Question

One day you walk out your front door looking for adventure. You quickly see a guy standing by the side of the road with a green dialogue bubble hovering over his head. You suspect that this might indicate that talking to him may lead to some kind of adventure so you do so. It turns out that he is a wizard of some sort who requires the tusks of a certain type of wild pig to make a potion. He tells you that the pigs live in forest on the outskirts of town. The potion can’t be made without at least one tusk but adding additional tusks makes it stronger. He proposes the following deal. [Here’s where this becomes an econ problem] If you bring him one tusk, he will give you 100 gold pieces. If you bring him 2, he will give you 180. For 3 he will give you 240, for 4 he will give you 290, for 5 he will give you 330, for 6 he will give you 360, for 7 he will give you 380 and if you give him 8 tusks he will pay you 390 gold pieces. (Assume you get the same amount of experience points regardless of how many tusks you bring back.) This sounds like an acceptable adventure for you so you take up your +1 longbow and head for the forest. When you get there, though, there is a hunter on the side of the road with a cart full of boar tusks trying to take the fun out of it. Apparently, he has killed all of the boars already so your only option is to buy them from him. He is willing to sell you one tusk for only 5 gold pieces. To get him to part with 2, you would need to pay him 15. 3 tusks will cost you 30, 4 will cost 50, 5 will cost 80, 6 will cost 120, 7 will cost 170 and 8 will cost 230. 1. How many tusks do you want to buy from the hunter and sell to the wizard in order to make the most profit? 2. How many gold pieces will you earn from this?

Answer 1

Now, let us first tabulate the given problem. The first column shows the number of tusks bought/sold, the second column shows the gold pieces the wizard pays us, the third column shows the pieces we pay to the hunter, and the fourth column shows the profit we make. Profit is calculated by subtracting the amount paid to the hunter from the amount received from the wizard, column 2 - column 1.

Number of tusks bought/sold	Wizard (Received)	Hunter (Paid)	Profit made
1	100	5	95
2	180	15	165
3	240	30	210
4	290	50	240
5	330	80	250
6	360	120	240
7	380	170	210
8	390	230	160

The table above follows the law of diminishing marginal utility. As the number of tusks bought/sold increases, the utility derived from them goes on diminishing.

The maximum utility (profit) for us derived at 5 tusks. For five tusks, we will pay 80 gold pieces to the hunter and receive 330 pieces from the wizard. Our profit here would be 330 - 80 = 250 gold pieces. This is the maximum that we can earn from this adventure.