1. The problem statement, all variables and given/known data When the income is greater than or less than the money required to buy the two goods at equilibrium (meaning when their marginal utility to price ratios are equal), how do I know which direction and how far from the equilibrium point to look at without evaluating every single combination's total utility, manually? 2. Relevant equations N/A 3. The attempt at a solution If I'm just trying to maximize total utility per dollar and I have no constrained income, I know to get the equilibrium quantity. That is to say, I know to buy the quantities of each good at which their marginal-utility-to-dollar ratios are equal. What I was initially trying to do, when the situation is not that of the previous paragraph, was to just purchase the one more good which has the highest marginal utility per dollar ratio until I no longer can purchase the good with the better marginal-utility-to-dollar ratio and, then, if I can afford the other good, I get it (unless its marginal utility is 0), but that doesn't always work. Please explain to me the/an algorithm to follow, which works for all cases, in an easy-to-understand manner since I am having a lot of difficulty with this! Any input would be GREATLY appreciated!