Essay Writer » Essay Blog » Intermediate Microeconomics

# Intermediate Microeconomics

Intermediate Microeconomics

# Examination Rules:

This is a take-home exam. You may not discuss the exam with anyone
except the instructors of the class. You are allowed to consult your
notes, the textbook and other sources, except other people. If anything
is unclear, please email the instructor. The instructor will remove your
name from the email, and then your questions along with the response
will be sent to all students in the class. The instructor will not discuss
the exam in person with any student.

Your solutions to the exam must be written-up clearly. All solutions, including workings, arguments, diagrams, and reasoning, must
be clearly written-up in black ink. Everything must be legible, graphs
should be labeled clearly, your arguments should be easy to follow, and
your final solutions should be easy to identify.
The clarity of solutions
will be a factor in the grading of the exam.
Please make sure that your
name and a page number is on every page of your solutions before you
hand them in.

There are two problems on the exam. All problems will be graded, and
each will be worth one half of the grade for this exam. The grading
on the exam will be
stricter than on problem sets, so please make sure
that you answer the questions carefully.

Intermediate Microeconomics

Late submission will not be accepted. If you submit the exam after
the deadline, you will receive a grade of 0.
By signing the declaration below, you affirm that you have understood
the rules of the exam and that the solutions you have submitted are
your own work (without any outside assistance). You should submit
the signed declaration along with your solutions.

## Academic Integrity Declaration:

I, , hereby declare that
I have understood and followed all rules of the exam, and that any
solutions submitted by me represent my own work.
Signature: Date:
2
Intermediate Microeconomics NYUAD, Spring 2018
Problem 1: Non-linear pricing
Suppose that there two goods X and Y , available in arbitrary nonnegative quantities (so the the consumption set is R2 +). The consumer
has preferences over consumption bundles that are strongly monotone,
strictly convex, and represented by the following (differentiable) utility
function:
u(x, y) = y + 2αx,
where x is the quantity of good X, and y is the quantity of good Y ,
and
α 0 is a utility parameter.
The consumer has strictly positive wealth
w > 0. The price of good
Y is pY = 1. However, the price of good X depends on the quantity
of good
X that the consumer purchases. In particular, pX(x) = 1x,
where
x is the quantity of good X the consumer purchases. (Note that
pX(x) is the price per unit when the consumer purchases x units).
(1) In an appropriate diagram, illustrate (i) the indifference map for
the consumer, and (ii) the consumer’s budget set. Make sure you
label diagrams clearly, and include as part of your answer any calculations about the slopes and intercepts of the indifference curves
and the budget line.
(2) Formulate and solve the consumer’s utility maximization problem,
and find the demand and value functions. Your demand and value
functions should be functions of the parameters
w and α.

Intermediate Microeconomics

(3)
Suppose w = 10. In an appropriate diagram, illustrate the demand
function for good
X, x(α|w = 10), and for good Y , y(α|w = 10).

### Intermediate Microeconomics

Problem 2: Endowment effect
Suppose that there two goods X and Y , available in arbitrary nonnegative quantities (so the the consumption set is R2 +).
Instead of being endowed with a fixed amount of wealth
w, the consumer has an initial endowment of the two goods, ¯ x > 0 and ¯ y > 0,
where ¯
x is the quantity of good X the consumer owns and ¯ y is the
quantity of good
Y the consumer owns. The consumer has no additional wealth, but the consumer can buy and sell goods X and Y at
the fixed prices
pX > 0 (for good X) and pY > 0 (for good Y ).
(1) In an appropriate diagram, illustrate the consumer’s budget set.
Make sure you label the diagrams clearly, and include as part of
your answer, the slope and intercepts of the budget line.
The consumer has preferences over consumption bundles that are strongly
monotone and strictly convex. However, the consumer’s preferences
depend on their initial endowment of the good. (Preferences with this
property are called endowment-dependent preferences and have been
studied widely by economists in recent years). In particular, the consumer’s preferences can be represented by the following “endowmentdependent” utility function:
u(x, y) = min 1 3 log x x¯ + 23 log y y¯ , 23 log x x¯ + 1 3 log yy¯ ,
where x is the quantity of good X, y is the quantity of good Y , and
x, y¯) >> 0 is the consumer’s initial endowment of the two goods.

Intermediate Microeconomics

(Note that the utility function u : R2 + R is not differentiable, but
the function
f(x, y|p, x, ¯ y¯) = p log x x¯ + (1p) log yy¯ is differentiable
for any parameters (
p, x, ¯ y¯) >> 0).
(2) In an appropriate diagram, illustrate the indifference map for the
consumer. Make sure you label the diagram clearly.
(3) Formulate and solve the consumer’s utility maximization problem,
and find the demand functions. Note that the demand functions
will depend on the parameters (
pX, pY , x, ¯ y¯) >> 0.
(4) For what prices (pX, pY ) does the consumer optimally decide to (i)
consume their initial endowment of the goods, (ii) sell some units
of good
Y to buy more units of good X, or (iii) sell some units of
good
X to buy more units of good Y ?

Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org)

Intermediate Microeconomics

Essay Help

Thesis Statement

Last Updated on September 14, 2019

Don`t copy text!
Scroll to Top