A consumer makes purchases of an existing product X such that the marginal utility is 10 and the price is $5. The consumer also tries a new product Y and at the current level of consumption it has a marginal utility of 8 and a price of $1. The utility-maximizing rule suggests that this consumer should ?

Increase consumption of product Y and decrease consumption of product X

Explanation:

The utility maximization rule states that consumers decide to allocate their money resources so that the last dollar spent on each product purchased yields the same amount of extra marginal utility.

based on the law of marginal utility, as long as one good provides more utility per dollar, the consumer will buy more of that good.

We will now examine the marginal utilities per dollar of the two goods- X and Y.

Marginal utility per dollar of good X = 10/5 = 2 units per dollar

Marginal utility per dollar of good Y = 8/1 = 8 units per dollar

This means that the consumer will purchase more of  Y than X since its marginal utility is higher.

consume more units of Y and less units of X until the utility per dollar is equal for both goods.

Explanation:

The utility-maximizing rule basically states that consumers will purchase the combination of goods that maximize the utility obtained per dollar.

This rule works with the diminishing utility law, which means that every additional unit consumed of a product will yield a lower utility.

In this case, product X yields 2 utils per dollar (= 10 / $5), while product Y yields 8 utils per dollar ( = 8 / $1). According to the diminishing utility law, the second unit consumed of product Y will no longer yield 8 utils per dollar, it will yield a lower amount of utils. On the hand, if you consume less of product X, the utils per dollar obtained by consuming lesser amounts will increase. I.e. the more you consume a good, the less utility you get from additional units consumed, and the less you consume a good, the more utility you get from consuming the remaining units.

Now we go back to the utility-maximizing rule, which tells us to consume more units of Y and less units of X until the utility per dollar is equal for both goods.

e.g.

                   product Y                                    product X

units consumed       utils per $            units consumed       utils per $

            1                         8                               8                           2

            2                        6                               7                           3

            3                        4                               6                           4

if this table was real, then the consumer should purchase 3 units of Y and 6 units of X