Beryllium-8 is an unstable isotope and decays into two α particles, which are helium nuclei with mass 6.68×10−27kg. This decay process releases 1.5×10−14J of energy. For this problem, let's assume that the mass of the Beryllium-8 nucleus is just twice the mass of an α particle and that all the energy released in the decay becomes kinetic energy of the α particles.

If a Beryllium-8 nucleus is at rest when it decays, what is the speed of the  α particles after they are released? (My answer = 1.5 x 10^6)

If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the slower-moving α particle after it is released? Assume that the α particles move entirely in the x-direction.

If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the faster-moving α particle after it is released?  Assume that the α particles move entirely in the x-direction.

Beryllium-8 is an unstable isotope and decays into two α particles, which are helium nuclei with mass 6.68×10−27kg. This decay process releases 1.5×10−14J of energy. For this problem, let's assume that the mass of the Beryllium-8 nucleus is just twice the mass of an α particle and that all the energy released in the decay becomes kinetic energy of the α particles.

a) If a Beryllium-8 nucleus is at rest when it decays, what is the speed of the  α particles after they are released?

b) If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the slower-moving α particle after it is released? Assume that the α particles move entirely in the x-direction.

c) If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the faster-moving α particle after it is released?  Assume that the α particles move entirely in the x-direction.

Markets for Factors of Production

Robert hires workers to pack the Haskap berries he is growing.

The market for Haskap berries is perfectly competitive, and the price of Haskap berries is $2 per bucket. The labour market is competitive, and the market wage rate is $16/hour.  

Table 1.0 below shows the workers’ total product schedule

Table 1.0

Answer the following:

1. What is the marginal product of the third worker hired, and what is that worker’s Value of Marginal Product?

2. How many workers will Robert hire to maximize profit and what will the workers produce?

3. If the market wage rate rises to $20/hour, how many workers will Robert hire?

1

INSTRUCTIONS

In 2018 the European Commission (EC) fined Google €4.34 billion for breaching Article 102 of the Treaty on the Functioning of the European Union (TFEU) and Article 54 of the EEA Agreement. [Hint: This is an essay type question and students are free to express their views provided that they are well grounded on economic analysis and are logically consistent. Students are allowed to use official sources that can be found online on the European Commission’s website and the answer should be at most two pages long].

a) Provide an overview of the case, briefly describing the undertaking company, and the infringements involved. [Mark: 1.0]
b) What were the relevant product and geographic markets that were delineated and on which criterion were they based? What economic arguments did the EC use to support its basic claim? [Mark: 1.0]
c) What were the factors justifying the dominant position of Google in the relevant markets? If you were an economic advisor of the undertaking company, what type of economic arguments would you bring against the claim of the EC? [Mark: 1.5]

QUESTION 1 (30%). Concrete is required for a reinforced concrete building. The 28-day target mean (cube) compressive strength should be 40 N/mm2. Use the BRE method to determine the concrete mix proportions for 0.05 m3 concrete (BRE tables and figures are attached below for each stage). (30%) The properties of materials and site conditions are as follows: - Cement strength class: 42.5 - Slump required: 50 mm - Coarse aggregate: crushed 20 mm (use 1:2 proportions for 10 mm and 20 mm combination); Fine aggregate: uncrushed (40% passes 600 micron sieve) - Minimum allowable cement content: 300 kg/m3; Maximum allowable cement content: 450 kg/m3 - Maximum allowable free w/c ratio: 0.55 - Relative density of aggregates (SSD): 2.65 - Free Moisture content for Coarse Aggregate: +1.0% - Free moisture content for Fine Aggregate: +1.0%

1.1 characterisitic compressive strength (MPa) and age (days): Proportion defective (%)

Consider the following three bonds:

Assume that coupons are paid every 6 months and the face values of all the bonds are $1,000.

(a) Suppose that the 0.5- and 1.5-year zero-coupon bonds are available. Determine their respective prices. (Keep 2 decimal places, e.g. xxx.12)

     P_Z0.5:               P_Z1.5:

(b) Determine the forward rate f _0.5,1 (in yearly term) on a 6-month Treasury bill 6 months from now. (Keep 4 decimal places, e.g. 0.1234)

(c) Determine the forward rate f_0.5,1.5 (in yearly term) on a 12-month Treasury bill 6 months from now. (Keep 4 decimal places, e.g. 0.1234)

(d) Price the 1.5-year coupon bond 6 months from now. (Keep 2 decimal places, e.g. xxx.12)?

1. Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $6 million. The equipment falls in the 5-year MACRS, it can be sold after 6 years for $500,000. The applicable depreciation rates are 20%, 32%, 19.20%, 11.52%, 11.52% and 5.76%. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.50 per trap and believes that the traps can be sold for $4 each. Sales forecasts are given in the following table. The project will come to an end in 5 years when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 12%.

Year 0: 0

Year 1: 0.5

Year 2: 0.6

Year 3: 1.0

Year 4: 1.0

Year 5: 0.6

Year 6: 0.2

Thereafter 0

1. What is project NPV?

Suppose a certain magazine evaluates products for consumers. The following table contains data for 15 compact sports utility vehicles (SUVs) from a certain year.

• Vehicle—name of vehicle
• Overall score—awarded based on a variety of measures, including those in this data set
• Recommended—Consumer Reports recommends the vehicle or not
• Owner satisfaction—satisfaction on a five-point scale based on the percentage of owners who would purchase the vehicle again (−−, −, 0, +, ++)
• Overall miles per gallon–miles per gallon achieved in a 150-mile test trip
• Acceleration (0–60 sec)—time in seconds it takes vehicle to reach 60 miles per hour from a standstill with the engine idling

(a) How many variables are in the data set?

(b) Which of the variables are categorical? (Select all that apply.)

Overall Score

Recommended

Owner Satisfaction

Overall Miles Per Gallon

Acceleration (0–60) Sec

Which of the variables are quantitative? (Select all that apply.)

Overall Score

Recommended

Owner Satisfaction

Overall Miles Per Gallon

Acceleration (0–60) Sec

(c) What percentage of these 15 vehicles are recommended? (Round your answer to the nearest percent.)

%

(d) What is the average of the overall miles per gallon across all 15 vehicles? (Round your answer to one decimal place.)

miles per gallon

(e) For owner satisfaction, construct a bar chart showing the percentage frequency for each of the owner satisfaction ratings.

A.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

• −−: 0
• −: 13.3
• 0: 40
• +: 20
• ++: 26.7

B.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

• −−: 0
• −: 13.3
• 0: 20
• +: 26.7
• ++: 40

C.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

• −−: 0
• −: 13.3
• 0: 20
• +: 40
• ++: 26.7

D.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

• −−: 0
• −: 26.7
• 0: 40
• +: 20
• ++: 13.3

(f) Show the frequency distribution for acceleration using the following intervals: 7.0–7.9, 8.0–8.9, 9.0–9.9, and 10.0–10.9. Construct a histogram showing the frequencies of each interval.

A.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

• 7.0–7.9: 1
• 8.0–8.9: 5
• 9.0–9.9: 3
• 10.0–10.9: 6

B.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

• 7.0–7.9: 1
• 8.0–8.9: 3
• 9.0–9.9: 5
• 10.0–10.9: 6

C.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

• 7.0–7.9: 1
• 8.0–8.9: 5
• 9.0–9.9: 3
• 10.0–10.9: 4

D.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

• 7.0–7.9: 1
• 8.0–8.9: 3
• 9.0–9.9: 4
• 10.0–10.9: 5

The City of Pfeiffer starts the year of 2017 with the general fund and an enterprise fund. The general fund has two activities: education and parks/recreation. For convenience, assume that the general fund holds $144,000 cash and a new school building costing $1,180,000. The city utilizes straight-line depreciation. The building has a 20-year life and no salvage value. The enterprise fund has $65,000 cash and a new $360,000 civic auditorium with a 30-year life and no salvage value. The enterprise fund monitors just one activity, the rental of the civic auditorium for entertainment and other cultural affairs.

The following transactions for the city take place during 2017. Assume that the city’s fiscal year ends on December 31.

Decides to build a municipal park and transfers $72,000 into a capital projects fund and immediately expends $20,600 for a piece of land. The creation of this fund and this transfer were made by the highest level of government authority.

Borrows $113,400 cash on a long-term bond for use in creating the new municipal park.

Assesses property taxes on the first day of the year. The assessment, which is immediately enforceable, totals $618,600. Of this amount, $525,800 will be collected during 2017 and another $51,600 is expected in the first month of 2018. The remainder is expected about halfway through 2018.

Constructs a building in the park in (b) for $40,000 cash so that local citizens can play basketball and other sports. It is put into service on July 1 and should last 10 years with no salvage value.

Builds a sidewalk around the new park for $10,000 cash and puts it into service on July 1. It should last for 10 years, but the city plans to keep it up to a predetermined quality level so that it will last almost indefinitely.

Opens the park and charges an entrance fee of only a token amount so that it records the park, therefore, in the general fund. Collections during this first year total $4,000.

Buys a new parking deck for $220,000, paying $22,000 cash and signing a long-term note for the rest. The parking deck, which is to go into operation on July 1, is across the street from the civic auditorium and is considered part of that activity. It has a 20-year life and no salvage value.

Receives a $110,000 cash grant for the city school system that must be spent for school lunches for the poor. Appropriate spending of these funds is viewed as an eligibility requirement of this grant. During the current year, $40,700 of the amount received was properly spent.

Charges students in the school system a total fee of $6,600 for books and the like. Of this amount, 90 percent is collected during 2017 with the remainder expected to be collected in the first few weeks of 2018.

Buys school supplies for $23,000 cash and uses $17,800 of them. The general fund uses the purchases method.

Receives a painting by a local artist to be displayed in the local school. It qualifies as a work of art, and officials have chosen not to capitalize it. The painting has a value of $83,700. It is viewed as inexhaustible.

Transfers $20,600 cash from the general fund to the enterprise fund as a capital contribution.

Orders a school bus for $102,000.

Receives the school bus and pays an actual cost of $105,000. The bus is put into operation on October 1 and should last for five years with no salvage value.

Pays salaries of $247,000 to school teachers. In addition, owes and will pay $30,800 during the first two weeks of 2018. Vacations worth $23,600 have also been earned but will not be taken until July 2018.

Pays salaries of $43,000 to city auditorium workers. In addition, owes and will pay $3,500 in the first two weeks of 2018. Vacations worth $5,800 have also been earned but will not be taken until July 2018.

Charges customers $150,800 for the rental of the civic auditorium. Of this balance, collected $127,600 in cash and will collect the remainder in April 2018.

Pays $10,400 maintenance charges for the building and sidewalk in (d) and (e).

Pays $16,200 on the bond in (b) on the last day of 2017: $5,800 principal and $10,400 interest.

Accrues interest of $15,000 on the note in (g) as of the end of 2017, an amount that it will pay in June 2018.

Assumes that a museum that operates within the city is a component unit that will be discretely presented. The museum reports to city officials that it had $48,500 of direct expenses this past year and $57,700 in revenues from admission charges. The only assets that it had at year-end were cash of $27,700, building (net of depreciation) of $346,300, and a long-term liability of $242,400.

Prepare the 2017 government-wide financial statements for this city. Assume the use of the modified approach.

Prepare a statement of net position. (Amounts to be deducted should be indicatedby a minus sign.)