Jeff Bezos and Elon Musk, the American entrepreneurs that have succeeded in their re- spective businesses, have recently decided to enter the market for space tourism with the ex- pectations that this business will grow exponentially in the coming decades. To reach their goals, Bezos launches the space tourism company Blue Origin (B), whereas Musk establishes the space tourism company SpaceX (S). The two companies choose strategically the quantities of spacecrafts they produce and sell. Because they use different technologies, Blue Origin and SpaceX have the following variable cost functions: VC(qB) VC(qs) = P 520gs + 20g 1400gs +40gs where 98 and qs are the quantities of spacecrafts produced by Blue Origin and SpaceX, respec tively. The world inverse demand function for spacecrafts is estimated to be as follows: p(Q) = 10740-20Q where Q=q8+gs and prices are expressed in U.S. dollars. Derive analytically showing your calculations: 1. Blue Origin's reaction function; 2. SpaceX's reaction function. 3. On a properly labeled graph plot the two reaction functions clearly indicating Blue Origin (on the z axis) and SpaceX (on the y axis). Derive analytically showing your calculations: 4. the quantities on and qs that maximize each firm's profits, that is, the Nash equilibrium for the Cournot model, and the profit-maximizing aggregate quantity Q = (a + qs); 5. the corresponding profit-maximizing market price p"; 6. the levels of profits II and II, that each company earns when choosing the profit- maximizing quantities. Which firm earns the highest profits, and why?