1. Suppose in a survey of n = 2000 students, 1200 responded that they prefer small classes and 800 responded that they prefer large classes. Let p denote the fraction of all students who preferred small classes at the time of the survey, and X ̄ be the fraction of survey respondents who preferred small classes. (Hint: X is distributed as a Bernoulli random variable) (a) Show that E(X ̄) = p and Var(X ̄) = p(1 − p)/n. (b) Use the survey result to estimate p, and calculate the standard error of your estimator. (Hint: Notice that this is the same as estimating the sample mean)

Question 3: Suppose buyers will pay $2000 for a good car (a 'plum') and $1000 for a bad car (a 'lemon'). All cars acquired by the sellers are lemons which they acquire for $1200 each. They can then choose to have mechanics fix the cars up – turning them from lemons to plums - for $300 each. Buyers cannot tell the difference between lemons and plums until after the purchase, and are riskneutral (i.e., will pay their expected valuation).

1. Explain why in equilibrium, no transactions are made.

2. Suppose the used car salesmen can commit to having the mechanics repair a q-fraction of the cars. (Once such an arrangement is made, they are committed to it.) For what values of q will the equilibrium still lead to no transactions, and for which values of q will transactions take place?

1. A 45 MPH design speed roadway with a 2000 ADT has a 6’ shoulder with a 12:1 slope. The shoulder immediately drains into a roadside ditch with 4:1 sideslopes, a bottom width of 4’. The bottom of the ditch is 1.75 feet deeper than the edge of the shoulder. The face of a rock cut is located 7’ from the center line of the ditch, away from the roadway. Is the rock cut located within the clear zone?  

Consider an economy that initially has a labor force of 2000 workers. Of these workers, 1900 are employed and each works 40 hours per week. 10 units of output are produced by each hour of labor. There are another 1500 adults in the economy who are not in the labor force.

A) What is the labor force participation rate?

The economy then enters a recession. Employment falls by 4%, and the number of hours per week worked by each employed worker falls by 2.5%. In addition, 0.2% of the labor force becomes discouraged at the prospect of finding a job and leaves the labor force.

B) After all of these changes, what is the new size of the labor force?

C) How many workers are unemployed now?

D) What is the new unemployment rate?

Research and develop a MS Word document of at least 2000 words that:

1) Discusses a renewable/sustainable energy project in the U.S.

2) The paper must include the background/history of the project. Who are the champions of the project? Who are the beneficiaries of the project? Is there an economical impact? Your opinion of the sustainability of the project.

3) State whether you are for or against the the effort and why.

4) Write a one or two paragraph conclusion stating what would you say to a decision maker to persuade them.

A. The expected demand for a regular component is 2000 units per year. The item can be purchased from Bonjo Limited. Their lists are shown in the table below. The ordering cost is $200 and the carrying cost per unit is 75%. The cost is $20.

You have just been promoted as the operations manager for this firm. Advise the purchasing manager in making the following decisions.

i. What is the economic order quantity?      

ii. If BONJO wants to consider quantity discount, what quantity should he order and why?  

B. Over the past year Jojo Ltd had annual sales of 10, 000 detergent paste ‘KEY’. The average quarterly sales for past 5 years have averaged; ?1 = 4000, ?2 = 3000, ?3 = 2000, and ?4 = 1000. Find the seasonal index.