13.12 Family labour supply A family with two adult members seeks to maximise a util ity function of the form U

(c, h1, h2), where c is family consumption and h1 and h2 are hours of leisure of each family member. Choices are constrained by c = w1(24 − h1) + w2(24 − h2) + n, where w1 and w2 are the wages of each family member and n is non-labour income.

a.

Without attempting a mathematical presentation, use the notions of substitution and income effects to discuss the likely signs of the cross-substitution effects ∂h1/∂h2 and ∂h2/∂w1.

b.

Suppose that one family member (say, individual 1) can work in the home, thereby converting leisure hours into consumption according to the function c1 = f

(h1), where f ′ > 0 and f ″ < 0. How might this additional option affect the optimal division of work among family members?