Answer to Question 1
The young mother's labor supply curve is backward bending. In other words, her labor supply curve is positively sloped at lower wage rates, indicating that a higher wage increases the quantity of labor she supplies. But when her wage reaches a certain amount, further increases in the wage decrease the quantity of labor she supplies and her labor supply curve becomes negatively sloped.
Answer to Question 2
The budget equation is QS = 18 - 0.75QG, where QS is the quantity of sandwiches and QG is the quantity of gasoline. To determine the slope of Joe's budget line, first notice that Joe's budget line intersects the vertical axis when Joe buys 18 sandwiches (which equals his income, 72, divided by the price of a sandwich, 4). Second, Joe's budget line intersects the horizontal axis when he buys 24 gallons of gasoline (which equals his income, 72, divided by the price of a gallon of gasoline, 3). So calculating the slope of Joe's budget line over the horizontal distance from 0 gallons of gasoline to 24 gallons of gasoline, the slope equals the vertical fall is -18 sandwiches divided by the horizontal distance of 24 gallons of gasoline, so the budget line's slope of -18 sandwiches/24 gallons of gasoline, which is -0.75 of a sandwich per gallon of gasoline.
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