Question

Maria always begins her day with a latte. She makes it by adding coffee and milk in the following proportions: for any three (fluid) ounces (fl oz) of coffee (x) she exactly wants four fl oz of steamed milk (y). In other words coffee and steamed milk are perfect complements.

1. In a diagram, plot Maria’s preferences (indifference maps). Depict three indifference curves that pass through the following bundles (4, 4), (2, 6) and (6, 8). What is the MRS at each of these points?

2. Find a utility function that represents these preferences. On the graph from 1) indicate the level of utility corresponding to each indifference curve.

3. Multiply your utility function by four and add to it a constant equal to one. How did the indifference map change (explain why)? How was the level of utility associated with the each indifference curve affected?

Answer 1

1)

MRS is Slope of IC

• (4,4), MRS = 0

• (2,6), MRS = 1

• (6,8) , MRS = NOT DEFINED

2) Utility function is Leontieff type

U(x,y) = Min{ 4x, 3y }

• U(4,4) = Min(16,12) = 12

U(2,6)= Min(8,18) = 8

U(6,8)= Min(24,24) = 24

3)U' = 4*U + 1

New IC Map will not change, preferences are not changed

Utility level with each IC rises

U(4,4)= 4*12+1 = 49

U(2,6)= 4*8 +1 = 33

U(6,8) = 4*24 + 1 = 97