Consider an income-leisure trade-off model with assets. Specifically, individual
ID: 1218160 • Letter: C
Question
Consider an income-leisure trade-off model with assets. Specifically, individuals have identical utility function
where c and L are consumption and labor, respectively. The time endowment is standardized to utility, so that leisure l = 1-L. The budget constraint is given as
where A is the amount of assets.
Question:
First, find the optimal point (c,L). How would the indifference curve-budget line program look like? Also define the point elasticitiy of labor supply with respect to wage. How is this value related to A or w?
Explanation / Answer
Answer. The equilibrium will be set where, the budget line of Wage and consumption is tangent on IC of consumer. At that point their, slopes will be equal. The slope of IC is MRS between consumption and Labour. The slope of budget line will be wage rate.
The point elasticity of labour supply wrt to wage will be - % change in labour supply / % change in wage rate.
Genrally, when wage rate increases, the labour supply increases upto a certain point, because after certain point, labour will choose leisure instead to go for work. While an increase in Assets, decreases the labour supply because it an additional source of income. As assets increases, income effect will induce him to choose more leisure and less work.