Brittany likes leisure (L) and consumption (), but she must work in order to purchase consumption, which takes away from leisure time. Her utility function is U(L,C)=1400L^(1/)+C so that MUl=(700/L^(1/2) and MUc=1.Consumption costs $1 per unit.Brittany can work for $20 per hour for a maximum of 2,000 hours per year. There is currently no income tax system.

Write down Brittany's optimization problem that determines her optimal amount of leisure and consumption and solve for her optimal L* and C*

Suppose the government introduces a welfare program that gives $5,000 in cash to anyone earning $10,000 or less. Individuals earning $10,001 and above receive $0.Upload a graph with consumption on the y-axis and leisure on the x-axis showing Brittany's budget constraint 1) without the welfare program, and 2) with the welfare program, assuming she can still work for $20 per hour for up to 2,000 hours. Be sure to label key points.

Solve for Brittany's new optimal* and C*with the welfare program. (Hint: You might try solving for* and C* assuming everyone gets the extra $5,000, checking whether the solution to that problem makes sense, and thinking about where she might move to in order to maximize her utility.