Excercise 1 （2excercise are related）

Each individual consumer takes the prices as given and chooses her consumption bundle,(x1,x2)ER^2, by maximizing the utility function: U(x1,x2) = ln(x1^3,x2^3), subject to the budget constraint p1*x1+p2*x2 = 1000

a) write out the Lagrangian function for the consumer's problem

b) write out the system of first-order conditions for the consumer's problem

c) solve the system of first-order conditions to find the optimal values of x1, x2. your answer might depend on p1 and p2.

d) check if the critical point satisfies the second-order condition

Exercise 2

a) suppose price of good 1 is 2, p1 = 2, and p2 = 1, use the results from exercise 1, part (c) to answer: How many units of good 1 and good 2 does an individual consumer demand?

b)still assume p1 = 2 and p2 = 1. what is the aggregate demand of good 1? what is the aggregate demand of good 2? how many units of good 1 (good 2, respectively) do all 1000 consumers demand together? (sum up all the individual demands from previous part (a))

c) the aggregate demand function of a good takes the market prices as an argument and maps them into the total units that are demanded. For given prices that the aggregate demand function of a good tell us how many units of that good are demanded by all 1000 consumers together. Use your results from Excercise 1, part (c) to derive that aggregate demand function for each good.

In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class.  Admission standards at the university were tightened in 2000.  In 2001, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class.  Let p1 and p2 be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.

Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999?  To determine this, you test the hypotheses

H0: p1 = p2, Ha: p1 > p2.

The z-test statistic is approximately 1.98, find the P-value, using a Standard Normal Table or your calculator.

Does Attractiveness Lead to Higher Marginal Revenue Product?

Economist David Hamermesh of the University of Texas, Austin, and Jeff Biddle of Michigan State University discovered that “plain-looking” people earn 5 to 10 percent less than people of “average” looks, who in turn earn 5 percent less than those who are considered “good looking.” Surprisingly, their research showed that the “looks effect” on wages was greater for men than for women. This wage differential related to appearance is not, contrary to popular belief, evident only in modeling, acting, or working directly with the public. Looks seem to account for higher earnings in jobs such as bricklaying, factory work, and telemarketing.

According to Hamermesh and Biddle, part of the wage differential may be created by the fact that attractiveness leads to higher marginal revenue product. More attractive persons may have higher

self-esteem, which in turn causes them to be more productive.

QUESTION: What are some other possible reasons that more attractive people tend to earn more?

Q2: You have just graduated from MBA program with finance major. Immediately after graduation you have been hired as a financial analyst in a highly prestigious listed company name Cornejo. Your first assignment is to estimate the cost of equity capital and stock price of the company. Your assistant gathered the following information for you:

• The dividend per share (DPS) record of the company over the last 5 years is as follows:

• Risk free rate is 3.5 percent
• Market risk premium is 5 percent
• Cornejo Co has an estimated beta of 1.10
• The company’s dividend growth rate is expected to remain constant for the foreseeable future.

Required:

1. Estimate the company’s cost of equity capital using CAPM.  
2. Draw and briefly define the security market line (SML).
3. Extrapolate a past growth rate. (
4. Estimate the current price of the company’s shares.
5. State clearly any limitations and assumptions that you made in your calculations.

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. a. What are the expected value and the standard error for the proportion of students that receive an A? b. Use an appropriate normal transformation to calculate the probability that the percentage of students that receive an A is 20% or less. c. Use an appropriate normal transformation to calculate the probability that the proportion of students who receive an A is between 0.20 and 0.35. d. Use an appropriate normal transformation to calculate the probability that the proportion of students who receive an A is not between 0.20 and 0.30

Q1.

A) List and differentiate the roles between the key players on a construction project.

B) In civil engineering, contractors may be broadly classified as either general or specialists, distinguish the two classes of contractors.

C) In a scenario of a project for construction of high rise lecture rooms building at Mulungushi University, a client, a Consultant and a Contractor are all Civil Engineers. Who is responsible for issuing instructions to the Contractor and explain why? (assignment question)

D) Who is responsible for paying temporal works on a construction site? Give a reason why?

Suppose that Musashi, an economist from an AM talk radio program, and Rina, an economist from a university in Massachusetts, are arguing over health insurance. The following dialogue shows an excerpt from their debate:

Rina: A popular topic for debate among politicians as well as economists is the idea of providing government assistance for health benefits.

Musashi: I think it is oppressive for the government to tax people who take care of themselves in order to pay for health insurance for those who are obese.

Rina: I disagree. I think government funding of health insurance is useful to ensure basic fairness.

The disagreement between these economists is most likely due to:

A: Differences in scientific judgments

B: Differences in Values

C: Differences between perception VS. reality

Despite their differences, with which proposition are two economists chosen at random most likely to agree?

A.Lawyers make up an excessive percentage of elected officials.

B. Minimum wage laws do more to harm low-skilled workers than help them.

C. Tariffs and import quotas generally reduce economic welfare.

New Macomb Wholesale Distributor made the following transactions in year 7.
Record all the transactions in general journal form.

feb 8th Bought inventory on account from Fountain Mfg. company for $18,600.00. terms 3/15, net 60.

feb 10th Paid $375 to Hare transport for shipping charges for inventory we are acquiring

feb 13th Sold merchandise on acct. to Alixx Co. for $92,500. All on acct. sales are with terms 1/10, net 30.
This merchandise cost us $55,500.

feb 16th Fountain Mfg. company issued us a 350.00 credit memo related to our purchase made on feb. 8th.

feb 17th Sold merchandise on acct. to Tyrone Sports Co. for $10,300. This merchandise cost us 9,455.

feb 19th Fully paid what is owed to Fountain Mfg.

feb 20th Alixx Co. returned 1/4 of what they purchased on the 13th.

feb 21st Alixx Co. fully paid what they owe us.

Mar 1st Tyrone Sports fully paid what they owe us.

Please add explanations to journal entires.

Show totals for debits and credits at the end.

Show All work please

Do you have food cravings? According to the New York Times, one of the largest studies of food cravings involved a survey of 1000 McMaster University students. The survey revealed that 97 % of the women in the study acknowledged specific food cravings while only 67 % of the men did. Assume that 600 of the respondents were women and 400 were men.

(a) Is there sufficient evidence to claim that the true proportion of women who acknowledge having food cravings exceeds the corresponding proportion of men? Test using α = .01.

(b) Why is it dangerous to conclude from the study that women have a higher incidence of food cravings than men?