Question

Suppose a two-person household. Person 1 has h₁ units of time available and takes l₁ units of leisure time, while person 2 has h₂ units of time available and takes l₂ units of leisure time. Collectively, the two persons in the household care about their total consumption c, their total leisure l = l₁ + l_2, and they have preferences over their total consumption and total leisure. But person 1 faces a market wage w₁ and person 2 faces a market wage w₂ with w₁ > w_2.

_{a) Draw the budget constraint faced by the two-person household. What will the household do, that is, how much does each household member work?}

_{b) What happens if the market wage of person 2 rises?}

_{c) Explain your results and interpret.}

Answer 1

a) Given information is:

Total units of time person 1 has = h1 Total unit of time person 2 has = h2

Leisure time of person 1 = l1 Leisure time of person 2 = l2

Market wage rate of person 1= w1 Market wage rate of person 2= w2

whereby w1> w2

Total consumption of household = c

Total leisure time of household = l1 + l2

a) Budget constraint equation for household will be:

w1*h1 + w2*h2 = c + (l1 + l2)

That is, the total income of the household should be equal to the total consumption plus total lesiure of the household. The drawing of the budget constraint is attached.

To determine how much each member would work, there would be two effects running for each member. One is income effect, which expresses the effect of purchasing power on the leisure and consumption choice of a person wheras other is substitution effect, which expresses effect of relative wage rate on the leisure and consumption choice of a person. Since, here w1 > w2, income effect would suggest that higher w1 implies more income of the household as person 1 for a given h1, hence person 1 would have higher l1 than l2 and higher c. However, by substitution effect since the relative wage of person 1 is high, then it implies person 1 can work less to have higher l1 than l2 and same level of c. The overall, allocation of l1, l2 and c depends on which of the two effects dominate.

b) If w2 rises, then again two effects run, that is, income effect and substitution effect. By income effect rise in w2 implies more income of the household as person 2 for a given h2, hence person 2 would have higher l2 and higher c. However, by substitution effect it implies person 2 can work less to have higher l2 and same level of c. The overall, allocation of l1, l2 and c depends on which of the two effects dominate.

c) Explained above.