Question 2 (20 points)
Total industry output is given by =1+2 and the industry demand curve is given by ()==(11+2). If costs are given by
()= ;=1,2, determine the payoffs (profits) for each firm.
Question 3 (20 points)
Assuming the duopoly described in question (2), derive the Nash equilibrium levels of output for each firm.
Question 4 (20 points)
Assuming the duopoly described in question (2), derive the reaction functions for both firms.
Question 5 (20 points)
How would the problem depicted in question (2) change if firms choose prices rather than output? State what the demand for good 1 would look like as a function of both prices 1 2.
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.
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.
Sample Answer
Sample Answer
Question 2
The total industry output is represented by (Q = q_1 + q_2), and the industry demand curve is given by (P(Q) = 11 – 2Q). The cost functions for the two firms are (C(q_1) = 1q_1) and (C(q_2) = 2q_2). To determine the payoffs (profits) for each firm, we need to calculate the individual firm profits based on the given information.
Let’s calculate the profits for each firm:
– Firm 1 profit ((\pi_1)) = (P(Q)q_1 – C(q_1))
– Firm 2 profit ((\pi_2)) = (P(Q)q_2 – C(q_2))
Question 3
In a duopoly scenario, the Nash equilibrium occurs when both firms choose their optimal strategy, considering the other’s choice. The Nash equilibrium levels of output can be derived by analyzing the reaction of each firm to the other’s output choice. By finding the point where neither firm has an incentive to deviate from their chosen output level, we can determine the Nash equilibrium.
Question 4
The reaction functions for both firms indicate how each one adjusts its output level in response to the other firm’s output choice to maximize its own profit. By differentiating each firm’s profit function with respect to its own output, we can derive the reaction functions.
– Firm 1 reaction function: Find (\frac{d\pi_1}{dq_1} = 0)
– Firm 2 reaction function: Find (\frac{d\pi_2}{dq_2} = 0)
Question 5
If firms choose prices rather than output, the demand for good 1 would be a function of both prices ((P_1,P_2)). The demand for good 1 can be expressed as (Q = f(P_1,P_2)), where (Q) is the quantity demanded of good 1 depending on the prices set by both firms.
The relationship between the prices set by each firm and the resulting demand for good 1 will determine the equilibrium in a price-setting duopoly scenario. Analyzing how changes in prices affect demand will be crucial in understanding the implications of price competition between the two firms.
