MidtermI Review Slides

8/12/2019 MidtermI Review Slides

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Econ 100A

Microeconomic Analysis

Midterm I Review

1



Announcement

PS 2 is due now

Exam policies:

No outside material and no calculators

No powdering your nose

No hoodies or hats while taking the exam

No grade if you keep working past allocated time No make-up exams



Announcements

You can go to any GSI office hours

No sections on Tuesday or Wednesday

Office hours:

Study session:

597 Evans, Friday 2/21, 10-12

639 Evans, Monday 2/24, 8-10



Reading for exam

Chapter 1

Chapter 3.1-3.4

Chapter 4.1 – 4.4 (excluding Slutsky equation)

Chapter 5.5 – up to shape of labor supply curve



What have we done so far?

We made assumptions on behavior in order to

allow ourselves to use math and graphs to solve

for optimal consumption

We can represent preferences with a utility

function if the consumer is rational

We can use nice graphs that allow for quickanalysis if more is better



Assumptions

Rationality:1. Completeness

2. Transitivity

3. More is better

Budget constraint:

1. We spend all of our income



Constrained Maximization

Given these assumptions we can use

constrained maximization tools to find what

would be the optimal consumption bundle,

given income and prices



How to…

Find uncompensated (Marshalian) demand for agood by solving the utility maximization or

expenditure minimization problem

Find compensated (Hicksian) demand by deriving

the expenditure function

Find whether the good is normal or inferior

Find the share of consumption for a specific good

Find whether there are corner solutions

(i.e. when the demand for one good is 0) Find whether goods are substitutes or complements

Find income and substitution effect



Question #14

For a given increase in INCOME, only one good

can be inferior.

A. True

B. False



Question #15

Let the price of good X decrease. If the

consumption of good X increases, it must be a

normal good.

A. True

B. False



Example

James consumes pizza and sushi, which he

regards as imperfect substitutes. One day he

wakes up to the terrible news that the price of

pizza doubled and that the price of sushi

tripled.

Draw an initial consumption bundle for James,

and a budget constraint after the price

changes. You may choose the axis.



Example continued

James parents hear about his hardships and

decide to increase his stipend so he can

purchase the same bundle he purchased

before. Add this budget constraint to your

graph.

Given the new prices and his additional

stipend, will James consume more or less

pizza/sushi than his initial bundle?



Utility Maximization

Consider preferences over good X and good Y

represented by the utility function,

U = X(Y-k)(1-)

Where 0 < < 1 & k > 0

Use Lagrangian method to find the demand for

X & Y



FOCS



Solution



Example continued

Let I = 1000, k = 100, = 0.5 and Py = 2

Find the demand for good X



Example

Is good X normal or inferior?

Is good X a substitute or complement for good

Y?



Example

Now let I = 100 and the rest of theparameters are the same.

What is the demand for good X?

What is the demand for good Y?



Example

What is the economic interpretation of k?



What is the economic interpretation of

k?

When income is lower than a certain threshold(Py·k), the consumer buys only good Y.

But when income is high enough to afford k

units of good Y (that is, when I PY· k) both

good X and good Y are purchased. k represents the baseline level of good k that is

required before consuming anything else.

If good Y was food, and good X was

entertainment, then k would be the survivallevel of food that a consumer requires before

being willing to spend any money on

entertainment.



Quasi-linear preferences

Quasi-linear preferences have 2 interesting

properties:

You can have a corner solution, where only one

good is being consumed

The level of consumption of one good is

independent of income



Example

Let U = X

0.5

+ Y



Question #16

An increase in income will shift the Engel curve

to the right.

A. True

B. False

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