Suppose a country’s production function has three factors of production: K—capital, L—the number of workers, and H—human capital. The production function is Y = (K^0.3)(L^0.4)(H^0.3). (a) What is the marginal product of labor? How does human capital affect the MPL?

(b) What is the marginal product of human capital? How does human capital affect the MPH?

c) What share of total income is paid to labor? What share of total income is paid to human capital?

(d) What share of total income would workers appear to receive?

(e) An unskilled worker earns the MPL, whereas a skilled worker earns the MPL plus the MPH. Using your above answers, find the ratio of the skilled wage to the unskilled wage. How does human capital affect this ratio? Explain.

PHYS/BIOL 464 Medical Imaging Instrumentation

MRI HW 8A

1. For a scanner with a maximum gradient strength of 20 mT m^-1 and a minimum transmitted bandwidth of 0.9 kHz, what is the thinnest slice that can be selected? (? = 42.6 MHz T^-1).

2. Which of the following is the bandwidth of a pulse with frequencies from 60.0015 to 60.0045 MHz?

(a) 3 kHz (b) 3 MHz (c) 0.3 Mhz (d) 60.0030 MHz.

3. Convert the following gradient strengths, expressed in terms of frequency, into T/m. (Assume ? = 42.6 MHz/T).

(a) 2 MHz/m; (b) 1 MHz/m; (c) 0.3 MHz/m.

4. Calculate the slice thickness for each of the gradients in problem 3 if the pulse bandwidth is 1.5 kHz.

5. Using the field gradient shown, which type of slice will be selected? Transaxial, Sagattal, or Coronal?

Use the following information to evaluate whether or not you should buy stock A.

                                Stock A                                                                                 S&P 500

                Probability                          Return                                  Probability          Return

                    0.1                                         -100%                                      0.3                     -30%

                    0.2                                          -10%                                       0.4                         15%

                    0.6                                          18%                                        0.3                         40%

                    0.1                                         130%

The current yield on the 10-year Treasury Note (risk-free rate) is 3.3%. The correlation between Stock A and the market is 0.53.   Hint One – Remember that the S&P 500 represents the market and that you can use the two probability distributions above to get the expected return and standard deviation for both Stock A and for the market (round calculations to 2 decimal places in percentage terms). Hint Two – You will use the SML to get the required return and you will need to calculate beta from the data provided (round beta to two decimal places).

A cereal manufacturer has two new brands of cereal which it would like to produce. Because resources are limited, the cereal manufacturer can only afford to produce one of the new brands. A marketing study produced the following probability distributions for the amount of sales for each of the new brands of cereal.

a. What are the expected sales of each of the new brands of cereal?

b. What is the standard deviation of the sales for each of the brands of cereal?

c. If both of the brands of cereal cost the same amount to produce, which brand of cereal do you think the cereal manufacturer should produce? Explain.

Corporation makes a product with the following standard costs:

The company reported the following results concerning this product in August.

The company applies variable overhead on the basis of direct labor-hours. The direct materials purchases variance is computed when the materials are purchased.

The variable overhead rate variance for August is:

Find the mean and standard deviation for the following, where possible,if not.explain why it is not.

a. x P(x) b. x P(x) c. x P(x)

0 0.1 -9 0.15 0 0.34

1 0.2 10 0.45 1 0.23

2 0.3 11 0.38 2 0.17

3 0.4   12 -0.21 3 0.26

-4 0.3

d. In a poll of 12 to 18yr. old females, conducted by theNokTerNoh!Magazine editor,Carolyn(Zleep D’Pri’D), found that 27%of them said that they expected to see a female soccer player on a team in the Men’s World Cup within 10 years. A random sample of 12 females from this age group was selected, by use of the formula;findi.P(Exactly 8 females share this view) (4pts)ii.P(Between 5-7 share this view) (6pts)

Since you became an expert in Corporate Finance and CAPM, now you want to make some money by investing in stocks. Instead of buying one stock, you will make a diversified portfolio using several stocks. Suppose that there are only 3 stocks in the market, and expected return, standard deviation, and correlations are as follows

Stocks Expected Return Standard Deviation

Stock A    5% 5%

Stock B    7% 10%

Stock C 10%    20%

Correlations Stock A Stock B Stock C

Stock A 1    0.4 -0.3

Stock B 0.4 1 0.7

Stock C -0.3 0.7 1

*Calculate Expected Return and Standard Deviation of Each Portfolio:
Portfolio 1: 30% in Stock A + 70% in Stock B
Portfolio 2: 60% in Stock B + 40% in Stock C
Portfolio 3: 50% in Stock A + 50% in Stock C

An certain brand of upright freezer is available in three different rated capacities: 16 ft³, 18 ft³, and 20 ft³. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has the following pmf.

(a) Compute E(X), E(X²), and V(X).

(b) If the price of a freezer having capacity X is 60X − 650, what is the expected price paid by the next customer to buy a freezer?

(c) What is the variance of the price paid by the next customer?

(d) Suppose that although the rated capacity of a freezer is X, the actual capacity is h(X) = X − 0.009X². What is the expected actual capacity of the freezer purchased by the next customer?

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $15 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.6 million with a 0.2 probability, $2 million with a 0.5 probability, and $0.3 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 60%, interest rate is 14%.

You run a company (Alpha) that is trying to enter the ice cream industry. The new line production requires an investment of 600,000 today and will be depreciated within 12 years with straight line depreciation method. In the 12th year the machine will be worth 3,500. Sales are estimated at 100,000 for each year but after the 12th year production will stop. The annual operating costs are 15,000 per year.

There are two competing companies (which have a 50% market share) Delta and Epsilon with the following financial data:

The interest-free rate is 1%, the expected market return is 8% and the tax rate is 24%. If all of the above sizes are on an annual basis, do you think that this investment should be made?