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