More from Chapters 1-3 Marginal analysis Today: Government size; Marginal analysis; Empirical tools; Edgeworth boxes.

More from Chapters 1-3Marginal analysis

Today: Government size; Marginal analysis; Empirical tools; Edgeworth boxes

Today: Four “mini-lectures”

Finish Chapter 1 Introduction to government size

Marginal analysis A review of what marginal means

Chapter 2 Causation versus correlation Statistical tools and studies

Begin Chapter 3 Edgeworth boxes

Size of government

The constitution gives the federal government the right to collect taxes, in order to fund projects

State and local governments can do a broad range of activities, subject to provisions in the Constitution 10th Amendment: Limited power in the federal

government Local governments derive power to tax and spend

from the states

Size of government

How to measure the size of government Number of workers Annual expenditures

Types of government expenditure Purchases of goods and services Transfers of income Interest payments (on national debt)

Budget documents Unified budget (itemizes government’s expenditures and

revenues) Regulatory budget (includes costs due to regulations)

(Table and figures)

Table 1.1, p. 9 Figure 1.1, p. 10 Figures 1.2 and 1.3, p. 11 Figures 1.4 and 1.5, p. 13

Summary: Size of government Government spending in the US, as a

percentage of GDP, has increased in the last 50 years

Other industrialized countries spend more than the US (as a percentage of GDP)

Composition of taxing and spending has changed in the last 50 years

Marginal analysis

Quick look at marginal analysis Important in many tools we will use this quarter We look at “typical” cases

Marginal means “for one more unit” or “for a small change”

Mathematically, marginal analysis uses derivatives

Marginal analysis

We will look at four topics related to marginal analysis Marginal utility and diminishing marginal utility The rational spending rule Marginal rate of substitution and utility

maximization Marginal cost, using calculus

Example: Marginal utility

Marginal utility (MU) tells us how much additional utility gained when we consume one more unit of the good For this class, typically assume that marginal

benefit of a good is always positive

Example: Diminishing marginal utilityBanana quantity

(bananas)Total utility (utils) Marginal utility

(utils/banana)

0 0

70

1 70

50

2 120

30

3 150

10

4 160

5

5 165

Diminishing marginal utility

Notice that marginal utility is decreasing as the number of bananas increases

Economists typically assume diminishing marginal utility, since this is consistent with actual behavior

The rational spending rule

If diminishing marginal utility is true, we can derive a rational spending rule

The rational spending rule: The marginal utility of the last dollar spent for each good is equal Goods A and B: MUA / pA = MUB / pB Exceptions exist when goods are indivisible or

when no money is spent on some goods (we will usually ignore this)

The rational spending rule

Why is the rational spending rule true with diminishing marginal utility?

Suppose that the rational spending rule is not true

We will show that utility can be increased when the rational spending rule does not hold true

The rational spending rule

Suppose the MU per dollar spent was higher for good A than for good B

I can spend one more dollar on good A and one less dollar on good B

Since MU per dollar spent is higher for good A than for good B, total utility must increase

Thus, with diminishing MU, any total purchases that are not consistent with the rational spending rule cannot maximize utility

The rational spending rule

The rational spending rule helps us derive an individual’s demand for a good

Example: Apples Suppose the price of apples goes up Without changing spending, this person’s MU per dollar

spent for apples goes down To re-optimize, the number of apples purchased must go

down Thus, as price goes up, quantity demanded decreases

MRS and utility maximization

Utility maximization Necessary condition is

that marginal rate of substitution of two goods is equal to the slope of the indifference curve (at the same point)

At point E1, the necessary condition holds Utility is maximized here

Marginal cost, using calculus

Suppose that a firm has a cost function denoted by TC = x2 + 3x + 500, with x denoting quantity produced Note fixed costs are 500

Marginal cost is the derivative of TC with respect to quantity MC = dTC / dx = 2x + 3 Notice MC is increasing in x in this example

Summary: Marginal analysis

Marginal means “for one more unit” or “for a small change” We can use derivatives for smooth functions

Marginal analysis is important in many economic tools Utility Rational spending rule MRS Cost functions

Empirical tools

Economic models are as good as their assumptions

Empirical tests are needed to show consistency with good theories

Empirical tests can also show that real life is unlike the theory

Causation

Economists use mathematical and statistical tools to try to find the effect of causation between two events For example, eating unsafe food leads you to get

sick How many days of work are lost by sickness due to

unsafe food? The causation is not the other direction

Causation

Sometimes, causation is unclear Stock prices in the United States and temperature

in Antarctica No clear causation

Number of police officers in a city and number of crimes Do more police officers lead to less crime? Does more crime lead to more police officers? Probably some of both

Empirical tools

There are many types of empirical tools Randomized study

Not easy for economists to do Observational study

Relies on econometric tools Important that bias is removed

Quasi-experimental study Mimics random assignment of randomized study

Simulations Often done when the above tools cannot be used

Randomized study

Subjects are randomly assigned to one of two groups Control group

Item or action in question not done to this group Treatment group

Item or action in question done to this group

Randomization usually eliminates bias

Some pitfalls of randomized studies Ethical issues

Is it ethical to run experiments when only some people are eligible to receive the treatment? Example: New treatment for AIDS

Technical problems Will people do as told?

Some pitfalls of randomized studies Impact of limited duration of experiment

Often difficult to determine long-run effect from short experiments

Generalization of results to other populations, settings, and related treatments Example: Effects of giving surfboards to students

UCSB students UC Merced students

Observational study

Observational studies rely on data that is not part of a randomized study Surveys Administrative records Governmental data

Regression analysis is the main tool to analyze observational data Controls are included to try to reduce bias

Conducting an observational study L = α0 + α1wn + α2X1 + … + αnXn + ε

Dependent variable Independent variables Parameters Stochastic error term

Regression analysis Here, we assume

changes in wn leadto changes in L

Regression line Standard error

wn

L

α0

Interceptis α0

Slopeis α1

Regression analysis

More confidence in the data points in diagram B than in diagram C Less dispersion in diagram B

Interpreting the parameters

L = α0 + α1wn + α2X1 + … + αn+1Xn + ε ∂L / ∂wn = α1

∂L / ∂X1 = α2

Etc.

Types of data

Cross-sectional data “Data that contain information on individual entities at a

given point in time” (R/G p. 25) Time-series data

“Data that contain information on an individual entity at different points in time” (R/G p. 25)

Panel data Combines features of cross-sectional and time-series data “Data that contain information on individual entities at

different points of time” (R/G p. 25)

Note: Emphasis is mine in these definitions

Pitfalls of observational studies Data collected in non-experimental setting Specification issues

Data collected in non-experimental setting Could lead to bias if not careful

Example: Education People with higher education levels tend to have higher

levels of other kinds of human capital This can make returns to education look higher than

they really are

Additional controls may lower bias Education example: If we had human capital

characteristics, we could include them in our regression analysis

Specification issues

Does the equation have the correct form? Incorrect specification could lead to biased results

Example: The correct form is a quadratic equation, but you estimate a linear regression

Quasi-experimental studies

Quasi-experimental study Also known as a natural experiment Observational study relying on circumstances

outside researcher’s control to mimic random assignment

Example of quasi-experimental study A new college opens in a city

Will this lead to more people in this city to go to college? Probably

These additional people go to college by the opening of the new school

We can see the earnings differences of these people in this city against similar people in another city with no college

Conducting a quasi-experimental study Three methods

Difference-in-difference quasi-experiments Instrumental variables quasi-experiments Regression-discontinuity quasi-experiments

Difference-in-difference method Find two similar groups of people One group gets treatment; the other does not Compare the differences in the two groups

Instrumental variables (IV) method Assignment to treatment group is not always

random This can lead to bias

IV analysis finds a third variable that has two characteristics Directly affects entry into the treatment group Is not directly correlated with the outcome variable

Regression-discontinuity method Have a strict cut-off point to get into treatment

group Examples: Income, test score

Compare those that are very close to the cut-off point

Pitfalls of quasi-experimental studies Assignment to control and treatment groups

may not be random Researcher needs to justify why the quasi-

experiment avoids bias Not applicable to all research questions

Data not always available for a research question Generalization of results to other settings and

treatments As before: Surfboards to UCSB students and UC

Merced students

Summary: Empirical tools

Empirical tools can be useful to test economic theory

Bias can be problematic in studies that are not randomized

Controls in observational studies may lower bias

Quasi-experimental studies can act like randomized experiments

Edgeworth boxes

Begin study of welfare economics Pure exchange economy

R/G chapter 3 For an in-depth look, see also Varian’s Intermediate

Micro book, chapters 30-33 We begin today with Edgeworth boxes

Edgeworth boxes

Simple study of distribution We will make extensive use of Edgeworth boxes,

Pareto efficiency, and Pareto improvements Edgeworth boxes are used for a two-person

economy Bottom left of Edgeworth box is origin for one person Top right of Edgeworth box is origin for other person See Figure 3.1, p. 34

Indifference curves See Figure 3.2, p. 35

Pareto efficiency

Nobody can be made better off without making another person worse off

In cases with “standard” indifference curves (ICs), the two ICs will be tangent to each other when Pareto efficiency is achieved

Pareto improvement

Reallocation of goods or resources that meets the following requirement At least one person is made better off without

anybody else being made worse off See Figures 3.3-3.6 (p. 35-37)

Contract curve

The set of all Pareto efficient points See Figure 3.7, p. 38

Usually goes from one person’s origin to the other person’s origin Origin of each person is Pareto efficient

Note that efficient points may or may not be “fair” in your mind Fairness is often not a topic brought up by

economists More on “fairness” later

Pareto Efficiency in Consumption

MRSaf = MRSaf

Adam Eve

At each point on the contract curve, the marginal rates of substitution for both Adam and Eve are equal

Summary: Edgeworth boxes

Two-person exchange economy Edgeworth box is the main tool used Pareto efficiency and Pareto improvements Contract curve

What have we learned today?

Size of government Some tools that are useful

Marginal analysis Empirical tools to test theory

Edgeworth boxes