Economics 311Money and Income

Chapter 2-Work Effort, Production, and Consumption-The Economics of Robinson Crusoe

Department of Economics

College of Business and Economics

California State University-Northridge

Professor Kenneth Ng

Friday, April 21, 2023

Administrative Details

First Homework. Due 2/14/2002 in class. Available on website—ng.csun.edu

The Basic Market Clearing Model Want to build a theoretical model of the economy.

Basic Market Clearing Model in Barro. Use the model to analyze the real world.

Will construct this model by concentrating on 3 key decisions made by a household. Work/Leisure-Chapter 2

How much to produce Real GDP.

Consumption Now vs. Consumption Later-Chapter 3 Whether to borrow or lend Interest rates

Money-Chapter 4 How much money to hold. Demand for money

These three key decisions will be analyzed with three graphs. Combine all three into the Basic Market Clearing Model-Chapter 5.

The Robinson Crusoe Economy Start out considering a person in isolation: no access to goods

markets, no access to financial markets, and no money. Whatever he consumes he must produce. Whatever he produces he must consume now (no saving).

Consider, in this simplest of economies, what determines output of goods-combination of two factors. If he works how much will he produce

Production Function or Production Possibilities Frontier- shows the tradeoff between consumption and leisure.

How much does he value leisure vs. consumption. Indifference curves between consumption and leisure—

shows his preferences between consumption and leisure. A firm understanding of these two theoretical constructs is a precursor

to using the model for analysis.

The Production Function

The production function relates the amount of time worked to the amount of goods produced.

Built in to any production function is the level of technology.

These numbers can be graphed.

Work Effort-L Output-F(L)=Y

1 hour 5 units

2 hours 9 units

3 hours 12 units

4 hours 15 units

Production Function: Relates Work Effort to Output. A Form of Production Possibilities

Frontier (PPF). )( tt lfy

The production function shows how much output (Y) will be produced by a household with a given amount of work effort (L) in a given time period (t).

The shape and position of the PF contain information.

Production Function: Relates Work Effort to Output. A Form of Production Possibilities

Frontier (PPF).

)( tt lfy

Why is the production function upward sloping?

As you work more you produce more.

Position of the PF Represents Technology or Productivity.

Suppose the state of technology improved.

For instance, suppose Robinson Crusoe was given an ax or a technological advance like the moving assembly line was made.

Or alternatively, the state of technology worsened—when we bombed Iraq.

What would happen to the PF?

Position of the PF Represents Technology.

•An improvement in technology would cause an upward shift of the production function.

•Any level of work effort now produces more output.

•The higher the PF for a given work effort, the higher the level of technology.

Analyzing Changes in the World-The First Step.

The purpose of the model is to use it analyze how changes in the real world will affect economic performance.

The first step in the analysis to be able to figure out how a given change in the world will shift the production function.

Suppose a country was subject to a natural disaster.

How would this affect the Production Function?

Analyzing Changes in the World-the First Step.

Suppose a country was subject to a natural disaster. How would this affect the Production Function.

It would shift the production function downward.

The loss of electricity, running water, etc. means that each hour worked produces less output.

Slope of the Production Function Represents the Marginal Product of Labor.

Marginal product of Labor: Given the amount a person is working how much extra output will a person get if he works one more hour. –MPL = slope of production function–Slope of Production Function = rise/run = change in output/change in labor.–MPL equals how much more output a person will get if he works one more hour.

Slope of the Production Function Represents the Marginal Product of Labor.

1

1

1

3labor

output

or

run

riseMPL

The steeper the production function the greater the MPL or the reward to work.

Change in Technology.

Suppose the state of technology improved.

For instance suppose you took away a secretaries typewriter and gave her a personal computer with a laser printer.

What would happen to the MPL or the slope of the production function.

Change in Technology.

What would happen to the MPL or the slope of the production function?

The production function would shift upward.

Not only would more output be produced at each level of work effort, but each additional unit of work would produce more additional output.

The slope of the PF would increase so MPL would increase.

Shape Production Function Represents the Diminishing Marginal Product of Labor.

Diminishing Marginal Product of Labor.

Show relationship between MPL and level of work.

MPL decreases as work effort increases.

As a person works more hours, his marginal output falls.

Curved production function.

Indifference Curves Between Work Effort and Consumption

Consider a person choosing between three combinations of leisure/labor and consumption-A, B and C.

Suppose he was indifferent between these three combinations, i.e. if given a choice between them he wouldn’t care which he received.

We could graph the combinations of work and leisure between which the person is indifferent.

This graph is called an indifference curve.

Labor Consumption

A 1 hour

1

B 2 hours

2

C 3 hours

3

Position of the Indifference Curve Denotes Happiness or Utility

Labor Consumption

A 1 hour 1

B 2 hours 2

C 3 hours 3

D 2 hours 1

E 2 hours 5

Consider combinations D and E.

Could they be on the same IC as combinations A, B, and C?

Explain.

Position of the indifference curve denotes happiness utility

Labor Consumption

A 1 hour 1

B 2 hours 2

C 3 hours 3

D 2 hours 1

E 2 hours 5

E must be preferred to B.

B must be preferred to D.

As you move to IC upward and the the left, you are getting happier or a moving to a more preferred combination of labor and consumption.

Position of the Indifference Curve Denotes Happiness or Utility

There are a whole family of IC’s which represent a persons preferences for labor vs. consumption.

When the person is able to move to an IC higher and to the left, the person is increasing his happiness or utility.

Slope of the IC represents Marginal Rate of Substitution

Marginal Rate of Substitution (MRS):

MRS measure the value of leisure.

The value of leisure is measured as the amount of consumption that is needed to get a person to voluntarily work one additional hour.

MRS is equal to the slope of a persons IC at a point.

Slope of the IC represents Marginal Rate of Substitution

Marginal Rate of Substitution (MRS):

What is the value of leisure or the MRS of between labor and consumption when the person depicted in the graph to the left is working 5 hours?

1

1

leisure

nconsumptiorun

riseMRS

Slope of the IC Represents Marginal Rate of

Substitution

Consider the two people depicted in the graph.

Which one is lazier—blue or green?

Answer the question first by simple inspection.

At point B whose IC is steeper?

What does the slope of the IC represent?

The blue IC represents a lazier person because the slope of the IC is greater, the MRS is higher, and the amount of consumption needed to get the person to voluntarily work an additional hour is greater.

Slope of the IC represents Marginal Rate of Substitution

Which one is lazier—blue or green?

Now answer the question using the MRS.

What is the slope of the green IC from B to D?

Answer—1

What is the slope of the blue IC from B to C

Answer—7

Who values leisure more—green or blue?

A Person’s Choice Between Leisure and Consumption.

Consider the person depicted in the graph.

The blue line is one of his IC’s.

The brown line is his PF or PPF.

Suppose the person is at point B. At that combination of labor and leisure what is his MRS and MPL?

MRS=7, MPL=1

If the MRS>MPL can the person be as happy as he can be at point B? Why or why not?

A Person’s Choice Between Leisure and Consumption.

He would be happier working less and consuming less.

The MPL of labor is 1. That means if gives up 1 hour of leisure he would get one more unit of consumption.

The MRS of labor is 7. That means that you would have to give the person 7 units of consumption to get him to voluntarily give up 1 unit of leisure.

Therefore, the value of leisure (MRS=7) is greater than the price of leisure (MPL=1) so the person would be better off consuming more leisure (less labor) and less consumption.

A Person’s Choice Between Leisure and Consumption.

Another way of stating the answer is the following:

The person will try to get to the highest IC that has at least one point in common with his PF.

At point B in the graph the person is on the blue IC.

What would happen to his level of utility or happiness if he moved to point F?

Because point F is on a higher IC, it means that F gives the person a higher level of utility than B and, therefore, F is preferred to B.

Changes in Production Function (1)

Each production function has two features position and slope.

A change in the world can change either of these features individually or it may change them both simultaneously.

When the position of the production function changes but it’s slope remains the same, the effect on the choice of leisure is called a wealth effect.

In the graph, a given amount of labor produces more output but an additional unit of labor produces the same additional output on the blue and red production functions.

Wealth Effects (1) A parallel shift in the PF causes a positive wealth effect.

The positive wealth effect can have different effects on work/leisure and output depending on the preferences of the workers, i.e. his IC’s. Leisure is a normal

good if a wealth increase causes an increase in leisure consumption.

Leisure is an inferior good if a wealth increase causes a decrease in consumption.

Wealth Effects (2) Consider a person who starts out

on the brown PF. He chooses the optimal

combination of labor/leisure and consumption, i.e. the point on the PF which on the highest IC.

Point A. Now suppose there is a change in

the world and the person’s PF shifts from brown to orange.

What kind of shift is this? Parallel shift.

If the point on the new PF is B, what has happened to the amount of leisure as he has gotten wealthier?

Is leisure normal or inferior? If the point on the new PF is C,

what has happened to the amount of leisure as he has gotten wealthier?

Is leisure normal or inferior? How has the increase in wealth

affected the person’s standard of living?

Changes in Production Function (2)

When the slope of the the production function changes but it’s position at a certain level of work effort remains the same, this is called a substitution effect.

In the graph, a given amount of labor produces the same output output at a given level of work effort, but an additional unit of labor produces more additional output on the red production function.

Substitution Effects A rotation of the PF

causes a substitution effect.

The substitution effect causes a shift in the optimal labor/leisure consumption bundle chosen by an individual.

Consider the shift of the PF from blue to red.

What has happened to the MPL at work effort L?

The person will adjust his work effort now that his MPL has increased.

Moving from A to B, what has happened to GDP?

Summary A parallel shift of the production function means a given level of

work effort produces more output but additional work effort produces the same additional output (MPL stays the same). A parallel shift causes a wealth effect. A parallel shift can cause an increase or decrease in

labor/leisure depending on whether a leisure is a normal or inferior good to a person.

A rotation of the production function at a point means a given level of work effort produces the same output but additional work effort produces more additional output (MPL has changed). A rotation causes a substitution effect because the reward to

work has increased. A rotation that increases the slope of the production function

always causes a decrease in leisure, an increase in work effort, and an increase in output, consumption, and GDP.

A Proportionate Shift in the Production Function

A proportionate shift of the production function causes a change in slope (a rotation or change in MPL) and a change in the position for a given amount of labor.

Example: Every level of work effort produces 20% more output.

A proportionate shift of the production function causes a wealth and substitution effect.

The overall effect of a proportionate shift in the PF depends on net effect of the substitution and wealth effects.

The substitution effect causes work effort to increase.

The wealth effect, if leisure is normal, causes work effort to decrease.

The wealth effect, if leisure is inferior, causes work effort to increase.

A Proportionate Shift in the Production

Function

Consider the change in the PF from blue to red.

Is this a proportionate shift? Yes. Both slope and

position at L are changing. The substitution effect is

shown as the movement from A to B. The dotted red PF has the

new slope but the same position as the solid red PF.

Therefore it shows the effect of the change in slope (MPL) only.

The income effect is shown as the movement from B to C. The movement from

dashed red to solid red is a parallel shift in the PF.

Therefore it shows only the wealth effect.

A Proportionate Shift Production Function Is leisure normal or inferior

for the person depicted in the graph?

Explain. Leisure is normal because

when you look at the pure wealth effect (B to C), leisure increases and work effort decreases as wealth increases.

Can you depict a person for whom leisure is inferior?

Is it possible for a proportionate shift in the PF causes a decrease in work effort (employment)?

A Proportionate Shift Production Function In the graph at the left,

the total change from the wealth and substitution effect (A to C) is a reduction in work effort.

The person is being paid a higher hourly rate but chooses to work fewer hours.

This is the result of the substitution effect, which increases work effort, and the wealth effect, which reduces work effort.

The total effect is a reduction in work effort because the wealth effect overwhelms the substitution effect.

Changes in Preferences.

The slope of the indifference curve is the MRS between leisure and consumption.

When the slope of an indifference curve increases, is leisure becoming more or less valuable?

The steeper the IC, the greater the slope, the more valuable leisure is to the individual.

If a person IC shifted from green to orange what would happen to the value of leisure? Explain.

Leisure has become less valuable because the amount of consumption needed to get the person to voluntarily give up an hour of leisure has decreased.

How to use the production function and indifference curves to engage in economic analysis.

Identify change in the world. Proposed change in government policy

Taxes and regulation. Natural events.

Weather, war, etc. Does the change in the world affect the production function or

indifference curves? Production Function.

Wealth effect? Substitution Effect? Both? Net effect?

Indifference curve Leisure more or less valuable? IC steeper or shallower?

How does the shift in the PF or IC effect the equilibrium choice of labor/leisure and consumption? Does the tangency of the IC and PF occur at a higher or lower level

of labor/leisure? Is the amount of goods produced at the new equilibrium higher or

lower than before?

Example 2

Consider a worker in the a coal mine. OSHA promulgates a new worker safety rule that

regulation that requires him to wear protective clothing.

It takes an hour at the beginning and the end of his shift to don the protective clothing.

What effect will this have on work effort? Assume that leisure is a normal good.

Example 2-Answer The protective clothing doesn’t effect the amount of output he produces in an hour, but for any work shift, because he has to put the protective suit on and off, he produces less total output.

Therefore, the OSHA regulation causes parallel shift in the PF (red to blue).

If leisure is a normal good, the OSHA regulation causes a negative wealth effect and a reduction in the amount of leisure.

Example (3)

Consider a single mother who has a child.

What effect will this have on GDP and unemployment?

Example (3)-Answer The birth of her child

does not effect the PF. If she goes to work, she will get paid the same.

The birth of her child effects the value of leisure (or non-work). Leisure is now

more valuable. Slope of the IC

(green) is steeper. Because leisure has

become more valuable, the single mother consumes more leisure (A to B).

Because she is working fewer hours, GDP has decreased and the unemployment rate will rise.

Example (1) Consider a person who makes $24,000 a year before

taxes, works 2000 hours a year and pays a 10% income tax.

Two tax cut proposals are proposed. A cut in his income tax rate to 5%. A lump sum tax rebate of $1200.

Draw the PF for both plans. Will the effect of these two tax cuts on GDP be the

same? Explain and show graphically. Which plan is more likely to increase employment and

reduce the unemployment rate? Turn in Tuesday. Will count as a homework.

Example 1-Answer

The red PF shows the reward to work before taxes.

The blue PF shows the proportionate shift caused by the 10% income tax rate.

Example 1-Answer

The proportionate shift to the green PF shows the effect of the decrease in the income tax rate to 5%.

The parallel shift to the purple PF shows the effect of the $1200 lump sum tax rebate.

Under either tax plan, if the person continues to work the same hours (L) they will get the same output (B to C).

Example 1-Answer

The proportionate shift in the PF causes a change in the slope of the PF.

The change in the slope or MPL will cause an increase in work effort, an increase in output and a reduction in unemployment.