Final answer:
A single mother with two children faces a labor-leisure trade-off, earning $8 per hour without government assistance. With a government program guaranteeing income, the effective wage after subsidies is $4 per hour. This changes the budget constraint and income opportunities for the mother.
Step-by-step explanation:
The question refers to the labor-leisure budget constraint faced by a single-parent family earning an hourly wage with and without government assistance. Specifically, a single mother with two children earning $8 per hour is considered. Without government assistance, working 2,500 hours per year would result in a maximum income of $20,000, whereas opting for 2,500 hours of leisure would lead to zero income. At point A, the mother chooses to work 2,000 hours a year, earning $16,000, balancing work and family responsibilities. This is the utility-maximizing choice considering her circumstances.
Under a government program guaranteeing a minimum income of $18,000, which decreases as earned income increases, the mother would face trade-offs between work and the effective wage rate, as her income from work would essentially be subsidized, but each dollar earned reduces the government contribution by 50 cents, resulting in an effective wage of $4.00 per hour. This changes the budget constraint, offering higher total income opportunities at every level of labor supplied.