We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here

worker  wages   los     size
1       46.3791 34      Large
2       37.3643 28      Small
3       58.9662 89      Small
4       47.4511 24      Small
5       98.45   90      Large
6       51.3039 205     Small
7       78.8469 52      Large
8       48.6907 47      Large
9       52.1521 39      Large
10      76.5752 147     Small
11      64.5643 32      Large
12      47.7774 28      Small
13      39.4675 16      Small
14      75.3756 25      Large
15      42.7038 95      Large
16      37.3256 21      Large
17      47.6141 24      Large
18      39.0678 64      Small
19      41.587  34      Large
20      64.102  50      Large
21      72.0744 79      Large
22      69.4551 99      Small
23      49.7729 57      Large
24      46.8856 72      Small
25      62.1589 38      Large
26      51.3016 106     Small
27      38.2666 135     Small
28      46.6623 17      Large
29      41.256  44      Large
30      50.9605 40      Large
31      52.8366 53      Small
32      47.635  74      Large
33      61.0205 79      Large
34      62.3736 82      Small
35      38.8286 52      Large
36      56.931  31      Large
37      72.1109 20      Large
38      70.1955 87      Small
39      70.9977 84      Large
40      60.4625 50      Small
41      69.0306 86      Small
42      47.8044 17      Small
43      66.7418 128     Large
44      40.8045 99      Small
45      56.4676 95      Large
46      82.3129 37      Small
47      49.438  102     Large
48      60.0954 28      Large
49      49.7582 27      Small
50      70.0533 155     Large
51      68.4439 56      Large
52      43.1397 42      Large
53      37.8087 154     Large
54      39.9629 102     Small
55      50.4422 42      Small
56      41.7852 162     Large
57      52.8019 63      Small
58      85.8806 119     Large
59      50.1035 25      Small
60      77.1412 122     Large

is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.

(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

(c) State carefully what the slope tells you about the relationship between wages and length of service.

(d) Give a 95% confidence interval for the slope.

(___,___)

QUESTION 7 - 6.3

I dislike using Microsoft Word and prefer to use other work processing software. However, nearly everyone that I work with uses Word, so I have to use this product when writing articles, books, and other research reports. For this reason, Microsoft Word holds a near-monopoly position in the word processor market. What is the barrier to entry that helps Microsoft maintain their market power?

QUESTION 8 - 6.3

Suppose there are 100 firms that sell athletic shoes and each has one percent of the market share. What is the HHI statistic for this market?

QUESTION 9 - 6.3

Suppose there are six firms in the breakfast cereal market. The four largest firms have 20 percent of the market share each, and the two smallest firms have 10 percent of the market share each. If one of the largest firms buys one of the smaller firms, what is the market share of the largest firm in the market after the buyout is concluded?

QUESTION 10 - 6.3

What happens to the profits of monopolistically competitive firms in the long run?

You are considering investing $1,400 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 18%, and Y has an expected rate of return of 14%. To form a complete portfolio with an expected rate of return of 9%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y, respectively. Show all calculation

a. 0%; 60%; 40%

b.50%; 30%; 20%

c.40%; 24%; 16%

d. 32%; 42%; 26%

Meridian Industries manufactures and sells two models of watches, Prime and Luxuria. It expects to sell 3,000 units of Prime and 1,000 units of Luxuria in 2016.The following estimates are given for 2016:

                                                                                  Prime    Luxuria

        Selling price                                                     $200        $500

        Direct materials                                                   20             50

        Direct labor                                                          40          150

        Manufacturing overhead                                  40          100

Meridian had an inventory of 200 units of Prime and 75 units of Luxuria at the end of 2015. It has decided that as a measure to counter stock outages it will maintain ending inventory of 350 units of Prime and 200 units of Luxuria. Each Luxuria watch requires one unit of Crimpson and has to be imported at a cost of $10. There were 100 units of Crimpson in stock at the end of 2015.The management does not want to have any stock of Crimpson at the end of 2016.

How many units of Prime watches must be produced in 2016?

What is the amount budgeted for purchase of Crimpson in 2016?

What is the total budgeted cost of sold for Meridian Industries in 2016?

The J. Mehta Company’s production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is as follows:

The Mehta firm can normally produce 100 stainless steel sinks in a month. This is done during regular production hours at a cost of $100 per sink. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices:

he can produce up to 50 more sinks per month in overtime but at a cost of $130 per sink;

he can purchase a limited number of sinks from a friendly competitor for resale (the maximum number of outside purchases over the four-month period is 450 sinks, at a cost of $150 each);

Or, he can fill the demand from his on-hand inventory (i.e. beginning inventory). The inventory carrying cost is $10 per sink per month (i.e. the cost of holding a sink in inventory at the end of the month is $10 per sink).

Back orders are NOT permitted (e.g. order taken in period 3 to satisfy the demand in later period 2 is not permitted). Inventory on hand at the beginning of month 1 is 40 sinks (i.e. beginning inventory at month 1 is 40 sinks)

Set up and formulate algebraically the above “production scheduling” problem as a TRANSPORTATION Model to minimize cost.

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data.

(a) Compute Σx, Σx², Σy, Σy².

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.)

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)

Use the intervals to compare the two funds.

75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.75% of the returns for the stock fund fall within a narrower range than those of the balanced fund.    25% of the returns for the balanced fund fall within a narrower range than those of the stock fund.25% of the returns for the stock fund fall within a wider range than those of the balanced fund.

Raner, Harris & Chan is a consulting firm that specializes in information systems for medical and dental clinics. The firm has two offices—one in Chicago and one in Minneapolis. The firm classifies the direct costs of consulting jobs as variable costs. A contribution format segmented income statement for the company’s most recent year is given:

Required:

1-a. Compute the companywide break-even point in dollar sales.

1-b. Compute the break-even point for the Chicago office and for the Minneapolis office.

1-c. Is the companywide break-even point greater than, less than, or equal to the sum of the Chicago and Minneapolis break-even points?

2. By how much would the company’s net operating income increase if Minneapolis increased its sales by $75,000 per year? Assume no change in cost behavior patterns.

3. Assume that sales in Chicago increase by $50,000 next year and that sales in Minneapolis remain unchanged. Assume no change in fixed costs.

a. Prepare a new segmented income statement for the company. (Round your percentage answers to 1 decimal place (i.e. 0.1234 should be entered as 12.3).)

(Using Matlab) Write a function to "smooth" a black-and-white image by replacing each pixel by the average of itself and its neighbors. In MATLAB a black-and-white image is just a matrix of 1s and 0s - 1 represents white, and 0 represents black.

To keep the algorithm simple, ignore the edges of the image - that is, do not change the first and last rows and columns.

function name = smooth_image()

input argument = input matrix

output argument = output matrix

The algorithm can be described as follows:

• Given an NxM input matrix
• make a copy of the matrix - this will be the output matrix
• loop over rows 2 to N-1 of the input matrix
• loop over columns 2 to M-1 of the input matrix
• take the average of the 3x3 submatrix centered on the current row & column
• set the corresponding element of the output matrix equal to this average

MATLAB:

Matrix M = [ 0 2 3 5; 7 3 8 4 ]

Write one command that stores all of the rows of columns 1, 2, and 3 of M into a matrix named M2.

1. The table shows the total utility (TU) that James receives from consuming different amounts of two goods X and Y, per month.

1. Fill in the other columns of the table by calculating the marginal utilities for goods X and Y and the ratios of marginal utilities to price for the two goods. Assume that the price of both goods X and Y is $3.

2. If James allocates $30 to spend on both goods, how many units will he buy of each?

3. How much will James spend on each good at the utility maximizing combination?

4. How much total utility will James experience by buying the utility-maximizing combination?

5. Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize his utility now?