Sony PS5 Pricing Sony has released its latest game console, Playstation 5 (PS5). The price is set to be $400 per console. It is rumored that Sony incurs a marginal cost of $450 to produce a PS5, which is higher than the price. In other words, Sony is losing money on each PS5 sold. Based on the following hypothetical model, you are asked to rationalize this seemingly suboptimal pricing. 110-5, where Q is measured in Sony on average earns an incidental revenue of $2 on each video game sold. The marginal cost of making and selling a video game is negligible. It is estimated that each PS5 console sold on average generates sales of 100 games over its life. The demand for PS5 is estimated to be Q = million units. (a) Write down Sony's profit function from selling the consoles and the video games expressed in terms of Q. (9 points) (b) Find the profit-maximizing price and output of PS5 consoles, where Sony acts as a monopoly. (20 points) (c) Discuss why the seemingly suboptimal pricing is in fact optimal, that it makes sense for Sony to lose profit at the point of sale of the console. (6 points)