apples cost £2 and pears cost £4. For John the marginal Utility (MU) of the last apple consumed was 4 and MU of pears was 12. For Paul MU of last apple was 3 and MU of last pear was 6. Which person is not maximising utility and how can you tell? What should they do?

To determine which person is not maximizing utility, we need to compare the marginal utility-to-price ratio (MU/P) for both John and Paul.

The formula for marginal utility-to-price ratio is:
MU/P = Marginal Utility / Price

Let's calculate the MU/P ratio for both individuals:

For John:
MU of last apple = 4
Price of apple = £2
MU/P ratio of apple = 4 / 2 = 2

MU of last pear = 12
Price of pear = £4
MU/P ratio of pear = 12 / 4 = 3

For Paul:
MU of last apple = 3
Price of apple = £2
MU/P ratio of apple = 3 / 2 = 1.5

MU of last pear = 6
Price of pear = £4
MU/P ratio of pear = 6 / 4 = 1.5

Based on the calculations, it appears that Paul is not maximizing utility because his MU/P ratio for apples is lower than for pears.

To maximize utility, a person should allocate their consumption in a way that the MU/P ratio for each good is the same. In other words, they should consume each good until the MU/P ratio is equal for both goods.

In this case, Paul should consume more apples and fewer pears because the MU/P ratio for apples is lower. By increasing his apple consumption and decreasing his pear consumption, Paul can equalize the MU/P ratio for both goods, which will help him maximize his utility.