Using the MU theory to derive the marginal utility for ice cream which is a normal good

Using the MU theory to derive the marginal utility for gobe which is a giffen good

Economists use the term Marginal Utility (MU) to mean the:(a) Additional satisfaction gained divided by the additional cost of the lastunit;(b) Total satisfaction gained when consuming a given number of units;(c) The process of comparing marginal units of all goods, which could bepurchased.(d) Additional satisfaction obtained by consuming one extra unit of agood

The technology used to produce ice cream improves. The equilibrium price and the equilibrium quantity

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.) (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 not y from that point, how would Lucy’s utility change? If you increase the amount of y but not 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. Unlike Lucy, however, Mary must have 2 scoops of ice-cream with every cone. Mary’s utility function is given by U(x, y) = min  x 2 , y . (d) In a separate diagram, draw a couple indifference curves for Mary. (Hint: Instead of drawing 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 diagram you have drawn in part (d), find Mary’s utility maximising consumption bundle

Collin likes milkshakes (m) and sushi (s). His preferenes over these two goods are representedby the following utility functionU (m, s) = 2√m + s.Collin’s income is $100 and the price of sushi is $10.(a) Suppose the price of milkshakes is initially $2. Find Collin’s optimal consumption bundle.