4. Do the following problems, using data set #3:

(a) Use the naïve forecasting method, the average of historical data method, and a 3-period moving average to estimate values of X.

(b) Calculate the Mean Absolute Error, the Mean Squared Error, and the Mean Absolute Percentage Error for each forecasting method.

(c) Based on your answers to (b), which the best forecasting method?

5. Do the following, using data set #3:

(a) Calculate a linear trend regression for X.

(b) Calculate a quadratic trend regression for X, using a 2-period model.

(c) Calculate the Mean Absolute Error, the Mean Squared Error, and the Mean Absolute Percentage Error for each forecasting method.

(d) Which model is better (a) or (b)? Explain.

#3

When performing calculations in the following problems, use the numbers in the table as-is. I.e., do NOT convert 8.5985 to 8.5985% (or 0.085985). Just use plain 8.5985.

1. Using the basic market model regression, ,R p = α + β R m + ϵ , what is the beta of this portfolio?

2. For precision, find the portfolio beta using the excess return market model: R p − R f = α + β ∗ ( R m − R f ) + ϵ

[Hint: compute annual excess returns first, then run regression.]

When performing calculations in the following problems, use the numbers in the table as-is. I.e., do NOT convert 8.5985 to 8.5985% (or 0.085985). Just use plain 8.5985.

1.

For precision, find the portfolio beta using the excess return market model: R p − R f = α + β ∗ ( R m − R f ) + ϵ

[Hint: compute annual excess returns first, then run regression.]

2. Using the excess return beta β∗ from the previous problem, what is Jensen's alpha for the portfolio?

The table shows data on asthma-related visits. Is there evidence that these visits vary by quarter? Can you detect a trend? A powerful test would be to run a multiple regression in Excel. If the function is already loaded, you will find it in Data> Data Analysis> regression. If not get help in adding the Analysis Tool Pak. To test for quarterly differences, create a variable called Q1 that equals 1 if the data are for the first quarter and 0 otherwise, a variable called Q2 that equals 1 if the date are for the second quarter and 0 otherwise and a variable called Q4 that equals 1 if the date are for the forth quarter and 0 other wise. ( Because you will accept the default, which is to have a constant term in your regression equation, do not include an indicator variable for quarter 3). Also create a variable called Trend that increases by 1 each quarter.

Year/Number of Years Since 1971/Number of stores

• Identify the initial value and the growth rate of your exponential model and explain what they mean in the context of Starbucks Stores. Put your explanations in a text box.

• Use your exponential model to predict the number of Starbucks locations in the following years:

1980, 1990, 2000, 2010, 2020, 2030, 2040, 2050

Case Monopoly power and competition policy We have seen that a monopoly creates a social loss compared to a perfectly competitive market. If it is possible to increase the level of competition in a monopolized market, then society is better off since social surplus increases. Competition policy (also known as antitrust policy) deals with markets where competition can arise; however, given the behaviour of some firms in those markets, competition is restricted. There are markets in which increasing the level of competition is not feasible, so competition policy does not apply. This is the case of a natural monopoly, which will be discussed at the end of this chapter. Broadly speaking, competition policy can be divided into policies to deal with monopoly power that already exists, and policies to deal with mergers that may increase monopoly power. While mergers will be discussed in the next chapter, here we discuss policies to address existing monopoly power. Since the UK belongs to the European Union, EU competition law takes precedence where it is relevant, essentially in the case of larger businesses with significant European or global activities. The original Common Market was created by the 1956 Treaty of Rome. The modern and enlarged EU is largely underpinned by the 1999 Treaty of Amsterdam. Article 81 of this treaty prohibits anti-competitive agreements (called cartels) that have an appreciable effect on trade between EU member states and which prevent or distort competition within the EU. Article 82 prohibits the abuse of any existing dominant position. A firm has a dominant position in a given market if it has a large market share in that market. For example, Microsoft has a dominant position in the market for operating systems (OS) for PCs, with a market share of around 90 per cent. Article 82 prohibits the abuse of a dominant position not the dominant position itself. A firm can become a dominant firm simply because it is more productive than the others and this is fine for competition policy. What is not fi ne is a firm that uses its dominant position to restrict competition in the market. Responsibility for enforcement of these articles lies with the European Commission. Although global businesses are increasingly subject to transnational competition law, many businesses still operate primarily within one country; national decisions are then appropriate. Within the UK, these are governed by the Competition Act 1998 and the Enterprise Act 2002. The latter made it a criminal offence, punishable by a jail sentence, to engage in a dishonest cartel. Two key institutions addressing UK competition policy are the Office of Fair Trading (OFT) and the Competition Commission. In particular, the OFT has the power to refer cases in which existing monopoly power may be leading to a ‘substantial lessening of competition’ to the Competition Commission for detailed investigation. Prior to the Enterprise Act 2002, the Competition Commission was asked instead to evaluate whether or not a monopoly was acting ‘in the public interest’, without any presumption that monopoly was bad, and many previous judgements of the Commission concluded that companies were acting in the public interest, for example because they had an excellent record of innovation, despite having a monopoly position.

Questions on case study:

1. Explain the ways in which a monopolist can abuse its power when compared to a perfect competitor.

2. In light of your answer to question 1, explain why it is important for monopolists to be regulated to protect the interests of consumers, as done by the OFT and the Competition Commission.

3. Discuss how monopolists can be beneficial to the economy and consumers.

3 Foreign country fiscal policy

During the World War I (1914-1918), the UK increases the government spending substantially to finance its military spending. However, the US government spending at that time did not increase much because of its non-intervention policy. Assume there were only two countries in the world, the US was a small open economy and UK was a large country, use IS??LM? model to graphically analyze how the increase of UK government spending change the real exchange rate (pounds/dollar) and the real output in the US, explain in detail.

Ahmet develops a computer controlled system to alleviate traffic jams in urban areas. He applies for the patent on 12 January 2013 in Turkey. The application is published on 12 August 2014 and the patent is granted on 3 March 2015. On 4 March 2015 City of London contacts Ahmet and ask for a license to use his new invention. Ahmet who realizes that the invention is not protected in UK attempts to get a patent but finds out that James has already applied for almost the same system on 10 August 2014 in UK.

1. Is it possible for Ahmet to get a patent in UK? Evaluate in terms of novelty, priority right and alternative ways of application (PCT and EPC).

2. Is it possible for James to get a patent in UK? Evaluate in terms of novelty.

3. From whom should City of London seek permission to use the system? Ahmet of James of both or none?

1. Ahmet develops a computer controlled system to alleviate traffic jams in urban areas. He applies for the patent on 12 January 2013 in Turkey. The application is published on 12 August 2014 and the patent is granted on 3 March 2015. On 4 March 2015 City of London contacts Ahmet and ask for a license to use his new invention. Ahmet who realizes that the invention is not protected in UK attempts to get a patent but finds out that James has already applied for almost the same system on 10 August 2014 in UK.

Answer the following questions accordingly

1. Is it possible for Ahmet to get a patent in UK? Evaluate in terms of novelty, priority right and alternative ways of application (PCT and EPC).

2. Is it possible for James to get a patent in UK? Evaluate in terms of novelty.

3. From whom should City of London seek permission to use the system? Ahmet of James of both or none?

Consider the ODE u" + lambda u=0 with the boundary conditions u'(0)=u'(M)=0, where M is a fixed positive constant. So u=0 is a solution for every lambda,

Determine the eigen values of the differential operators: that is

a: find all lambda such that the above ODE with boundary conditions has non trivial sol.

b. And, what are the non trivial eigenvalues you obtain for each eigenvalue