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.216-217) and another on the “new economy” (pp.218-219). 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 8-2. 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.

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

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

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

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

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

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

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

Indifference Curves

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

Indifference Curves

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:

The Budget Constraint

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

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

Graphical Optimization

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!

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

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

Example Maximization problem: Solution: ,

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

A Pure Income Effect

An Increase in the Wage

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

Graph of

The Marginal Product of Labor

Effect of an Increase in Productivity

Effect of an Increase in Productivity

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

Graphical Profit Maximization

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!

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

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

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?

Average Workweek in U.S.

Average Workweek in U.S.

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

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

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

Profit Maximization First order condition:

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

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?

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

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

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

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

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

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)

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

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

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

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:

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

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

The Diagram

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

Example: Log Utility FOC for and

Computing Consumption Example I: Example II:

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

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

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

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

Generational Structure

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

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

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

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

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:

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

Example Parameter choices: The law of motion is:

Graph of the Law of Motion

Convergence

Capital Over Time

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

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

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:

The Law of Motion after a Change in Productivity

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

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

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

Convergence from Different Initial Conditions

Catching-up after a destruction of Capital

Two Countries with Different Discount Factors

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

Revisiting the Asian Miracle

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!

Log of GDP per capita in the Asian Tigers

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