Suppose that Alyssa spends all her income on video games and DVDs and her marginal utility per dollar from video games equals that from DVDs. Is Alyssa maximizing her utility? Now, suppose that the price of a DVD falls
Should Alyssa change the combination of goods she consumes? If yes, how? Explain.
If Alyssa spends all her income on video games and DVDs and her marginal utility per dollar from video games equals that from DVDs, both utility maximization conditions are met and therefore Alyssa maximizes her utility. If the price of a DVD falls, Alyssa's marginal utility per dollar from DVDs becomes greater than that from video games. Therefore, if she spends a dollar more on DVDs and a dollar less on video games, her utility gain from the increased consumption of DVDs will be greater than her utility loss from the decreased consumption of video games and hence her total utility increases. So, to maximize her utility, Alyssa should increase her consumption of DVDs and decrease her consumption of video games.
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