Question

At a workers utility maximizing level of leisure and income, their marginal utility with respect to leisure is 5, their marginal utility with respect to income is X, their hourly wage is $6, and their non-labor income is $50. What must X equal?

Answer 1

Answer

Lets first find budget constraint :

Y = wH + Yo

where Yo = non labor income = 50, w = hourly wage = 6, H = Total labor hours worked

L + H = T where L = leisure, T = Total time available

=> Y = 6(T - L) + 50

=> Y + 6L = 6T + 50

We can consider as budget constraint and thus Price of Y = 1 and Price of T = 6

Utility maximizing condition :

In order to maximize utility a consumer consumes that quantity at which Marginal Utility / Price of all goods are equal.

Here, (Marginal Utility / Price) of Leisure = 5/6 and (Marginal Utility / Price) of Income = X/1

According to above utility maximizing condition :

5/6 = X/1 => X = 0.83 and Hence X = 0.83