• Generate data of length n=100 from a Gaussian AR(2) model with phi1=0.5 and phi2=0.2 and input variance sigma^2=1. Afterwards, pretend the values of phi1, phi2 and sigma^2 are unknown.
  i. Use the R function ar() to fit an AR(p) model to your data. As options for the ar() function, first use aic = TRUE. What estimated order did aic minimization give for your data? Try three different fitting methods, method="yule-walker", method="ols"and also method="mle". Do you see significant differences between the methods?
  ii. Repeat the above by setting aic = FALSE and method="yule-walker". First select order p=1; what do you observe in your estimates? Now select order p=3 and then p=5; what do you observe?
  iii. Fit an ARMA(p,q) model to your data using the R function arima(). Specify the orders (p,q) to be fitted as either (2,0) or (1,1) or (2,1). Compare your results under these three specifications. [Note that ARMA(p,q) is the same as ARIMA(p,0,q) so in R function arima() you need to select the middle order to be 0.]

Consider an economy with identical individuals who live for two periods. Half of the workers are in the 1^st, the other half in the second period of life. Their utility function is ut= log(ct) in each period. They work in the first period and receive an income 100 and are retired in the second period and receive no income. They can save as much of their income as they like in bank accounts, earning an interest rate of r per period. They do not leave bequests.

Write down their lifetime budget constraint.

What is the individual's optimal consumption in each period? How much savings does he or she do in the first period?

_________________________

Now, the government sets up a social security system. Each worker has to pay 50 pounds as long as he is working. The money is put it in the bank and transferred back to them with interest when they are retired. What is the name for this type of social security system?

How does the system affect the amount of private savings? How does the system affect national savings (total savings in society)?

What is the effect on social welfare, if we assume that the government interest rate is the same as the private interest rate?

What is the effect on social welfare, if we assume that due to economies of scale the government interest rate is higher than the private interest rate?

Ten randomly selected people took an IQ test A. The next day they took a very similar IQ test B. Their scores are shown in the table below.

1. Use a 0.05 significance level to test the claim that, on average, people do better on the second test than they do on the first.

(a) State the null and alternative hypotheses. (Type muD for the mean of the differences in test A - test B.)
H0 :
H1 :

(b) Find the rejection region.
Reject H0 if t<

(c) Find the test statistic. (If necessary, round the sample mean and sample standard deviation to 2 decimal places. Also round your final answer to 2 decimal places.)
t =

(d) Do these samples provide significant evidence that, on average, people do better on the second test than they do on the first? (Type: Yes or No )



2. Construct a 95% confidence interval for the mean of the differences in test A - test B. (Round your final answer to 2 decimal places.)
(  ,  )

Sweet Company’s outstanding stock consists of 1,200 shares of noncumulative 4% preferred stock with a $100 par value and 10,200 shares of common stock with a $10 par value. During the first three years of operation, the corporation declared and paid the following total cash dividends.

The total amount of dividends paid to preferred and common shareholders over the three-year period is:

Multiple Choice

$14,400 preferred; $27,200 common.

$11,200 preferred; $30,400 common.

$9,600 preferred; $32,000 common.

$4,800 preferred; $36,800 common.

$11,800 preferred; $29,800 common.

Halverstein Company's outstanding stock consists of 11,900 shares of cumulative 5% preferred stock with a $10 par value and 5,100 shares of common stock with a $1 par value. During the first three years of operation, the corporation declared and paid the following total cash dividends.

The amount of dividends paid to preferred and common shareholders in Year 2 is:

Multiple Choice

$5,100 preferred; $5,100 common.

$0 preferred; $10,200common.

$5,950 preferred; $4,250 common.

$10,200 preferred; $0 common.

$7,140 preferred; $3,060 common.

After all of your glorious battles against the common enemy, you finally decide to retire from hack & slash and live peacefully for the rest of your life. You decide to deposit some (1000 gold) of your hard-earned gold to a bank that earns you the most interest for a 20-year period. You have three options to choose from: Bank of Orgrimmar, Bank of Stormwind and Bank of Ironforge. Each of the banks have different payment plans to choose from as given below: Bank of Orgrimmar: Deposit 50 gold at the end of each quarter for the first 5 years. Then, for the next 15 years, the bank suggests a rate of 5% compounded quarterly. Bank of Stormwind: Deposit 1000 gold now (year 0), then for the next 20 years the bank suggests a rate of 3% compounded annually. Bank of Ironforge: Deposit 100 gold at the end of each year for the first 10 years. Then for the next 10 years, the bank suggests a rate of 8% with a continuous compounding. Which bank should you deposit your gold? Propose your own counteroffer to any bank you favor the most (you may offer to change the interest periods, payment periods or interest rates. Be realistic in your counteroffers!)

Saxum Vineyard, in Paso Robles, CA, is one of the more than 8,000 wineries in the United States. While Saxum produces a number of different kinds of wine, they focus their production on Syrah (also known as Shiraz). Saxum sells their wines all over the United States. Suppose you manage a vineyard like Saxum and want to determine how much you should charge for your Syrah. Suppose the market demand function for Syrah is as follows.

QD = 200 - 38.18PO + 8.35PS - 2Pc + 10Inc + .8TS + .5M21

Where QD is monthly demand for bottle of Syrah (in millions), PO is the price of Syrah in the market, PS is the average price of substitute bottles of wine (other varieties), Pc is the average price of a pound of cheese and is used to gauge the price of complimentary goods, Inc is average US per capita income (in thousands), TS is the number of wine trade shows and competitions each year which firms can attend to market their wines, and M21 is the number (in millions) of millennials in the US over the age of 21. This last variable is included to capture a change in consumer preferences; millennials are drinking wine at a much higher rate than previous generations.

The market for Syrah also has supply, produced by wineries similar to Saxum Vineyard and your winery, which can be stated as follows.

QS = -100 + 22.93PO - 5PPI - 10PS + 8Temp + 1Sup

Where QS is monthly supply of bottles of Syrah (in millions), PO is the price of Syrah in the market, PPI is the Producer Price Index (an index used to gauge changes in the costs of production in the US), PS is the price of substitute wines which could easily be produced instead of Syrah, Temp is the expected temperature during the harvest season for grapes, and Sup is the number of wineries that supply Syrah in the market (in thousands).

Using the market supply and demand functions for Syrah given, fill in the template provided with the coefficients for each function.

Using the information below, fill in the values for each of the variables except Price of Syrah.

Demand:

-Price of Substitutes: $18

-Price of Cheese: $15

-Income: $53,000

-Trade Shows/Competitions: 3

-Millennials = 45 million

Supply

-PPI: 111

-Price of Substitutes: $18

-Temperature: 60

-Number of Suppliers: 8,000

a)   When the price of Syrah increases by $1, do supply and demand increase or decrease?                                  
b)   By how much? What is the effect on quantity demanded and quantity supplied?                                   
                       a)       b)      
                   Quantity demanded ____ by _______ million bottles.  
                   Quantity supplied ________ by _________ million bottles.  
c)   Does a $1 decrease in the price of substitute bottles of wine shift the demand and supply curves to the left or right?
                                  
d)   By how much?

                                  
                       c)       d)      
                   Demand curve is shifted to the _______ by ________ million bottles.  
                   Supply curve is shifted to the ________ by __________ million bottles.  
e)   Suppose the price of Syrah is currently $22 per bottle. How many bottles will be demanded and supplied monthly?

                                  
                   Price of Syrah =   $22.00              
                   Bottles demanded = _______ million          
                   Bottles supplied = _________ million          
f)   Is there a shortage or a surplus?

  
g)   How much is the shortage or surplus?

                                  
                       f)       g)      
                   There is a _______ equal to _______ million bottles.  
h)   If the market price of Syrah falls to $16 per bottle, how many bottles will be demanded and supplied monthly?

                                  
                   Price of Syrah =   $16.00              
                   Bottles demanded = __________ million          
                   Bottles supplied = ________ million          
i)   Is there a shortage or a surplus?

                                  
j)   How much is the shortage or surplus?                                  
                       i)       j)      
                   There is a ________ equal to _______ million bottles.  

                                  

Retail price                                                   : $449                                    

            Retail margin                                     : 42.5%

            Wholesale margin                                        : 27.5%

            R & D on hearing aid, FY’s 2019, 2020   : $119,000

            Introductory promotional outlays, FY2021: $159,000

            MBR’s fixed manufacturing costs             : $155,000 per year (FY 2021)

            Variable manufacturing costs/unit : $95

            Retailer’s salesperson’s commission      : 2% of retailer’s selling price

            MBR’s sales commission paid                   : 4% of manufacturer’s selling price

            Population of Big Smoke”                           : 2,975,000

            Proportion of population over 60 years    : 18%

1. What is MBR’s (show your logic)

1. unit contribution margin ($)?         

Contribution per unit = Unit selling price – unit variable cost

                                    = $449 - $95

                                    = $354

2. unit contribution margin ratio (%)? 

Contribution margin = unit selling price – unit variable cost

                                                           Unit selling price

                                    = $449 - $95

                                                            $449

                                                = $354

                                                               $449

                                                            =.789 = 78.9%

(b) How many units must MBR sell in the first year (2021) to break even? Carefully explain, including any assumptions that you make. 

Break-even= ____total dollars fixed costs_____   

                        Unit selling price – unit variable costs

                    =             $119,000

                                    $449-$95

                    =336.16 = 337 Units.

If using the outlay = 278,000

                                    354

                                =785.31= 785

I decided the MBR and promotional is a fixed cost because no matter how many units need to be sold. Didn’t consider the promotional outlay because it was for 2021.                  

3. If 15% of the “over 60” population is hearing impaired, what is MBR’s break-even market share in 2021? (Identify and explain any assumption(s) that are necessary).    

Break Even

     Population = 2,975.000

      Population over 60 = 2,975.000 X .15 = 446,250

      Breakeven = 337 units

                        = (337/446,250)

                        = .76%

      Breakeven = 792 units

                        = (785/446,250)

                        = .18%

d) Given MBR’s market share (see (c) above), assess MBR’s prospects of breaking even in 2012. 

Stocks and Their Valuation: Discounted Dividend Model

The value of a share of common stock depends on the cash flows it is expected to provide, and those flows consist of the dividends the investor receives each year while holding the stock and the price the investor receives when the stock is sold. The final price includes the original price paid plus an expected capital gain. The actions of the marginal investor determine the equilibrium stock price. Market equilibrium occurs when the stock's price is (PICK ONE: less than, equal to, greater than) its intrinsic value. If the stock market is reasonably efficient, differences between the stock price and intrinsic value should not be very large and they should not persist for very long. When investing in common stocks, an investor's goal is to purchase stocks that are undervalued (the price is (PICK ONE: above, below, equivalent to) the stock's intrinsic value) and avoid stocks that are overvalued.

The value of a stock today can be calculated as the present value of (PICK ONE: a finite, an infinite) stream of dividends:

This is known as the constant growth model or Gordon model, named after Myron J. Gordon who developed and popularized it. There are several conditions that must exist before this equation can be used. First, the required rate of return, r_s, must be greater than the long-run growth rate, g. Second, the constant growth model is not appropriate unless a company's growth rate is expected to remain constant in the future. This condition almost never holds for (Pick One: Mature, Start-up) firms, but it does exist for many (Pick One: Mature, Start-up) companies.

Which of the following assumptions would cause the constant growth stock valuation model to be invalid?

1. The growth rate is zero.
2. The growth rate is negative.
3. The required rate of return is greater than the growth rate.
4. The required rate of return is more than 50%.
5. None of the above assumptions would invalidate the model.

(Pick One statement above)

Write a program in JAVA

"When a share of common stock of some company is sold, the capital gain(or,sometimes, loss) is the difference between the share’s selling price and the price originally paid to buy it. This rule is easy to understand for a single share, but if we sell multiple shares of stock bought over a long period of time, then we must identify the shares actually being sold. A standard accounting principle for identifying which shares of a stock were sold in such a case is to use a FIFOprotocol—the shares sold are the ones that have been held the longest (indeed,this is the default method built into several personal finance software packages).For example, suppose we buy 100 shares at $20 each on day 1, 20 shares at $24on day 2, 200 shares at $36 on day 3, and then sell 150 shares on day 4 at $30each. Then applying the FIFO protocol means that of the 150 shares sold, 100were bought on day 1, 20 were bought on day 2, and 30 were bought on day3. The capital gain in this case would therefore be 100·10+20·6+30·(−6),or $940. Write a program that takes as input a sequence of transactions of the form “buy x share(s) at $y each” or “sell x share(s) at $y each,” assuming that the transactions occur on consecutive days and the values x and y are integers. Given this input sequence, the output should be the total capital gain(or loss) for the entire sequence, using the FIFO protocol to identify shares."

Your program should prompt the user to input a single string that represents a sequence of transactions. Use semicolon (‘;’) to separate the transactions in your input string. For example, your program should support the following input string:

“buy 100 share(s) at $20 each;buy 20 share(s) at $24 each;buy 200 share(s) at $36 each;sell 150 share(s) at $30 each;buy 50 share(s) at $25 each;sell 200 share(s) at $35 each;”

The output of your program should be the total capital gain (or loss) for the entire sequence, using the FIFO protocol as explained in P-6.36. For instance, the output for the example input should be: 1070

• Consider using built-in Java classes, e.g., classes that implement the interface java.util.Queue

2) At the start of the new year, Adriana finds out that the price of her economics textbook increased from $100 to $120, She along with her classmates plans on purchasing the textbook, but falls from 10 students to 9 students. At the same time, the minimum wage increased from $11.50 to $12.00. What is Adriana’s income elasticity?

3) Ernesto is looking to purchase a new vehicle as his income has increased from $2,000 per month to $3,000 per month, so his purchase increases from 0 to 1 vehicle. He see’s a new Mercedes Benz that decreased its price from $45,000 to $42,000. What is Ernesto’s income elasticity of demand for a Mercedes Benz vehicle?

4) Cris, a dedicated employee at Google just found out that he will be recognized for the employee of the year award, plus an additional pay increase of 10%. He along with several top employees from other states rush to purchase Porsche 911 4S vehicles resulting in a 7% increase in the quantity demanded. What is Cris’ income elasticity of demand for a Porsche 911 4S?

5) Jerry, an addict of Jamba Juice finds out about his 3% increase in pay, so he plans on increasing his Jamba Juice consumption by 5% not to mention Jamba Juice’s 1% price decrease. However, he plans to decrease his consumption of Tropical Smoothie by 2%. What is Jerry’s cross-price elasticity of demand for a Tropical Smooth with respect to the price of Jamba Juice?

6) Matthew is an addicted coffee drinker and proud patron of Starbucks, so he keeps an eye out on the prices of coffee. He finds out that Starbucks increases its price of a grande frappuccino from $3.50 to $4.00, so he expects many patrons to consume less grande lattes from 2 to 1 per week, and to find an alternative. He lives by a Coffee Bean and Tea Leaf café and his opportunity for a grande frappucino is a medium ice blended. He plans to consume more medium ice blended drinks increasing his quantity demanded from 1 to 5 per week. What is the cross price elasticity of demand for a medium ice blended drink with respect to a grande frappuccino’s price?