Question

decreased in order to reach the efficrent scale. 2. SpaceX is company considering building a hyperloop (a sealed system of tubes through which passenger pods travel free of air resistance and friction) from San Francisco to New York City. This system would dramatically reduce transportation times along the route. The hyperloop would cost $2.4 billion to build and nothing to maintain a. The following table gives the anticipated demand over the lifetime of the hyperloop. Find total revenue and marginal revenue for the various possible quantities of crossings. If SpaceX were to build the hyperloop, what would be its profit-maximizing price? Would that lead to the efficient level of output? Why or Why not? Price per Crossing Number of Crossings Total Revenue Marginal Revenue Marpalke in Millions in Millions 100 200 300 500 600 Profit maximizing price = Efficient output level? b. SpaceX is interested in maximizing profits, should it build the hyperloop? What would be its profit or loss? Profit c. If the government were to build the hyperloop, what price should it charge assuming its goal is to maximize welfare? Price

Answer 1

2a. Given below is the completed table.

Price $	No. of crossings (millions)	Total Revenue (millions)	Marginal Revenue
8	0	0	-
7	100	700	700
6	200	1200	500
5	300	1500	300
4	400	1600	100
3	500	1500	-100
2	600	1200	-300
1	700	700	-500
0	800	0	0

• Profit maximizing price is where Total Revenue (TR)- Total cost(TC) is maximized. As per the table ,the maximum Revenue that can be earned from building the hyperloop is 1600 million or 1.6 billion. Further Total cost of project is 2.4 billion. So total loss incurred = 2.4 - 1.6 = 0.8 billion. Here there is no profit maximizing price but rather loss minimizing price will be $4.
• Efficient output level will be anywhere including the end points between 300 to 400 crossings. This is because loss from the project is minimized at this level. Further at this level Marginal Revenue from production reaches its maximum and is still increasing at decreasing rate. Beyond this level, Marginal Revenue turns negative and more losses will pile up if more crossings are built above this level.

b. If SpaceX wants to maximize profits it should not build the hyperloop as the project will incur losses.The lifetime total revenue from the project is not sufficient to cover costs.The minimum loss from the project when it is operating at full efficiency will amount to 0.8 billion.

c. The welfare from the hyperloop will be maximum when consumer surplus is maximum.

This will be (Maximum price consumers are willing to pay - Price consumer actually pays) ×Maximum Quantity demanded.

or, Consumer surplus= (8-0) ×800 =$ 6400 million or $6.4 billion.

Therefore government should build 800 no. of crossings and charge $0 to maximize welfare.

d. The present cost of the project is 2.4 billion and the maximum wlfare that can be achieved is of $6.4 billion. Therefore if the cost overun is greater than $(6.4 - 2.4)

= $4billion then the project is undesirable as any extra dollar spent beyond $6.4 billion will not cause any further increase in consumer welfare.