Fruit flies, like almost all other living organisms, have built-in circadian rhythms that keep time even in the absence of external stimuli. Several genes have been shown to be involved in internal timekeeping, including per (period) and tim (timeless). Mutations in these two genes, and in other genes, disrupt timekeeping abilities. Interestingly, these genes have also been shown to be involved in other time-related behavior, such as the frequency of wingbeats in male courtship behaviors. Individuals that carry particular mutations of per and tim have been shown to copulate for longer than individuals that have neither mutation. But do these two mutations affect copulation time in similar ways? The following table summarizes some data on the duration of copulation for flies that carry either the tim mutation or the per mutation (Beaver and Giebultowicz 2004):

b) Do the populations carrying these mutations have different variances in copulation duration? Enter the calculated F-value.

c) Do the populations carrying these mutations have different variances in copulation duration? Finish this hypothesis test and describe your conclusion.

3.50

Passedix is a game of chance played with three fair dice. Players bet whether the sum of the faces shown on the dice will be above or below ten. During the late sixteenth century, the astronomer and mathematician Galileo Galilei was asked by the Grand Duke of Tuscany to explain why “the chance of throwing a 9 with three fair dice was less than that of throwing a 10.” (Interstat, Jan. 2004) The grand duke believed that the chance should be the same because “there are an equal number of partitions of the numbers 9 and 10.” Find the flaw in the Grand Duke’s reasoning and answer the question posed to Galileo. Hint: What the Grand Duke was saying is: There are six ways to get a 9: 1+2+6; 1+3+5; 1+4+4; 2+2+5; 2+3+4; 3+3+3. There are also six ways to get a 10: 1+3+6; 1+4+5; 2+2+6; 2+3+5; 2+4+4; 3+3+4. [10 pts] 3.56 Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd} B: {Sum of the numbers showing is 9, 11, or 12} Are events A and B independent? Why? [10 pts]

Matlab

Given an array of monthly rainfall that covers some number of years

(where each column is a month and each row is a year)

create a function YEARLY that prints the average rainfall for each year

For example, if the information below were to be stored in a 5x12 matrix RAIN...

     J F M A M J J A S O N D
2003 1 2 1 2 1 2 1 2 1 2 1 2
2004 1 1 1 1 1 1 1 1 1 1 1 1
2005 2 2 2 2 2 2 2 2 2 2 2 2
2006 1 2 3 1 2 3 1 2 3 1 2 3
2007 5 1 2 4 3 3 5 1 2 4 3 3

Then the function YEARLY(RAIN) would print the result

average rainfall for year 1 is 1.500000
average rainfall for year 2 is 1.000000
average rainfall for year 3 is 2.000000
average rainfall for year 4 is 2.000000
average rainfall for year 5 is 3.000000

Note that only the rain amounts (not the labels) are stored in the input array (RAIN).

De Beers, a diamond mining and distribution firm, is one of the most successful monopolies in history. The firm used numerous tactics to successfully control supply and demand. Read the article 'Here's why diamonds are so expensive' (Links to an external site.), and watch the video 'Why engagement rings are a scam' (Links to an external site.) [warning: contains strong language], and respond to the following prompts in a post with a minimum of 250 words. Feel free to bring in additional references to these reply posts. Using economic principles and models, explain how De Beers are able to set high prices for their diamonds? In recent times, rival firms in Canada, Australia, and Russia have found huge deposits of precious stones. What would happen to prices and supply of diamonds if De Beers allowed their competitors to enter the diamond market. Use economic principles and models to explain your answers. In 2004, De Beers was charged by the US Department of Justice for violating antitrust laws. What is the purpose of antitrust laws? What other kind of government policies exist in dealing with monopolies? Now that you have learned about De Beers and the diamond market, would you spend or expect your partner to spend two months of your/your partner's salary on an engagement ring? Explain your answer.

Case: Airport Authority

The Airport Authority (AA) has been under considerable pressure from the Regional Government to increase capacity at Changow Airport. Originally built fifty years ago as a small regional airport serving a population of 250000, Changow's single runway is at full capacity for 20 hours of the day. The region's population has climbed to over 5 million and much of this growth in air travel is due to the rapid economic expansion of the region from industry and tourism.

The options facing the AA are not attractive. To increase capacity at Changow presents some serious engineering problems on the only available land to the north, over which a new runway must be built. The problems are due to local geology and some regular flooding from the Hankse River delta flowing nearby. A residential population of about 1 million lives within an area of 15 kilometers to the north of the airport and they believe that their lives would be affected severely by a major new runway.

Moreover, economic developments close to the airport crowd right up to the southern boundary, which is the only suitable means of access from Changow city for a wider road. The land close to the east and west boundaries contains mainly high income residential properties, mixed with isolated green sites, containing rare natural plants, exotic birds and other small wildlife. The State Government recently designated some of these areas as ‘National Heritage Sites’.

The other option is to build a completely new airport at Fongow, at a distance of forty kilometers from Changow, in agricultural land, presently farmed by thousands of small holders, whose families have worked the land there for many generations. New access roads would be needed, plus, perhaps a railway system which would require many bridges and tunnels, and the airport would be close to high wooded hills. There are doubts about the operational feasibility of building an airport so far from the regional capital.

The local political representatives, all members of the governing coalition, favor expansion of Changow airport on the grounds of ‘national economic development’, ‘social progress’ and national pride. So does local business, which claims that the current airport is holding back economic expansion in the region. Airport passengers, business and tourist alike, are plagued by long delays to flights and missed connections, and traffic jams during access and egress/way out along the airport's single and inadequate southern road to Changow city.

Public disquiet/worry about proposals to expand Changow airport have surfaced and are attracting media interest. The main opposition comes from local residents around the airport, though they do not yet form a majority. On the southern boundary, people living along the main road to the airport oppose widening the road because this would mean demolishing many thousands of homes. People living just behind these houses oppose widening because this brings the new road right up to their properties. A ‘Homes Before Roads’ campaign is underway.

People to the north oppose a new airport runway because of the impact during construction and afterwards on the residents who would have to move to make way for it, and on those left behind, who would be near aircraft taking off and landing. A ‘Hands off the Hankse’ campaign has been formed.

1. Summarize the main finding(s) of the case.

a. How do you calculate a commodity's price elasticity of demand?

b. If a commodity's elasticity is -1.25, is its price elasticity elastic or inelastic? Explain. What does that imply about the relative changes in price and quantity?