Question 3Lucy consumes only scoops of ice-cream (x) and cones (y). Moreover, she insists on consumingthese two goods in the combination of 1 scoop of ice-cream and 1 cone. If there are more scoopsof ice-cream than cones, she throws the extra ice-cream away. If there are more cones thanscoops of ice-cream, she throws the extra cones away. Her utility function for ice-cream andcones is given byU(x, y) = min {x,y}.(The function min {x,y} returns the smaller number between x and y. In other words, if x < y,min {x,y} = x; if x > y, min {x,y} = y; and if x = y, min {x,y} = x = y.)(a) Draw a couple of indifference curves for Lucy. Put ice-cream on the horizontal axis. (Hint:Draw the 45° line. Choose a point on the line. If you increase the amount of x but noty from that point, how would Lucy's utility change? If you increase the amount of y butnot x from that point, how would Lucy's utility change?)(b) Suppose each scoop of ice-cream costs $2, and each cone costs $1. Lucy has an income of$6. Draw her budget line in the diagram you have drawn in part (a).(c) Using the diagram you have drawn, find Lucy's utility maximising consumption bundle.Lucy's sister, Mary, also insists on a particular combination of ice-cream and cones. UnlikeLucy, however, Mary must have 2 scoops of ice-cream with every cone. Mary's utility functionis given by¹{2,}.U(x, y) = min(d) In a separate diagram, draw a couple indifference curves for Mary. (Hint: Instead ofdrawing the 45° line, draw the line y = x/2. Then follow the procedures as in part (a).)(e) Mary faces the same prices as Lucy, but has an income of $10 instead. Using the diagramyou have drawn in part (d), find Mary's utility maximising consumption bundle.

Given information; Lucy consumes two goods, i.e., only scoops of ice cream (x) and cones (y) Her…

Lucy consumes only scoops of ice-cream (x) and cones (y). Moreover, she insists on consuming these two goods in the combination of 1 scoop of ice-cream and 1 cone. If there are more scoops of ice-cream than cones, she throws the extra ice-cream away. If there are more cones than scoops of ice-cream, she throws the extra cones away. Her utility function for ice-cream and cones is given by U(x, y) = min {x,y}. (The function min {x,y} returns the smaller number between x and y. In other words, if x < y, min {x,y} = x; if x > y, min {x,y} = y; and if x = y, min {x, y} = x= y.)