do by handwriting Continuous random variable X has th.pdf

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Discuss the issue of vertical integration. Refer to the various motives that can lead to vertical integration. - Consider then the following quantitative exercise. A monopolist upstream firm (1) produces an intermediate good with no costs. A monopolist downstream firm (2) uses this intermediate good as an input to produce a final consumption good, whose market demand is Q = 60 p2. The cost function of firm 2 is made of a fixed cost of 5 plus the cost of the intermediate good. We assume that the intermediate good is used in the production of good 2 as follows: 2 units of the intermediate good are needed for each unit of production of the final good 2. Compute the total aggregate profits of firms 1 and 2, and price p2 for the final good. Argue and check that aggregate profits are lower than they would be if the two firms chose to vertically integrate, and that the price of the final consumption good 2 would be lower if the two firms vertically integrated..

do by handwriting
(Continuous) random variable, X has the density function f(x)={2(1x),0,for0x1elsewhere (a) Sketch
the graph of this p.d.f. (b) Determine and sketch the graph of the distribution function of X. (c) Find
i. P(0X0.5) ii. P(0.25X0.75) iii. P(X=0.75) iv. P(X0.75) (3+3+(4+4+2+2)=18marks)

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a.) Find the optimal quantity of the public good that would be supplied by the government. What is the total willingness-to-pay and the total cost of supplying this quantity of the public good? b.) If both citizens must be taxed equally to provide tax revenue to pay for provision of the public good, will it receive a majority vote (i.e., will both citizens support the measure)? Explain your reasoning.

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3. Voluntary contributions toward a public good Dina and Juanita are considering contributing toward the creation of a bulding mural. Each can choose whether to contribute $300 to the building mural or to keep that $300 for a new suit Since a building mural is a public good, both Dina and Juanita wilf benefit from any contributions made by the other person. Specifically, every dollar that ather one of them contributes will bring each of them $0.70 of benefit. For example, if both Dina and Juanita choose to contribute, then a total of $600 would be contributed to the building mural. So, Dina and Juanita would each receive $420 of benefit from the building mural, and their combined benefit would be $840. This is shown in the upper left cell of the first table. Since a new suit is a private good, if Dina chooses to spend $300 on a new suit, Dina would get $300 of benefit from the new suit and Juanita wouldn't receive any benefit from. Dina's choice. If Dina still spends $300 on a new suit and Juanita chooses to contribute $300 to the building moral, Dine would still receive the $210 of benefit from Juanita's generosity. In other words, if Dina decides to keep the s300 for a new suit and Juenita decides to contribute the $300 to the public project, then Dina would receive a total benefit of $300+$210=8510, 3 uanita would receive a total benefit of 3210, and their combined benefit would be $720. This is shown in the lower left cell of the first table. Complete the following table, which shows the combined benefits of Dina and Juanita as previously described.Of the four celts of the table, which gives the greatest combined bencfits to Dina and Juanita? When both Dina and Juanita contribute to the building mural When neither Dina nor Juanita contributes to the building mural When Dina contributes to the building mural and Juanita doesn't, or vice versa Now, consider the incentive facing Dina individuolly. The following table looks similar to the previous one, but this time, it is partially completed with the individual benefit data for Dina. As shown previously, if both Dina and Juanita contribute to a public good, Dina receives a benefit of $420. On the other hand, if Juanita contributes to the building mural and Dina does not, Dina receives a benefit of $510. Complete the right-hand column of the following table, which shows the individual benefits of Dina: Hint: You are not required to consider the benefit of Juanita. If Juanita decides to contribute to the building mural, Dina would maximize her benofit by choosing to the building mural, On the other hand, if Juanita decides nok to contribute to the building mural, Dina would maximize her benefit by choosing building mural. These results illistrateIf Juanita decides to contribute to the building mural, Dina would maximize her benefit by choosing to the bulleng mural. On the other hand, if Juanita decides not to contribute to the building mural, Dina would maximize her buiding maral. These result.

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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence. The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth. Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration. The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority. Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages. Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.

The Roman Empire A Historical Colossus.pdf

The Roman Empire A Historical Colossus.pdf

The Roman Empire A Historical Colossus.pdf

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