Work as a consumer choice: utility maximization with a time constraint, and backward-bending supply.
Warming up the engine…
Labor supply as consumer choice: utility over consumption and leisure, constrained by time and the wage, the wage is the price of leisure.
Optimum: MRS(leisure, consumption) = w; backward bend when income effect beats substitution
A raise makes leisure pricier (work more, substitution) but also makes you richer (work less, income). At high wages the income effect can win, bending labor supply backwards, why surgeons golf on Fridays.
Non-labor income shifts the constraint up without changing its slope, pure income effect, hours fall.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at L 12, C 36.
Equilibrium: L* = 12.0, C* = 36.0
Current equations
Working is buying consumption with your hours. Every hour of leisure you keep is an hour of wages you give up, so the wage is the price of leisure. The budget line shows every combination of free time and spending you can afford; the best point is where it touches your indifference curve.