Consider a two-period model in which there is a fixed supply of a depletable resource. The demand for this resource is constant over both periods and is given as:
P = 176 – 0.4Q and MC = 44
There is an initial resource endowment (supply) of 1000 units of the depletable resource.
a. Based on this information, what it the amount of the resource extracted in each period. Show your work as well as a graph showing the outcome in each period.
b. Now suppose the initial resource endowment (supply) is now given to be only 400 units of the good and you are told the discount rate (factor) is determined to be 8 percent. Given this information, how much of the resource will be extracted in time period 1 and time period 2 if you desire to satisfy the condition that the present value of the marginal benefit from the last unit in period 1 equals the present value of the marginal net benefit in period 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
The Amount of Resource Extracted in Each Period
a. To determine the amount of the resource extracted in each period, we need to find the quantity that maximizes the net benefit, which is the difference between the demand function and the marginal cost.
The demand function is given by: P = 176 – 0.4Q
And the marginal cost is given as: MC = 44
To find the quantity that maximizes net benefit, we set the marginal cost equal to the marginal benefit (which is the slope of the demand function) and solve for Q:
44 = -0.4
Simplifying, we have:
0.4Q = 132
Q = 330
Therefore, the amount of the resource extracted in each period is 330 units.
To graphically represent this outcome, we can plot the demand function and the marginal cost on a graph with Q (quantity) on the x-axis and P (price) on the y-axis.
Graph
The point where the demand curve intersects with the marginal cost curve represents the quantity extracted in each period, which in this case is 330 units.
Resource Extraction with a Reduced Initial Supply
b. Now let’s consider a scenario where the initial resource endowment is reduced to 400 units and a discount rate of 8 percent is applied.
The present value of a future benefit (B) or cost (C) can be calculated using the following formula:
PV = B / (1 + r)^t
Where PV is the present value, r is the discount rate, and t is the time period.
In this case, we want to solve for Q1 and Q2, which represent the quantities extracted in period 1 and period 2, respectively.
Let’s denote Q1 as the quantity extracted in period 1 and Q2 as the quantity extracted in period 2. The present value of the marginal benefit from the last unit in period 1 can be calculated as:
PV1 = (176 – 0.4Q1) / (1 + 0.08)
The present value of the marginal net benefit in period 2 can be calculated as:
PV2 = (176 – 0.4Q2 – MC) / (1 + 0.08)^2
To satisfy the condition that PV1 equals PV2, we set these two equations equal to each other and solve for Q1 and Q2:
(176 – 0.4Q1) / (1 + 0.08) = (176 – 0.4Q2 – MC) / (1 + 0.08)^2
Simplifying this equation, we have:
176 – 0.4Q1 = (176 – 0.4Q2 – MC) / (1 + 0.08)
Now let’s substitute the values for MC and solve for Q1 and Q2:
176 – 0.4Q1 = (176 – 0.4Q2 – 44) / (1 + 0.08)
Multiplying both sides by (1 + 0.08), we get:
(176 – 0.4Q1)(1 + 0.08) = 176 – 0.4Q2 – 44
Expanding and simplifying, we have:
193.6 – 0.448Q1 = 132 – 0.4Q2
Rearranging terms, we get:
0.448Q1 – 0.4Q2 = 61.6
To find Q1 and Q2, we need another equation. Since we are told that the demand is constant over both periods, we can set Q1 equal to Q2:
Q1 = Q2
Substituting this into our equation, we have:
0.448Q1 – 0.4Q1 = 61.6
Simplifying, we get:
0.048Q1 = 61.6
Q1 = 1283.33
Since Q1 cannot be a fractional value, we round down to the nearest whole number:
Q1 ≈ 1283
Since Q1 and Q2 are equal, this means that Q2 is also approximately equal to 1283 units.
Therefore, if we desire to satisfy the condition that the present value of the marginal benefit from the last unit in period 1 equals the present value of the marginal net benefit in period 2 with a reduced initial supply of 400 units and a discount rate of 8 percent, approximately 1283 units of the resource will be extracted in each period.
