Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

Probability Taste Design A Design B

0.2 more conservative 180 520

0.5 no change 230 310

0.3 more liberal 350 270

1) If you decide to choose Design A for 70% of the production lines and Design B for the remaining production lines, what is the coefficient of variation of your investment?

2) If you decide to choose Design A for 90% of the production lines and Design B for the remaining production lines, what is the expected profit?

3) If you decide to choose Design A for 90% of the production lines and Design B for the remaining production lines, what is the risk of your investment ?

1. The next several questions refer to the case of an economy with the following equations: Y = 3K + 2L, with K = 1000 and L = 1500 G = 1230, T = 500 I = 1020 - 1000r C = 1070 + 0.5(Y-T) (Assume a closed economy: Y = C + I + G; NX = 0) Compute the equilibrium level of the interest rate.

choices

0.07

0.05

0.3

0.1

2. For the case above, compute the equilibrium level of investment.

980

900

1000

750

950

3. For the case above, compute the equilibrium level of consumption.

3700

3820

3750

4000

4200

4. For the model economy above, suppose government spending is raised to 1250 (instead of 1230). Compute the amount by which investment falls.

10

15

0

30

20

5. In the case above, the amount by which investment falls is _____ the amount by which government spending rises.

less than

more than

the same as

Greta has risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 10% per year, with a standard deviation of 16%. The hedge fund risk premium is estimated at 12% with a standard deviation of 31%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.

Question ： Calculate Greta's capital allocation using an annual correlation of 0.3 (2 decimal places)

S&P ？？？%

Hedge    ？？？%

Risk-free asset ？？？%

A car is going at 11.2 m/s on a horizontal straight road. When the traffic light is 30 m away, it turns red.
The reaction time of the driver is 0.3 s.
The car stops just before the traffic light with constant deceleration when the break is applied.

1. Find the time it takes for the car to stop, from the moment the light becomes red.

2. Plot speed of the car on y-axis and the time on the x-axis, taking t=0 at the

   moment when the traffic light turns red.

3. In the table provided below fill-up the blanks. It will help you to plot the graphs.

4. Plot the acceleration as a function of time.

5. Plot the distance covered as a function of time, using the v vs. t graph, taking zero

   at t=0.

3. Nestlé is a manufacturer of dairy products. His administration conducted an analysis of the chocolate division. As part of this analysis, it has been determined that personal income, sales prices and advertising expenses are the three main variables that affect the demand for chocolates. It has been estimated that the income arc elasticity for chocolates is 1.5 and that the arc price elasticity of demand is -2.0, as well as the arc elasticity of advertising is .8

a) Using these elasticities and the data below, calculate the missing sales:

Year Income Price Advertising Sales
2016 $ 1000 $ 400 $ 120 850
2017 $ 1100 $ 400 $ 130
2018 $ 1100 $ 450 $ 140

b) The company also has information that reveals that a competitor plans to reduce the price of its chocolates from $ 500 to $ 381 a box by 2017. The marketing department has estimated that the cross elasticity between the two companies is 0.3. How will the quantity react? Nestlé defendant? (calculate)

1. Develop an estimated regression equation that could be used to predict the program expenses (%) given fundraising expenses (%)

Program Expenses % (pred) = ? + ? Fundraising Expenses (%) up to 2 decimals

Problem: Suppose you are part of an economic analysis team charged with recommending a policy response to pesticide risks. Your team decides to use risk-benefit analysis as its risk management strategy. On the risk side of the analysis, your team reviews the following data from the risk assessment process. Interpret each of these quantitative findings about pesticide risk, by stating precisely what the numerical value(s) mean or imply in each case. Be specific. (i) Pesticide W: Reference Dose (RfD) = 0.005 (ii) Pesticide X: threshold level of 0 for infants and children (iii) Pesticide Y: carcinogenic risk of 0.0075 percent (iv) Pesticide Z: a dose (D)-response (R) function modeled as R = 0 for all D < 0.6, R = – 0.3 + 0.5D for all D ≥ 0.6. On the benefit side of the analysis, briefly describe two distinct benefits to society that are relevant to a risk-benefit analysis of pesticides.

3. [8 marks] Suppose a survey is conducted by Ipsos, a Canadian market research polling firm, on user satisfaction with cell phone coverage across the country. They sample 10 customers at random without replacement. Assume all sampled customers are independent. Suppose 30% of users nationwide are satisfied with their cell phone coverage.

a) [5 marks] Calculate the probability that 3 or more of the 10 randomly sampled cell phone customers are satisfied with their cell phone coverage.

b) [1 mark] Why is the probability that exactly 3 out of the 10 randomly sampled customers are satisfied with their cell phone coverage different from 0.3? Please answer in at most three sentences.

c) [1 mark] On average, in a sample of 10 customers, how many do you expect to be satisfied with their cell phone coverage?

d) [1 mark] Calculate the variance of the random variable associated with the number of satisfied customers.

Using R:

1. Generate AR(1), AR(2), MA(1), MA(2), and ARMA(1,1) processes with different parameter values, and draw ACF and PACF. Discuss the characteristics of ACF snd PACF for these processes.

2. Generate AR(1) process {X_t}. Compute the first difference Y_t = X_t - X_(t-1). Draw ACF and PACF of {Y_t}. What can you say about this process? Is it again a AR(1) process? What can you say in general?

3.For the AR(2) processes with the following parameters, determine if AR(2) processes are stationary. Without drawing the graphs, what can you say about ACFs.
(a) ϕ1=1.2, ϕ2=−0.2

(b) ϕ1=0.6, ϕ2=0.3

(c) ϕ1=1.2, ϕ2=−0.7

(d) ϕ1=−0.8, ϕ2=−0.7

4. For the process Xt = ϕXt−2+Zt, determine the range of ϕ for which the process is stationary.