Assumptions: The 24 hours of the day can be divided into hours of work and hours of leisure. Americans work more than Europeans.
Therefore:
1. Americans value leisure more because they work more to be able to spend and enjoy it more.
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2. Europeans value leisure more because they grant it more time of the day than Americans.
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Hint: Try using one of Prof. Mankiw's Ten Principles of Economics: "the cost of something is what you give up to get it", and consider cost as the measure of value.
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Spoiler warning: the solution comes..
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Solution:
It is impossible to say (compare valuations), because using Mankiw's opportunity cost principle as a measure of value leads to a paradox:
(a) Americans are supposed to value leisure more because, when that is taken as desired (and the length of working as the measure of cost), they forgo more of it to have it (work more).
(b) At the same time, however, the very same principle applied to Europeans and work says that Europeans value work more, when that is taken as desired (and the length of non-working as the measure of cost), because they forgo more of it (wait so much) to have it.
From the latter it follows that Americans and Europeans value work differently. Hence, it is impossible to measure the value of leisure by the amount of work (as the first proposition does)*. And since it is impossible to measure the value of leisure, it is also impossible to measure the value of work, because the only variable we would be using is the amount of leisure (not-working).
Or the same paradox put otherwise: Americans can easily be thought to enjoy work more than Europeans because they devote more time to it. At the same time, they can be thought to enjoy leisure more than Europeans, because they work so much for it. Both of these propositions cannot be true at the same time, however, because Americans cannot be said to value -both- leisure and work more than Europeans just because they devote more time to -one- of these (Europeans could then be equally attributed the same - see (b) and * for this).
The terrifying conclusion is, however, that in the real world, with x things to value, it is equally impossible to (inter-personally) compare utility. For that, we would need a universal (read: equally valued) unit of measurement. Money comes close, but since we cannot put monetary value on leisure (the work-leisure problem - we don't know how much utility would be somebody foregoing to earn money), we cannot say money is valued by all to the same extent. Therefore, it cannot be used as a unit of comparison.
To sum up: everything is relative and we really know close to nothing. That's when the 'second best' solutions in science become the 'first best'.. :)
* - In case we use the ratios of leisure to work as a measure of work's value - that is, (b), then the valuation of leisure (value of work times the amount of work) would be higher also for Europeans, which is in contradiction with (a) - using the same Mankiw's principle. Here's the calculation:
If American and European work-leisure is divided in ratios of 2:1 and 1:2 respectively, the valuation of leisure would be (value of work times the amount of work): 1/2*2 (=1) for Americans, and 2/1*1 (=2) for Europeans.
In case we want to use the ratio of leisure from all available time as a measure of work's value, and the time as a ratio of all time available, then the numbers are: 1/3*2/3 for Americans, and 2/3*1/3 for Europeans, which makes them value leisure equally. :) If that is the case, then they can by the same token (mutatis mutandis) value work equally as well :)
