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Fund Raising at the Margin
The MR = MC profit maximization rule could be applied to fund raising.

Todd plans to throw a series of small preview parties to raise funds for his completed independent film. He sends out invitation letters to 20 guests at a time to ask how much each of them would donate to the event. He will accept a donation if it at least covers his variable cost per head. The responses to his first mailings (arranged in descending order by the dollar amount of donation) are as follows:

The caterer wants $100 as a cover charge for the whole event and $10 each guest.

1. How many guests should he invite to his first preview party to maximize his raised funds?

2. When should Todd draw the line between accepting and rejecting the donation?

3. Does maximizing his Gross Profit always result in positive Net Profit?

Diagram

Marginal profit = MR - MC

To maximize Gross Profit, MR must be at least equal to MC.

That means only the first 9 guests should be invited.

But Gross Profit must be net of Fixed Cost to see if there is any Net Profit

Fixed Cost = 100

Net Profit = Max Cumulative Gross Profit Fixed Cost = 305 -100 = 205