A firm is originally operating as a single-price monopolist that faces a market demand curve P(Q)=29716Q and total cost curve equal to TC(Q)=88,000+22Q, with constant MC equal to MC(Q)=22 for all units produced.

Part (a): How much output does the firm produce and at what price is each unit sold for?

Part (b): Calculate the firm's profit.

The firm now realizes there are actually two distinct groups of consumers that purchase their product, with the following demand functions:

P(q1)=3211/2q1

P(q2)=2851/4q2

Their total and marginal cost curves have not changed.

If the firm wanted to successfully practice third-degree price discrimination:

Part (c): How many units of output would they sell to group 1 and how much will each consumer in group 1 pay?

Part (d): How many units of output would they sell to group 2 and how much will each consumer in group 2 pay?

Part (e): How much profit is earned by the firm when they practice third-degree price discrimination?

Part (f): How much did profits rise by when the firm switched to using price discrimination?