Maria is a single mother. Every week she has 100 hours available to split between leisure and work. If she works, she can earn 20 dollars per hour.

(a) Write down the equation for her budget constraint and illustrate it with a graph.

(b) Suppose we want to improve her economic conditions with the following welfare program: the program provides an income guarantee of 300 dollars and a benefit reduction of 50 percent (for each dollar that she earns, the program reduces 50 cents on her benefit). Draw her new budget constraint.