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Because value(X) is constant, your observation boils down to a comparison of value(8 hours leisure time) and value(X) + 2 * value(3 hours leisure time). I did

Because value(X) is constant, your observation boils down to a comparison of value(8 hours leisure time) and value(X) + 2 * value(3 hours leisure time). I did consider the value of leisure time, which I arbitrarily set to $100/hr (I just called this time, but unsold time can be exchanged 1:1 for leisure time). You seem to be objecting to my assumption that the marginal value of time is constant for the workers. I agree with this objection (in fact, I raised it myself in the footnote). However, even without this simplifing assumption, there are still situations where selling ones time is a net positive. >By restricting the entire world to the two actors wanting to produce one X one can keep money out of the equation. My entire argument can be made without invoking money. Indeed, I believe the non monetary form is more compelling, but also more abstract. Again, I will invoke the idea indifference. We say that things X and Y have equal value to person A if she is just as happy receiving 1 X as she is receiving 1 Y. With this concept we can replace "money" with any object of value and have an equivalent analysis. Of course, the selected object would itself have diminishing returns, but this is equivalent to an increasing marginal value of ones time, which I have already addressed. Ultimately, to properly explore this route, I would formalize an abstract notion of "utility" as an equivalence class over indifference. I hope this explanation makes sense, doing it properly would take far to much effort to put into an internet comment. >where is this money coming from, From selling the X to the society? The above framework provides a nice way to sidestep this issue. Let U be the utility function. So U(5 hours) is the value of 5 hours of time. [0]. For simplicity, assume that A and B share a utility function. Suppose that A and B are not selling X, but rather using it themselves (for simplicity, suppose that X is a widget that A and B can share without conflict). We know that X is worth at least 2 * U(5 hours). Suppose that 2 * U(5 hours) > U(8 hours). In this case, by my previous argument, it would be preferable for A to do all of the work, and B to barter something worth between U(8 hours) - U(5 hours) and U(5 hours) for his share of X. Ultimately, this argument is just a rediscovery of the value of trade and specialization. To translate a minimum wage into this framework, we would define some artificial lower bound for the compensation A needs to be provided in a trade such as this. If this minimum value is less than U(8 hours) - U(5 hours) or U(5 hours), then we are just influencing how wealth gets distributed between A and B. However, if the minimum value to big, than the above trade is prohibited, even though we have seen that it is strictly beneficial. >will this raise the price or decrease the monetary value of an hour of work? What do you mean by "monetary value of an hour of work". Returning to a more realistic employer/employee example, there are two important monetary values: the value the employee gives to an hour of work, and the value the employer gives to an hour of work. From the employer perspective, the value of an hour of work is V(X)/T, where V(X) is the value of X [1], and T is the time spent making it. V(X) is independent of how long it took to make, which means that as the work takes longer, the value of an hour goes down to the employer. From the employee perspective, the issue is a question of their utility function. Assuming a reasonable utility function, I would expect the marginal value of an hour to increase to the employee. That is to say that the employee needs more money to be indifferent to working the last 2 hours than she does for any of the prior 2 hours. If this is the case, than the value of an hour to the employee goes up with the time. [0] More formally, U(5 hours) is the equivalance class of objects for which the person would be indifferent to spending 5 hours of time to obtain. [1] Or rather, V(X) is the labor-excluded profit of X.

danbruc 10y ago
Okay, after rethinking it once a gain I will move a bit towards your position. By increasing the required work for one X from 8 to 10 hours we are definitely introducing an inefficiency so we are losing something somewhere, we are doing 2 hours of unnecessary work. Assuming both agents can share the X or get to use half the X in both scenarios, we can just leave it out of the equation as mentioned before. If one gets the same value from X in both scenarios, then working 5 hours is strictly preferable over working 8 hours and not working is strictly preferable over working for 5 hours. So this looks somewhat like the prisoner's dilemma. Let A and B be the scenario that agent A respectively agent B works 8 hours and AB the scenario that both agents work 5 hours each. Then the preferences for agent A are B > AB > A and for agent B they are A > AB > B. But that doesn't help much, no matter which transition you consider, one agent will be better off and one will be worse off. So there is still a conflict. I acknowledge that an inefficiency gets introduced when the work is split but also want to maintain that 3 hours of leisure time twice is more valuable than 8 hours of leisure time once. Surly value can not increase and decrease at the same time. I am more certain that the inefficiency is real than what the shape of the value function for leisure time is so I will pick the former one and conclude that 8 hours of leisure time are - contrary to my earlier comment - more valuable than 3 hours of leisure time twice. So do I have to say that maximizing the total value is the wrong metric? Do I have to try to assign a value to the fairness of work distribution? Why wouldn't that already show up in the individual value functions? I am a bit stuck here. But I may have a way around that, I am just not sure how good the argument is. One obvious problem is that in case agent A does all the work, then agent B has no means to transfer some of the additional value from his additional leisure time to A. Maybe he could give away some of his share of X. But now I can no longer ignore the value function for X and that hopefully saves my argument and I avoid the conflict between decreasing and increasing total value without the need to explicitly appeal to the value of fair work work distribution because it is in the two value functions for X and leisure time. But I am not sure, I did not think this fully through. I think in the end it boils down to nonlinearities between the individual and the global view, i.e. we can globally waste 2 hours of work but still increase the total value because we have to take the global set of things, split it up for all individuals, push them through the nonlinear value functions and then sum it up again. Now it is no longer necessary that a global loss of 2 hours results in a global loss of value even if all the individual value functions are monotone.

danbruc 10y ago

Okay, after rethinking it once a gain I will move a bit towards your position. By increasing the required work for one X from 8 to 10 hours we are definitely introducing an inefficiency so we are losing something somewhere, we are doing 2 hours of unnecessary work. Assuming both agents can share the X or get to use half the X in both scenarios, we can just leave it out of the equation as mentioned before. If one gets the same value from X in both scenarios, then working 5 hours is strictly preferable over working 8 hours and not working is strictly preferable over working for 5 hours. So this looks somewhat like the prisoner's dilemma. Let A and B be the scenario that agent A respectively agent B works 8 hours and AB the scenario that both agents work 5 hours each. Then the preferences for agent A are B > AB > A and for agent B they are A > AB > B. But that doesn't help much, no matter which transition you consider, one agent will be better off and one will be worse off. So there is still a conflict. I acknowledge that an inefficiency gets introduced when the work is split but also want to maintain that 3 hours of leisure time twice is more valuable than 8 hours of leisure time once. Surly value can not increase and decrease at the same time. I am more certain that the inefficiency is real than what the shape of the value function for leisure time is so I will pick the former one and conclude that 8 hours of leisure time are - contrary to my earlier comment - more valuable than 3 hours of leisure time twice. So do I have to say that maximizing the total value is the wrong metric? Do I have to try to assign a value to the fairness of work distribution? Why wouldn't that already show up in the individual value functions? I am a bit stuck here. But I may have a way around that, I am just not sure how good the argument is. One obvious problem is that in case agent A does all the work, then agent B has no means to transfer some of the additional value from his additional leisure time to A. Maybe he could give away some of his share of X. But now I can no longer ignore the value function for X and that hopefully saves my argument and I avoid the conflict between decreasing and increasing total value without the need to explicitly appeal to the value of fair work work distribution because it is in the two value functions for X and leisure time. But I am not sure, I did not think this fully through. I think in the end it boils down to nonlinearities between the individual and the global view, i.e. we can globally waste 2 hours of work but still increase the total value because we have to take the global set of things, split it up for all individuals, push them through the nonlinear value functions and then sum it up again. Now it is no longer necessary that a global loss of 2 hours results in a global loss of value even if all the individual value functions are monotone.