# Does the supply curve always slope up?

I was working through a thought experiment which appears to violate the Law of Supply (i.e., that supply curves are non-decreasing).

Suppose that a worker is paid by the hour and, given his hourly rate and financial situation, chooses to work 10 hours per day. One day, his employer exogenously (so, not reflecting an increase in the worker's marginal productivity) raises the worker's hourly rate by 25%. The worker is now capable of earning the same salary by working only 8 hours per day. Valuing a couple of extra hours with his family more than a larger salary, he chooses to reduce his hours to 8 per day.

Am I missing something?

• Congratulations!! :) You have discovered the backward bending labor supply curve :) en.m.wikipedia.org/wiki/Backward_bending_supply_curve_of_labour
– erik
Sep 14, 2021 at 4:47
• @erik you should post this as an answer, not a comment. To the OP, as erik points out this is a well-known fact. Also, in a decreasing-cost industry, long-run market supply is downward sloping because returns to scale allow costs to decrease as quantity increases. Sep 14, 2021 at 6:24
• @MichaelGmeiner you should post this as an answer, not a comment. :) Sep 14, 2021 at 7:24

The law of supply applies to production rather than consumption. The difference is that in the production theory the firm maximizes its profits without any budget constraint and views its profits from different outputs in the same way. In essence, there is no income effects but only substitution effects.

In your case, you are assuming that the marginal utility from increasing income above current level is 0, so that the person will allocate his time to leisure which has a positive marginal benefit. In other words, the income effect dominates and the salary is not a normal good. You can assume such a utility function if you like, but it makes no sense in the analogy of firm where the firm only values its profits from some certain goods to some upper bounds.

• "salary is not a normal good" Salary is not a good at all? Sep 14, 2021 at 7:27
• "the income effect dominates" This is not accurate, it is the endowment income effect that is in play with labor supply. Sep 14, 2021 at 7:27

When it comes to income in particular, treating currency as the good, and time as the currency to turn it into a currency-demand driven curve will highlight the open market forces behind this phenomenon.

Each unit of currency(hereafter : dollar) earned has a marginal utility that is dependent on the dollars earned previously in the given time frame. Knowing this, it become evident that a pay increase directly increases marginal utility, but the distribution of that utility is clustered earlier in the day. This leads to a phenomenon where you achieve the same level of utility after fewer hours, and the remaining hours provide less marginal utility than they did before the raise. Overall utility is increased, and marginal utility of an hour of leisure can remain the same, which can lead to the lowered utility of the final hours being less than the marginal utility of the leisure time.

It's not irrational, or even terribly counter-intuitive, when you consider leisure time to be a consumed good, and treat currency as the substitute consumed good. In this case, supply is time (or hours of the day), and is perfectly inelastic and locked at 24 hours. This turns demand (measured as utility of the individual) into a comparison of 2 substitute goods: utility from earned currency, and utility from leisure time. The ideal intersect will end up shifting toward more leisure time and more overall utility as a result.