You expect a share of stock to pay dividends of $1.00, $1.25, and $1.50 for each of the next 3 years. After that, the dividends will grow at the sustainable growth rate until infinity. a. Calculate the sustainable growth rate assuming the company generates a rate of return of 20% on its equity and maintain a plowback ratio of 0.3. b. Assuming investors expect a 12% rate of return on the stock, what is the price of the stock today?

In the market A the price a company charges per product is $ 20 and its marginal cost is $ 10. In market B, another company sells a product at $ 30 and its marginal cost is $ 20. i) Who has greater market power company A or company B? ii) If we now know that the elasticity of demand is -2 in the market A and -0.3 in the market B. Who has greater market power? Why?

Customers at a fast-food restaurant buy both sandwiches and drinks. The mean number of sandwiches is 1.5 with a standard deviation of 0.5. The mean number of drinks is 1.45 with a standard deviation of 0.3. The correlation between the number of sandwiches and drinks purchased by the customer is 0.6. If the profit earned from selling a sandwich is $1.50 and from a drink is $1, what is the expected value and standard deviation of profit made from each customer.

Given the following information, please estimate the expected return and risk for the portfolio

USE THREE DECIMALS FOR ALL OF THE ANSWERS.

Health experts’ estimate for the sensitivity of coronavirus tests, as they are actually used, is 0.7. They also think the specificity is very high. Suppose specificity is 0.99 and that the health experts’ estimated sensitivity is correct (0.7).

a. In a population where 20% of the population is infected with the coronavirus, what is the probability that a person who tests positive actually is infected?  

b. Continued. What is the probability that a person who tests negative actually is not infected?

In the US, testing initially was very selective. In other words, as of early April 2020, only patients (i) with symptoms (ii) who contacted the health care system were being tested. For the most part, tests were not obtainable on demand, and there was very limited testing of asymptomatic people, even if they had been in contact with someone who had tested positive.

When testing is selective, then for interpreting results of testing, what matters is not the fraction of the entire population who are infected, but rather the fraction of the tested population who are infected.

c. If the prevalence of infection in the tested population is 0.8 (in other words, if 80% of people tested have the infection), what is the probability that a person who tests positive actually is infected?

d. Continued. What is the probability that a person who tests negative actually is not infected?

What can you learn from comparing your answers to parts a and b with your answers to parts c and d? The article also makes this point:

“Dr. Smalley said a negative result is more likely to be accurate in places like Louisville where the prevalence is low, but could be virtually useless in New York, where it is high.”

In other words, Louisville’s situation is similar to parts a and b, and New York’s situation is similar to parts c and d (qualitatively).

Now let’s see what is implied by the study of Wuhan patients that the WSJ article describes. Here’s another quote:

“A February study of about 1,000 patients in Wuhan, China, who were hospitalized with suspected coronavirus there, where the pandemic began, found that about 60% tested positive using lab tests similar to those available in the U.S. But, almost 90% showed tell-tale signs of the virus in CT scans of their chests, the article, published in the journal Radiology, found, suggesting many patients in the group were testing negative despite active coronavirus infections.”

Here, the population is “patients hospitalized for something that seems like coronavirus”. In that population, 90% of people were infected (if we take the CT scans as definitive). But 60% of this population tested positive. Note that 60% is not the sensitivity of the test, because this includes people who were not infected and who tested positive.

e. Let’s “back out” the sensitivity of the test, instead of assuming a value for sensitivity. Using 0.9 as the prevalence of infection with Covid-19 in the tested population; using 0.99 as the specificity of the test (same as in the previous parts of this problem); and using 0.6 as the fraction of the population who tested positive, calculate the implied sensitivity of the test. HINT: Use the law of total probability.    

f. Continued. In this situation (in the situation of the Wuhan study), what is the probability that a patient who tested negative actually was not infected?

g. Suppose the goal was for the probability to be at least 0.75 that a patient who tested negative actually was not infected, in the conditions of the Wuhan study. What is the minimum value of sensitivity that would allow this goal to be achieved?

Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below.

f(x) =

(a) Graph the pdf.

Obtain the cdf of X.

Graph the cdf of X.

(b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.)


(c) Using the cdf from (a), what is P(0.3 < X ≤ 0.65)? (Round your answer to four decimal places.)


What is P(0.3 ≤ X ≤ 0.65)? (Round your answer to four decimal places.)


(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)


(e) Compute E(X) and σ_X. (Round your answers to four decimal places.)

(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)

The economist for the ABC Truck Manufacturing Corporation has calculated a production function for the manufacture of their medium-size trucks as follows: Q = 1.3L0.75 K 0.3 where Q is number of trucks produced per week, L is number of labor hours per day, and K is the daily usage of capital investment.

a. Does the equation exhibit increasing, constant, or decreasing returns to scale? Why? ( 5 marks)

b. How many trucks will be produced per week with the following amounts of labor and capital?

Labor Capital

100 50

120 60

150 75

200 100

300 150

c. If capital and labor both are increased by 10 percent, what will be the percentage increase in quantity produced?

d. Assume only labor increases by 10 percent. What will be the percentage increase in production? What does this result imply about marginal product?

e. Assume only capital increases by 10 percent. What will be the percentage increase in production?

f. How would your answers change if the production function were Q = 1.3L0.7 K 0.3 instead? What are the implications of this production function? ( 5 marks)

6. In Experiment 13, the class studied the aquation of [Co(NH3)5Cl]2+. Below are sets of absorbance data taken during this study using 1.2 x 10-2 M [Co(NH3)5Cl]2+ in 0.1 and 0.3 M HNO3.

0.1 M HNO3

t (min) A @ 550 nm

15 0.346

30 0.314

40 0.300

60 0.280

75 0.264

0.3 M HNO3

t (min) A @ 550 nm

15 0.492

30 0.446

40 0.420

60 0.393

75 0.372

The first-order rate constants can be determined using the following equation ln(A-A) = -kt + ln(A0-A) where A0 is the initial absorbance at 550 nm before aquation began to occur.

A. (10 POINTS) What is the value of A? (show work)

B. (20 POINTS) Plot ln(A-A) vs. t and give the values of k and A0 for both sets of data above (attach both plots and show all work).

C. (5 POINTS) Based upon the above rate constants, by which mechanism to you believe that the aquation is occurring? Explain.

A stock (S) has an expected return of 15% and standard deviation of 5%. A bond (B) has an expected return of 10% and standard deviation of 2%. Correlation coefficient between S and B is 0.2. An investor wants to allocate 25% of her portfolio to S and the remainder of her portfolio to B. What is the expected return and variance of this portfolio?