(a) Write out functions for the Willingness to Pay for both consumers, WTP and WTPL (b) Write out the profit-maximizing condition the firm uses when setting the quantity q. Determine the optimal level of q. How does q compare to the amount that would be sold to the high demand consumer in a competitive market? (c) Write out the profit-maximizing condition the firm uses when setting the quantity q when the firm wants to insure that high-demand consumers do not want to take the contract L. (incentive compatibility). Determine the optimal level of q. How does qz compare to the amount that would be sold to the low demand consumer in a competitive market? (d) Find the amounts that should be charged for q and q (TL and TH), and write out the contracts H and L. What is the average price ($/minute ) of each user