A worker divides her time between leisure (L) and work days (H), and derives utility from consumption of an aggregate good (C) and from leisure, based on the following utility function: . The worker has a total of 30 (fully divisible) work days at her disposal. She also receives $1,000 Utopian Dollars per month in unearned income. The daily wage is $200.

Write down the workers budget constraint, and depict it on a graph with leisure on the horizontal axis and consumption on the vertical axis.

Calculate the workers optimal amount of consumption and leisure, and the workers labor supply. Show on the graph the optimal consumption bundle.

What is the workers daily reservation wage, i.e., the minimum wage necessary for him to be willing to work a positive amount of hours?

Following the publication of a report on poverty, which showed that many households consume less than $2,000 a month, the government decides to launch a new welfare program. Welfare payments are a declining function of earned income. Specifically, the welfare subsidy S is equal to:

S = Max{1000 - 0.5wH, 0}

Calculate the new budget constraint equation, and add the new budget line to the graph you drew in part b).

How does the new welfare law affect labor supply and consumption?