Sports Statistics

by | Aug 27, 2021 | Sports

Q1: You are attending a championship soccer match with your family. In your pocket only $40 to spend on Popcorns(S) and Cokes (C), supposed to allocate such amount to maximize satisfaction of the two goods, where the price of popcorn is $5 and the price of coke is $4, looking at the table below:
Various levels of S and C MUs MUs/Ps MUc MUc/Pc
1 40 120
2 30 80
3 25 40
4 20 32
5 15 16
6 10 8
MUs = marginal utility of popcorn, Ps = price of popcorn
MUc = marginal utility of coke, Pc = piece of coke

Answer the followings:

  1. Fill up the blanks above?
  2. Find the combination of popcorns and cokes yields and the level of utility, subject to the budget constraint?
  3. Calculate the total utility of the optimal consumption of the two good?
  4. What is the marginal rate of substitution(MRS) in such case?
  5. State the budget equation in this case?
  6. Graph the budget line and an indifferent curve, showing the optimal point?
  7. What does the indifferent curve represent? How it relates to the indifference map?
  8. What is the level of marginal utility per dollar spent, where you get the maximization or the optimal equation of the two goods?
  9. The demand curve is derived from the marginal utility concept, explain?
  10. Can you classify this case as a corner solution? Explain?

Q2: Decided on open tailor shop, the following table gives the level of outputs(shirts) produced daily, with the least cost of input combinations (labor wage(w) = $300, and cost of capital, sewing machine(r) = $200) per day:
output Labor # Capital # Long run total cost (LTC) Long run average cost(LAC) Long run marginal cost(LMC)
100 10 7
200 12 8
300 20 10
400 30 15
500 40 22
600 50 30
700 60 42
Answer the followings:

  1. Fill up the blanks above?
  2. Write down the cost equation?
  3. State the total production function?
  4. Draw up the graph for LAC and LMC in relation to the output?
  5. Graph the Isoquant curve as well as the Isocost curve, with the optimal input combination?
  6. In this case, you are operating in competitive market, what are the characteristics of such market?
  7. At which price you are supposed to sell the shirt?
  8. Draw up the expansion path for outputs and costs in the table above?
  9. What is the approximate level of output(varies discretely by 100 units in the table), where profit is maximized and you are economically and technically efficient?
  10. What is the Marginal Rate of Technical Substitution (MRTS) in this case?
  11. Is the cost structure in the question long-run cost or short-run cost ones, what is the difference between the two, and how can they be related?
  12. There are many factors reduce costs, and shift LAC downtrend, identify three of them?
  13. At which level of output is the Minimum Efficient Scale(MES)?
  14. What kind of demand curve you are facing in this market?
  15. Is this competitive market, what is the economic profit, and should it be different in value from the opportunity cost? Explain?

Q3: Abdullah want to expand the capacity of his restaurant, but not sure of the 2020 economic growth (GDP) of the Saudi economy. He has the probability of 40% that the economy will maintain the expected growth rate in 2019 (1.8%) and the probability of 60% it will be little higher (2.1%) as the IMF forecasted. Accordingly, the table below is:
Growth rate 2.1% 1.8%
Probability Dist. 60% 40%
Profit Profit($Million) Profit($Million)
A. Decision maintain capacity 100 persons 3 2
B. Decision expand capacity by 20% 4 1
Answer the following:

  1. Compute the expected profits for both decisions?
  2. Based on the expected profit only, which decision should Abdullah make?
  3. Compute the Standard Deviation for decisions A and B, facing Abdullah?
  4. Which decision would Abdullah make, using the coefficient of variation?
  5. If Abdullah has no idea of the probability distribution of economic growth, operating in uncertainty world. Using the information above, what decision would Abdullah make, according to each of the following rules:
    A. Maximax:
    B. Maximin:
    C. Minimax Regret:
    D. Equal Probability:
  6. Which decision is riskier, and how can you classify yourself as risk lover or averter or neutral?

Sample Solution

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.


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God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.

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