4) Consumer utility

You are given the above total utilities for different consumption amounts of goods A and B. The consumer has a budget of 60, the price of A is 4, and the price of B is 5.

a) Calculate all the marginal utilities and marginal utility – price ratios and display them on a table. Show all your work.
b) Prepare a separate table that shows all the possible combinations of A and B, and their respective utilities. Add one to the total utility of each combination for each unspent unit from the budget (for combinations where not all the 60 can be spent).

2

c) Which combination maximizes utility? Explain in detail, using two pieces of evidence.
d) Graph your result using a budget line and an indifference map.

-The budget line should be precise with properly scaled x- and y- axes.
- Show a few indifference curves; at least one not optimal, at least one not attainable, and the optimal one, with correct point of tangency.

Dexter Brothers Inc. reported net income available to common shareholders of $4,200,000 last financial year. The company has paid $1.20 dividend per share for the 1,000,000 common shares outstanding. The company’s capital structure is included of 40 percent debt, 10 percent preferred shares and 50 percent common shares. The company were taxed at 40 percent. *

(a) If the common shares are priced at $50 and the dividend is expected to grow at 5 percent per year for the foreseeable futures, determine the company’s cost of retained earnings. (b) If underpricing and flotation costs on new common share amount to $10.00 per share, compute the company’s cost of new common share financing. (c) The company can issue $2.00 dividend preferred shares for a market price of $25.00 per share. Flotation costs would amount to $3.00 per share. Calculate the cost of new preferred stock financing. (d) The company is considering to issue new bond with a par value of $1,000, 8 percent coupon rate with 5 years maturity. The company’s old bond currently trading at $1,100 per bond. Flotation cost would amount to $25 per bond. Calculate the new cost of debt financing. (e) Determine the Dexter Brothers new weighted average cost of capital (WACC) if the company decided to issue new shares. (f) Currently Dexter Brothers is in view of accepting a new project offering return of 8 percent. Should the company accept or reject the project. Justify your answer.

1. For their uniforms, the Vikings soccer team has a choice of six different styles for the shirts, five for the shorts, and five colours for their socks. How many different uniforms are possible? A) 16 B) 150 C) 60 D) 55

2. The Niagara Ice Dogs have 4 people trying out for goal. Their coach wants to try a different goalie in each of the three periods of an exhibition game. In how many ways can the coach choose the three different goalies for the game? A) 12 B) 24 C) 7 D) 55 E) 20

3. How many arrangements of the word ALGORITHM begin with a vowel and end with a consonant? A) 18 B) 5040 C) 90720 D)181440 E) 362880

4. From a class of 14 boys and 9 girls, how many ways can I choose a committee of 6 to analyze classroom productivity with and equal number of boys and girls? A) 126 B) 252252 C) 30576 D) 448

5.A bag contains three green Christmas ornaments and four gold ornaments. If you randomly pick a single ornament from the bag, what is the probability that it will be green? A) 3/4 B)3/7 C)4/7 D)4/3

6. A bag contains three green Christmas ornaments and four gold ornaments. If you randomly pick two ornaments from the bag, at the same time, what is the probability that both ornaments will be gold?
A) 4/7 B) 2/7 C)3/7 D) none of the above

7. How many 4 digit number can be made using 0 -7 with no repeated digits allowed?
A) 5040 B) 4536 C) 2688 D) 1470

8. A coin is tossed three times. What is the probability of tossing three heads in a row?
A) 3/8 B)1/8 C)1/2 D)7/8

9. Two standard dice are rolled. What is the probability of rolling doubles (both the same number)?
A) 1/6 B)1/4 C)1/36 D) 5/36

10. There are 50 competitors in the men’s ski jumping. 30 move on to the qualifying round. How many different ways can the qualifying round be selected? A) 50! B) 30! C) 80 D) 1500 E) 1.25 × 1046

11. How many ways can the manager of a baseball team put together a batting order of his nine players, if the shortstop must bat 3rd?
A) 40320 B) 504 C) 362880 D) 120960

12. If a CD player is programmed to play the CD tracks in random order, what is the probability that it will play six songs from a CD in order from your favourite to your least favourite? A)1/6 B)2/3 C)1/720 D)5/6 E) 1/360

13. A group of eight grade 11 and five grade 12 students wish to be on the senior prom committee. The committee will consist of three students. What is the probability that only grade 12 students will be elected, assuming that all students have an equal chance of being elected?

A researcher is investigating the effects of emotion and gender on cooperation. He randomly assigns participants to one of three conditions: control, guilt, happiness
After inducing one of the three emotions, the researcher measures each participant's level of cooperation in a game, on a scale from 1 to 10.

Men:
Control: 5 4 7 4 3 5 5 6
Guilt: 6 9 7 8 6 7 7 8
Happiness: 8 7 8 9 9 6 8 9

Women:
Control: 6 3 5 5 4 7 6 3
Guilt: 3 7 7 4 8 5 4 6
Happiness: 7 6 9 9 7 8 9 8

What statistical test should we do here? Report the results.

2. Using two of the Magnificent Seven tools listed below (other than Cause-and-effect diagram) • Histogram or stem-and-leaf plot

• Check sheet

• Pareto chart

• Defect concentration diagram

• Scatter diagram

• Control chart

Hair color in the United States is known to be 40% blond, 40% brown, and 20% black. Miranda does a study to see if the proportions match, and her survey showed 43 people with blond hair, 32 people with brown hair, and 15 with black hair. Use a chi-square test with a level of significance α=0.05.

Question text

7-step Hypothesis Testing Problem

Complete the 7 steps in Excel and upload the file here

Two major automobile manufacturers have produced compact cars with the same size engines.We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data show the results of the test.

At the 0.05 level of significance, conduct a 7-step hypothesis test to determine whether there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles.

Suppose the following data are selected randomly from a population of normally distributed values. 41 51 43 48 44 57 54 39 40 48 45 39 40 Construct a 95% confidence interval to estimate the population mean.

consider that we have one stock, ZEE Electronics, that today is worth $50 and one period later will be worth either $75 or $40. We will denote these prices as ZEE = $50, ZEE+ = $75, and ZEE– = $40. Another stock, CYT Technology, is today worth $38 and one period later will be worth $60 or $32. Thus, CYT = $38, CYT+ = $60, and CYT– = $32. Assume that the risk- free borrowing and lending rate is 4%. Also assume no dividends are paid on either stock during the period covered by this example. Find arbitrage return for ZEE and CYT technology, if exist