grows at the same rate as capital
Therefore capital/output ratio is constant

79. Remaining Growth Facts
Labor and capital shares are constant because of Cobb-Douglas technology
Return to capital:
Constant because K and z both grow at rate g

80. Convergence from Different Initial Conditions

81. Catching-up after a destruction of Capital

82. Two Countries with Different Discount Factors

83. Summary The model explains all the growth facts
Driving force is exogenous, constant productivity growth combined with decreasing returns to capital
Explains catch-up of Germany of Japan after the war

84. Revisiting the Asian Miracle

85. Unraveling the Puzzle
Asian Tigers started with low capital stock after World War II
Rapid growth through capital accumulation is exactly what model predicts
There is no Asian miracle!

86. Log of GDP per capita in the Asian Tigers

87. Limits of the Neoclassical Growth Model
Technological progress is just assumed, not explained
Model does not offer a perspective on stagnation throughout history and in poor countries