AutoInvoice is an online payment system provider for small businesses, specializing in the needs of auto body shops. They have collected extensive data on the shops' willingness to pay for AutoInvoice to process transactions. Assume that AutoInvoice supplies to 1000 similar auto body shops, and that each identical shop needs up to 1000 transactions per month to be processed. Each shop is willing to pay $4 for each of the first 100 transactions, $2 for each of the next 500 transactions and $1 for each of the remaining 400 transactions. AutoInvoice's marginal cost of executing a transaction is zero. Problem 3a) (5 points) If AutoInvoice is going to charge a simple price per transaction for its service, what price maximizes its profit? Problem 3b) (3 points) If AutoInvoice sets its price at $2 per transaction, how much consumer surplus does each auto body shop get? Problem 3c) (5 points) AutoInvoice's CEO wants to change its pricing model. AutoInvoice would charge a monthly subscription fee equal to the surplus you found in part (b) and then shops who subscribe would also pay $2 per transaction. How much profit per month will AutoInvoice make from this subscription-and-price plan? Problem 3d) (5 points) What subscription-and-price-per-transaction combination would maximize AutoInvoice's monthly profits? Problem 3e) (5 points) AutoInvoice has implemented the plan you found in part (d). However, your marketing department has identified another potential set of customers: there are 1000 auto glass installers potentially interested in AutoInvoice's payment system. Each of the glass installers is willing to pay up to $2 to process up to 300 transactions per month. AutoInvoice's CEO wants to add a second option in its pricing model: instead of the subscription-and-price you found, a customer could choose to pay a flat $2 per transaction. Will this attract the glass installers? Do you foresee any problems with this? Problem 3f) (7 points) Assuming the CEO is adamant about offering the flat $2 per transaction (with no quotas on the number of transactions allowed), what other product offering should AutoInvoice have in order to maximize its profit? Problem 3g) (5 points) If AutoInvoice's fixed costs are $1m per month, how much monthly profit will AutoInvoice make?