The number of visitors to the historic Museum for 25 randomly selected hours is shown.

15   53   48   19   38   86   63   98   79   38   26   39   67   89   62   28   35   54   88   76

31 47   53   41   68.

Exercise 1

1. What is the sample size?
2. Is the variable qualitative or quantitative?
3. Is the variable discrete or continuous?
4. What is the level of measurement?

Exercise 2

In order to organize the following data in to 5 classes:

1. What is the range of the data set?
2. Find the width of the classes
3. What will be the first class limit?
4. What is the first class boundary?
5. What is the first class midpoint?
6. What is the frequency for the first class?

A researcher would like to determine if relaxation training will affect the number of headaches for chronic headache sufferers (n = 8). A week before training, each participant recorded the number of headaches experienced. Participants then receive relaxation training and following training the number of headaches were recorded again. The following results were provided:

• ΣD = -16
• SS = 14

Determine whether the results indicate a significant difference in chronic headaches after relaxation training? Use an alpha .05, level of significance. type the hypotheses (words or notation), critical boundary, standard error, t-score and decision including notation, decision and an explanation why.

Calculate Cohen’s d if appropriate

Consider a thin flat rectangular region that of size 4 x 2 m2 and it is electrically insulated at its four corners. (A)Solve Laplace’s equation  2 V(x,y) = 0 in the rectangular region 0 < x < 4 m and 0 < y < 2 m using the separation of variable technique subject to the following boundary conditions:
V(0,y) = 0
V(4,y) = q(y) = 50 sin (3π y / 2)
V(x,0) = 0
V(x,2) = f(x) =100 sin (π x / 4)
(B) Use the result of part (A) to find the corresponding electric field inside the region.

EMT plc has a wide range of manufacturing activities, principally within the UK. The company operates on the divisionalized basis with each division being responsible for its own manufacturing, sales and marketing, and working capital management. Divisional chief executives are expected to achieve a target 20% return on sales.

A disagreement has arisen between two divisions which operate on adjacent sites. The Office Products Division (OPD) has the opportunity to manufacture a printer using a new linear motor which has recently been developed by the Electric Motor Division (EMD). Currently there is no other source of supply for an equivalent motor in the required quantity of 30,000 units a year, although a foreign manufacturer has offered to supply up to 10,000 units in the coming year at a price of £9 each. EMD’s current selling price for the motor is £12. Although EMD’s production line for this motor is currently operating at only 50% of its capacity, sales are encouraging and EMD confidently expects to sell 100,000 units in 2018, and its maximum output of 120,000 units in 2019.

EMD has offered to supply OPD’s requirements for 2018 at a transfer price equal to the normal selling price, less the variable selling and distribution costs that it would not incur on this internal order. OPD responded by offering an alternative transfer price of the standard variable manufacturing cost plus a 20% profit margin. The two divisions have been unable to agree, so the corporate operations director has suggested a third transfer price equal to the standard full manufacturing cost plus 15%. However, neither divisional chief executive regards such a price as fair.

EMD’s 2018 budget for the production and sale of motors, based on its standard costs for the forecast 100,000 units sales, but excluding the possible sales to OPD, is as follows: (£000) Sales Revenue (100,000 units at £12.00 each) 1,200 Direct Manufacturing Costs Bought-in materials 360 Labour 230 Packaging 40 Indirect Manufacturing Costs Variable overheads 10 Line production managers 30 Depreciation Capital equipment 150 Capitalized development costs 60 Total manufacturing costs 880 Sales and Distribution Costs Salaries of sales force 50 Carriage 20 General Overhead 50 Total costs 1000 Profit 200 Notes (1) The costs of the sales force and indirect production staff are not expected to increase up to the current production capacity. (2) General overhead includes allocations of divisional administrative expenses and corporate charges of £20,000 specifically related to this product. (3) Depreciation for all assets is charged on a straight line basis using a five year life and no residual value. (4) Carriage is provided by an outside contractor.

Required: (a) Calculate each of the three proposed transfer prices and comment on how each might affect the willingness of EMD’s chief executive to engage in interdivisional trade. (b) Outline an alternative method of setting transfer prices which you consider to be appropriate for this situation, and explain why it is an improvement on the other proposals.

BXP Inc., a UK importing firm anticipates an outflow of 186 million Danish Krone (DKK) in 6 months. BXP’s managers are worried about the course of the DKK/£ exchange rate over the next 6 months and they decide to hedge. The current spot and forward rates are S0=6.1718 DKK/£ and Ft=6 months=6.2035 DKK/£. BXP can borrow/lend at a £-interest rate of 3.57% and a DKK-interest rate of 5.15%.
a) How can BXP hedge its position using the forward market? Calculate the 6-month ahead cash flow BXP can lock in with the forward hedge.
b) How can BXP hedge its position using the money markets? Calculate the 6-month ahead cash flow BXP can lock in with the money market hedge.
c) Why do the two hedges result in different amounts that can be “locked in”? Which of the two hedges is best for BXP Inc.? Would things be different if BXP was attempting to hedge an inflow of DKK?

1. In the UK sales of music CDs per year have declined from 60 million in 2013 to 48 million in 2016 and further to 32 million in 2018.

   1. (a) What was the average rate of change in CD sales from 2013 to 2016 and what was the average rate of change from 2016 to 2018.

   2. (b) Based on this data, is number of CDs sales decreasing linearly? Give a reason for your answer.

2. The cost of producing x solar panels is c(x) = 1000 + 500x − 20x2 (in dollars).

   1. (a) Using the definition of the derivative from lectures, compute the marginal cost when 10 solar panels have already been produced.

   2. (b) Compare this to the actual extra cost for producing an 11th solar panel.

   3. (c) Work out the equation for the tangent to the graph of c(x) at x = 10.

Differential Rail Pricing Employed by a UK Rail Company: A Case Study in Price Discrimination

Introduction

The discussion is about Virgin Trains and its joint venture with the Stagecoach Group. The focus will be on the Virgin Trains East Coast line which operates between London and Edinburgh. East Coast has a market share of “just over 30 per cent” of the public transport market including airlines which are also in competition with the railways The discussion will focus on Virgin’s ability to vary its pricing between peak and off peak periods of the day. It also has the technological ability to charge different prices according to how far in advance the passenger is booking.

Discussion

Virgin has managed to successfully increase the number of passenger journeys by exploiting their dominant market power through price discrimination. Business travellers pay more for their rail tickets while leisure travellers tend to pay less because they can be more “flexible with their travel plans" The offer of cheap fares has been used to fill the trains during off peak periods.

Price discrimination has been used by Virgin to segment the travel market so that revenue can be maximised. There is a difference between the peak (commuting) period where the price elasticity of demand is inelastic and the off peak (leisure) period where price elasticity is price elastic .. Under price discrimination, the monopolist rail company assumes that some business travellers are willing to pay a price above a level where marginal cost equals marginal revenue. The monopolist rail company (Virgin-Stagecoach) seeks to “maximise revenue and generate excess profit” . It is for this reason that the monopolist does not want to charge a single price. Instead, they will segment the market and charge more to consumers who are willing to pay extra to travel at the peak period.

Virgin will want to maximise its load factor, which measures its ability to sell all of the available seats on the train . The train operation is a fixed cost and operates regardless of whether there are no passengers or whether the train is full. There will still be fuel and staffing costs which do not vary according to the number of passengers. It is necessary for Virgin to sell as many train tickets as possible to offset its costs. Demand theory suggests that additional demand can be generated from lower prices. If a passenger wants a train ticket 3 months in advance then they can purchase one for a low price. This is because there are many seats available and Virgin wants to make sure that they achieve a sufficient level of sales. Once a sufficient level of rail sales has been obtained then they can charge a higher price to later ticket bookers.

Answer the following Questions

Mention the first two degrees of price discrimination? What degrees of price discrimination are practiced by the UK Rail Company?

How is price discrimination beneficial to the monopolisr UK railt?

Is the concept of elasticity in any way related to price discrimination? Explain diagrammatically drawing references from the case?

At four UK hospitals, patients with severe asthma were screened for fungal sensitization by skin prick testing. those 3,610 who were positive by skin prick were randomized to one of two treatment regimens: 1,805 were assigned to take an antifungal agent in tablet form while 1,805 were assigned to take a similar looking placebo tablet. The primary end point was the development of a particular type of lung infection by 32 weeks. By the end of the study, 1,492 of those who had taken the antifungal agent had not developed the lung infection, whereas 1,064 of those who had taken the placebo had not developed the lung infection. There was no loss to follow-up and no censoring except for administrative censoring.

a) What is the study design?

b) Generate a contingency table:

c) Calculate the 32-week cumulative incidence for those exposed and unexposed to the antifungal agent, respectively. (CI= #new cases of disease during a given time period/total population at risk)

d) Calculate and interpret the risk ratio between exposed group and unexposed group. (RR= CI exposed/ CI unexposed)

1. In 2019, its first year of operations, Brighton Finance Corporation, based in London, UK, had the following transactions regarding its investments (currency in British pound, £):

May. 1 Purchased 600 Clifford Ltd. common shares for £60 per share. This investment is held for trading purposes.

June. 1 Purchased 1,000 bonds of Gladstone Inc. at face-value price of £100 each. These bonds bear interest at 6%, which is paid semi-annually on November 30 and May 31 each year. They were also purchased for trading purposes.

July. 1    Purchased 4,000 Waterloo Corporation common shares for £70 per share. This represents 25% of the issued common shares. Because of this investment, the directors of Waterloo have invited a Brighton’s executive to sit on their board.

Sep. 1 Received a £1-per-share cash dividend from Waterloo Corporation.

Nov. 1 Sold 200 Clifford Ltd. common shares for £63 per share.

Nov. 30 Interest on the Gladstone Inc. bonds was received.

Dec. 15 Received a £0.50-per-share cash dividend on Clifford Ltd. common shares.

Dec. 31 On this date, the fair values per share were £55 for Clifford Ltd. and £73 for Waterloo Corporation. The fair value of the Gladstone bonds was £101 each. Waterloo reported a profit for the year ended December 31, 2019, of £100,000.

Instructions:

1. Make journal entries on the above transactions up to Dec. 15.
2. Prepare the adjusting journal entries required to report the investments at their fair value and accrue any investment revenue at the end of 2019.
3. Show the partial presentation of each investment and the related investment income reflected in Brighton’s 2019 statement of financial position and income statement.