Final answer:
Option D is the correct answer. If Thanatos sells one additional unit in a Cournot equilibrium market, both Thanatos' and Alcyoneus's profits are likely to decrease due to the potential impact on market price and each firm's market share.
Step-by-step explanation:
The scenario describes a duopoly (a market with two producers) in which both Alcyoneus and Thanatos are providing internet access in Olympus at a Cournot equilibrium. In this context, if Thanatos decides to sell one additional unit, moving from 250 to 251 units, it may trigger several outcomes. Given the information provided, if both firms are operating at a profit-maximizing level, an increment in quantity supplied by Thanatos could potentially decrease Thanatos' profits due to a possible reduction in market price from increased supply, assuming demand is unchanged. Moreover, an increase in output by Thanatos potentially leads to a decrease in Alcyoneus's profits, since the additional supply by Thanatos could lower the market price, reducing the profitability of each unit sold by Alcyoneus or causing them to lose market share. Therefore, the most likely outcome from Thanatos increasing production by one unit is option D: will decrease; will decrease.