Back to the original question, if the amount of apples he can purchase goes down, can he make up the shortfall by substituting pears?

A few basics, we assume the consumer knows what he likes, knows the total cost of everything, and the consumer tries to get the most out of his money.

With these assumptions, we consider the 10 apples 6 pears, bundle to be his 'most preferred' bundle. In other words, this is the best he could get with his money. The only way he could fully substitute pears for apples in the case of a price increase is if he A. considers apples to be just as good as pears, and B. there is no price difference. This means, that before the price change, 16 apples or 16 pears, or any other total of apples + pears that adds up to 16 is just as good. It also means that he just choose 10 apples, 6 pears by complete randomness, because he does not see any difference between apples and pears. If the price of apples goes up, he will buy 16 pears. Because 16 pears was already considered just as good as 10 apples, 6 pears, his utility (happiness) did not change. This also requires that there is no decreasing marginal utility for pears or apples, at least below a total of 16.

This is the only example I can think of where he could make up the shortfall of a price increase. But, this example requires several circumstances that are just not normal, perfect substitutes, no decreasing marginal utility within our possible bundles, and no increase in the price of pears due to the increase in price of a substitute*. __So, the answer is, no, he cannot make up the loss of happiness from less apples by buying more pears, unless we have a very rare set of circumstances.__

*Note: His purchase of more pears should not increase the price, however if everyone considers pears a substitute for apples, when apples price goes up, a large number of people buy more pears, and that shifts the supply curve, causing the price of pears to increase. Ugh, I completely forgot, substitutes by definition increase in price together, so unless only a very few people consider apples and pears substitutes, then the price increase in apples will decrease their utility, this just makes the rare case where he does not end up worse off even rarer (or non-existant).