ECO 3031 of 3Stony Brook UniversityFall 2016ASSIGNMENT: MIDTERM I PREPARATIONDue: Optional, but you should use it to pre...

Get help with any kind of assignment - from a high school essay to a PhD dissertation

  1. Order Custom Essay, Course Work, Research and Term Papers

Stony ECO 303 - ASSIGNMENT MIDTERM I

April 14, 2018

ECO 303

1 of 3

Stony Brook University


Fall 2016

ASSIGNMENT: MIDTERM I PREPARATION
Due: Optional, but you should use it to prepare for the midterm.
Instructions: This is an optional assignment whose purpose is to prepare you for the midterm.
It consists of six problems. I strongly recommend that you attempt to prepare all questions. On
Tuesday’s Midterm I will pick four questions at random from this assignment which you will need to
answer.
1. Michele, who has a relatively high income I , has altruistic feelings toward Sofia, who lives in such
poverty that she essentially has no income. Suppose Michele’s preferences are represented by the
utility function
1 ? ?
UM .cM ; cS / D cM
cS ;

where cM and cS are Michele and Sofia’s consumption levels, appearing as goods in a standard
Cobb-Douglas utility function. Assume that Michele can spend her income either on her own
or Sofia’s consumption (though charitable donations) and that $1 buys a unit of consumption for
either (thus, the “prices” of consumption are pM D pS D 1).
(a) Argue that the exponent ? can be taken as a measure of the degree of Michele’s altruism by
providing an interpretation of extreme values of ? D 0 and ? D 1. What value would make
her a perfect altruist (regarding others the same as oneself)?
(b) Solve for Michele’s optimal choices and demonstrate how they change with ? .
(c) Suppose that there is an income tax at rate , i.e. net income now is just .1
Michele’s optimal choices under the income tax rate.

/I: Solve for

(d) Now suppose that besides the income tax rate , there are charitable deductions, so that
income spent on charitable deductions is not taxed. Argue that this amounts to changing the
price pS from $1 to $.1 /. Solve for the optimal choices under both the income tax rate and
charitable deductions. Does the charitable deduction have a bigger incentive effect on more
or less altruistic people?
2. Suppose that a fast-food junkie derives utility from three goods—soft drinks .x/, hamburgers .y/,
and ice cream sundaes .z/—according to the utility function
U.x; y; z/ D x 0:5 y 0:5 .1 C z/0:5 :

Suppose also that the prices for these goods are given by px D 1; py D 4; and pz D 8 and that this
consumer’s income is given by I D 8:
(a) Show that, for z D 0, maximization of utility results in the same optimal choices as in the
case of a Cobb-Douglas utility function U.x; y/ D x 0:5 y 0:5 . Show also that any choice that
results in z > 0 (even for a fractional z ) reduces utility from this optimum.
(b) How do you explain the fact that z D 0 is optimal here?

(c) How high would this individual’s income have to be for any z to be purchased?
1

ECO 303

2 of 3

3. Consider the utility function
u.x; y/ D .x C 2/.y C 3/;

x 0; y 0

with the accompanying budget constraint:
px x C py y I;

px ; py ; I > 0:

(a) Fix a given utility level U > 0 and find an explicit expression for the indifference curve
defined by the utility level U > 0. Then, derive an explicit expression for the marginal rate
of substitution between good x and good y .
(b) Draw the indifference curve (for this associated level of utility U ) and carefully label the graph
and its elements.
(c) Show that the utility function is strictly increasing (and hence monotone) in x and y .
(d) Now formally state the utility maximization problem and briefly describe its content, in particular what constitutes the choice variables, and what constitutes parameters.
(e) Provide an argument why in the present utility maximization problem, we can restrict attention to the case where the budget constraint holds as an equality. (The argument should not
involve the explicit computation of the optimal choices.)
4. Consider the utility function
U.x; y/ D min.2x C y; x C 2y/

(a) Draw the indifference curve for U.x; y/ D 20. Shade the area where U.x; y/ 20.
(b) For what values of ppyx will the unique optimum be x D 0?
(c) For what values of

px
py

will the unique optimum be y D 0?

(d) If neither x and y is equal to zero, and the optimum is unique, what must be the value of yx ?
5. Consider a consumer with a utility function U.x; y/ D e .ln.x/Cy/

1=3

.

(a) What properties about utility functions will make th is problem easier to solve?
(b) Which of the non-negativity constraints will bind for small I ?
(c) Derive the Marshallian demand functions and the indirect utility function (using the original
utility function).
(d) Derive the expenditure function in terms of the original utils u.
6. There are two goods, food and clothing, whose quantities are denoted by x and y and prices px
and py respectively. There is a consumer whose income is denoted by I and utility by U: His utility
function is
p
U.x; y/ D xy:
(a) Find this consumer Marshallian demand functions. Find the indirect utility function and the
expenditure function.
(b) Initially I D 100; px D 1 and py D 1. What quantities does the consumer buy, and what is
his resulting utility?
(c) Now the price of food rises to px D 1:21, while income and the price of clothing are as before.
What quantities does the consumer buy and what is his resulting utility?
2

ECO 303

3 of 3

(d) Suppose the increase in the price of food was caused by the government levying a tax of 21%
on food. What is the government revenue from this tax? Hint: At the new prices, calculate the
optimal consumption bundles .x ; y /. Then calculate .1:21 1/x .
(e) If the government wants to compensate the consumer by giving him some extra income, how
much extra income would be needed to restore him to the old utility level. (Hint: Use the
expenditure function.) Is the government’s revenue from the tax on the good itself sufficient
to provide this compensation? What is the economic intuition of your answer?
(f) If the government tries to compensate the consumer by giving him enough extra income to
enable him to purchase the same quantities as he did at the original income and prices of part
(b), how much extra income would the government have to give him ? With this income and
the new prices, what quantities will the consumer actually buy? What will be his resulting
utility?










OUR SERVICE CHARTER






  • 100% Confidentiality

    We mind about the interests of our clients holistically. It is for this reason that we maintain high-level confidentiality in regard to our clients’ personal information. Importantly, we use the information for purposes that relate with our services only. The only information that we require relates to our clients’ writing needs. It is also important to note that our clients’ payment information is secure with us. If there is any query in regard to the payment information, then our support team is always willing to provide any clarifications in a prompt manner. Confidentiality extends to the fact that a client made use of our services. It means that we hold our relationship with our clients in secrecy. Importantly, our confidentiality measures beat any advanced security measure that can identify any information regarding our relationship with our clients. It means that our clients transact with us freely without any fear of information leakage.

  • Free Revisions

    The papers that we deliver usually reflect a high quality level. However, there is always a room for any additional fine-tuning touch in line with a client’s preference without any additional charges. To begin with, a client has discretion to make a choice on their preferred top writer from our team. Such a writer could have handled past work for the client and received a positive review from the same. It means that the client has confidence of the quality of service that the writer delivers. Secondly, a client has an option of making use of our editing services. Our editors are always on standby to revise the paper and ensure that it matches with the expectations of a client that the instruction brief had detailed. The revision covers content adjustment that removes off-topic details, addition of sources, removal of language style errors, and assessment of the referencing style in order to enhance compliance.

  • Excellent Quality Work

    Grammar is one of the elements that we take seriously in our service delivery. Beside the use of spell checkers, we progressively take our writers through the essentials of a quality paper that features information clarity. Importantly, we encourage our writers to avoid coming up with a paper that deviates from the elements that appear on the client’s instruction brief. It means that the papers that we deliver denote well researched information that is rich in details. Additionally, the papers usually contain exhaustive details on any instruction that a client submitted. It is the tireless application of our writers’ efforts that makes us stand out when it comes to the delivery of excellent quality work. Notably, our writers use quality resources when digging up information that a paper requires. They are usually aware of the sources that contain rich information. Our past clients have proved that we give nothing short of quality work through giving us a positive feedback.

  • 24/7 Customer Support

    Our team of writers prides in high-level competence. The writers have the required expertise that enables them to deliver quality papers that match with the requirements of the grading rubric. In the absence of the rubric, we ensure that the writers follow the clients’ instruction brief to the letter. We can confidently assure our clients to expect nothing short of a pass from the papers that we deliver. Importantly, we have qualified writers who handle different areas of study. This diversification enables us to allot clients’ orders to the writer who is well seasoned in the subject area of study. It also enables the team to become more professional due to specialization. Our clients should put their trust in our service delivery and expect to successfully attain high grades at all times. The fact that we offer free revision reflects our dedication in delivering high quality papers that match with our clients’ expectations.




Related Questions