Assuming that the individual has zero non-labour income and faces the income budget line of JZ, the individual would choose point A as the ‘optimal’ utility-maximizing point as it is the highest attainable indifference curve(tangent to the income budget line or MRS = |w/p|). At this point A, the individual will work Ls1 hours, enjoy La leisure hours and enjoy an income of Ca. Assuming the individual has attained a source of non-labour income, for example inheritance or lottery winnings, represented by vertical distance ZX on the graph. The income budget constraint will now become a kinked line KXZ. The presence of non-labour income allows the individual to reach a higher indifference curve and the new ‘optimal’ utility-maximizing point is the ‘tangency’ position at point B on indifference curve U3 and line KXZ. At point B, the individual will work Ls2 hours, enjoy Lb leisure hours and enjoy an income of Cb. The effect of the increase in non-labour income comparing Point A and B is An increase in utility (from U1 to U2) An increase in leisure time from La to Lb and a decrease in labour supply hours from Ls1 to Ls2 An increase in total income from Ca to Cb
The key result is that desired hours of work will decrease(increase) when non-labour income increases(decreases), assuming leisure is a normal good.
Effect of Increase in Non-Labour Income in Labour Participation
Assuming there is no non-labour income, the income budget line is represented by the line JZ and the ‘optimal’ utility-maximizing point is Point A on the indifference curve U0 and line JZ (where MRS=|w/p|). The individual will work Ls1 hours and enjoy La hours of leisure. Consider an increase in non-labour income represented by XZ, assuming no change in wage rate, the income budget line will be parallel to JZ or KXZ. The new kinked budget line will allow the individual to reach a higher indifference curve U1 and enjoy...