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Blackbeard's demand functions for grog, x 1 , and bread, x 2 , are (if his income and the goods' prices are such that he
Blackbeard's demand functions for grog, x 1 , and bread, x 2 , are (if his income and the goods' prices are such that he buys positive quantities of both goods): x 1 = 2p 1 M p 1 p 2 and x 2 = 2p 2 Mp 1 p 2 (Aside: As an exercise, you can show that these are indeed the demand functions if Blackbeard's utility function is: U(x 1 ,x 2 )=(x 1 1)(x 2 1).) Starting from the situation where Blackbeard's income is M=9, the price of grog is p 1 =2, and the price of bread is p 2 =1, how does Blackbeard's optimal bundle change if the price of grog, p 1 , increases by a small amount (and all else remains the same)
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