While other forms of urban transportation still exist, assume that Uber and Lyft are the only two companies that provide transportation that can be called with an integrated phone app - "on-demand transportation". They are unique transportation companies in that respect and compete largely (and fiercely) with each other.

Market demand for 'on-demand transportation' is as follows:

P=60002Q

Where P= price in thousands of miles traveled and Q is thousands of miles.

Total costs for Uber are:

TCUber=400,000+3qUber2

Total costs for Lyft are:

TCLyft=450,000+2qLyft2

If Uber and Lyft each act to maximize profits:

1. What will be the output quantities for each firm?

2. What is total output for the market and market price?